The P2 Tower: Re-Neighbouring the Vertical City (MArch) by Emergent Technologies and Design [EmTech] Selected Dissertations Repository

Re-Neighboring the Vertical City

Puja Bhagat (M.Arch.), Jonathan Wong (M.Arch.)

ARCHITECTURAL ASSOCIATION SCHOOL OF ARCHITECTURE GRADUATE SCHOOL PROGRAMMES PROGRAMME: EMERGENT TECHNOLOGIES AND DESIGN YEAR: 2022-2023

COURSE TITLE: MArch. Dissertation DISSERTATION TITLE: The P2 Tower: Re-Neighboring the Vertical City STUDENT NAMES: Puja Bhagat (M.Arch.), Jonathan Wong (M.Arch.)

DECLARATION: “I certify that this piece of work is entirely my/our and that my quotation or paraphrase from the published or unpublished work of other is duly acknowledged.”

SIGNATURE OF THE STUDENT:

Puja Bhagat (M.Arch.) DATE: 12 January 2024

Jonathan Wong (M.Arch.)

Puja Bhagat Puja Bhagat is an M.Arch student at the Architectural Association. Her interests lie in investigating emerging material fabrication systems and robotic processes through the intersection digital and physical environments. She is particularly interested in the union of bamboo weaving and concrete, as an act of combining a delicate, intimate craft with an industrial material.

Jonathan Wong Jonathan Wong is an M.Arch student at the Architectural Association and holds a B.Arch and B.Sc in Mathematics from Penn State University. As he sees it, mathematics should no longer be merely an analytical tool in architecture, but instead, it should further our knowledge about the field and push it into new frontiers. Therefore, he believes a new understanding about the role mathematics can play in architecture will redefine the ways in which we approach issues of sustainability.

COURSE DIRECTORS

Dr. Elif Erdine Dr. Milad Showkatbakhsh FOUNDING DIRECTOR

Dr. Michael Weinstock

M.SC. TEAM MEMBER

Tuoan Pan STUDIO TUTORS

Dr. Naina Gupta | Paris Nikitidis Felipe Oeyen | Dr. Alvaro Velasco Perez Lorenzo Santelli | Fun Yuen

Acknowledgments The team would like to express gratitude towards everyone who supported the evolution of this thesis. The team would particularly like to thank Dr. Michael Weinstock, Dr. Elif Erdine, and Dr. Milad Showkatbakhsh, along with our tutors Dr. Naina Gupta, Paris Nikitidis, Felipe Oeyen, Dr. Alvaro Velasco Perez, Lorenzo Santelli, and Fun Yuen, for guiding us at every stage of design. Their unique insights and fruitful discussions pushed the domain of the thesis to new levels. The team would also like to thank Tuoan Pan for his dedication, teamwork, and insightful contributions during the M.Sc. phase.

Table of Contents 00 Abstract.................................................................................. xii 01 Introduction............................................................................ 14 02 Domain................................................................................... 16 Rise of the Tower Block.................................................................................. 18 Which Public? Which Private?....................................................................... 24 Quantifying the Publicness of Public Spaces............................................ 25 The Private Tower Block................................................................................ 27 A Case Study of Three Hong Kong Towers.............................................. 27 Visions for an Adaptive Architecture.............................................................. 30 Towers and Timescales................................................................................... 32 Adaptability through Digital Fabrication........................................................ 34 Towards An Urban System............................................................................. 36 The Broadacre City................................................................................. 36 The 15-Minute City................................................................................ 36 Simulating Sociability..................................................................................... 40 Types of Pedestrian Simulations.............................................................. 40 Pitfalls of Existing Pedestrian Simulations.............................................. 40 Discussion...................................................................................................... 42 Bibliography.................................................................................................. 44

03 Methods.................................................................................. 46 3.1 Public-Private Evaluation Method............................................................ 48 The Parameters and Sociability Calculation Method................................. 48 3.2 Urban Network........................................................................................ 54 3.2.1 Temporal Graph Network............................................................... 54 Weighted Shortest Path.......................................................................... 56 Dijkstra’s Algorithm............................................................................... 56 3.3 Pedestrian Simulations............................................................................. 58 3.3.1 Network-Based Social Pedestrian Simulation................................. 59 3.3.2 Socio-Spatial ................................................................................. 59 Pedestrian Simulation............................................................................. 59 3.4 Tower Organization.................................................................................. 60 3.4.1 The Principles of Bamboo Stems as a Structural System................. 60 3.4.2 Co-Evolutionary Algorithms for Private-Public Distribution.......... 61 3.5 Program Relationships............................................................................. 62 3.5.1 Small-world Network as a Spatial Relationship System.................. 62 3.6 Fabrication and Material System............................................................... 64 3.6.1 Additive Manufacturing: Robotic 3D Printing................................. 64 3.6.2 Material Systems:.......................................................................... 65 Fiber-Reinforced Cementitious Composites............................................. 65 3.6.3 Material Systems:.......................................................................... 66 Bamboo Strip Weaving as Rebar Reinforcement and Formwork............... 66 3.7 Analysis Tools.......................................................................................... 68 3.7.1 Finite Element Analysis (FEA)...................................................... 68 3.7.2 Computational Fluid Dynamics (CFD)........................................... 68 3.7.3 Artificial Neural Network (ANN)................................................... 68 Bibliography.................................................................................................. 70

04 M.Sc. Recap............................................................................ 72 4.1 Tower Morphology................................................................................... 76 Design Research Phase........................................................................... 76 Design Development Phase..................................................................... 76 M.Arch. Phase Next Steps...................................................................... 76 4.2 Structural System.................................................................................... 78 Design Research Phase........................................................................... 78 Design Development Phase..................................................................... 78 M.Arch. Phase Next Steps...................................................................... 78 4.3 Public-Private Distribution....................................................................... 80 Design Research Phase........................................................................... 80 Design Development Phase..................................................................... 80 M.Arch. Phase Next Steps...................................................................... 80 4.4 Programmatic Topology and Organization................................................ 82 Design Research Phase........................................................................... 82 Design Development Phase: Topological Relationships............................ 82 Design Development Phase: Programmatic Organization......................... 83 M.Arch. Phase Next Steps...................................................................... 83 4.5 Material Fabrication System..................................................................... 86 Component Design and Material Fabrication System............................... 86 Design Research Phase........................................................................... 86 Design Development Phase..................................................................... 86 M.Arch. Phase Next Steps...................................................................... 87 Discussion...................................................................................................... 92 Bibliography.................................................................................................. 94

05 Research................................................................................. 96

5.1 Revised Artificial ..................................................................................... 98 Neural Network.............................................................................................. 98 5.2 Temporal Graph Network......................................................................... 100 5.2.1 Temporal Urban Graph Optimization - Independent Shifts.............. 102 5.3 Weighted Shortest ................................................................................... 104 Walk Algorithm............................................................................................. 104 5.3.1 Weighted Shortest Path Experiment.............................................. 106 5.4 Co-Evolutionary Algorithms..................................................................... 108 5.4.1 Co-Evolutionary Algorithm - Exploration....................................... 109 5.4.2 Co-Evolutionary Algorithm - Post-Analysis................................... 114 5.5 Pedestrian Simulations............................................................................. 116 5.5.1 Network-Based Social Pedestrian Simulation Functionality............ 116 5.5.2 Network-Based Social Pedestrian Simulation Experiments............. 117 5.5.2.1 Pedestrian Simulation Experiment 01......................................... 118 5.5.2.2 Pedestrian Simulation Experiment 02......................................... 120 5.5.3 Socio-Spatial Pedestrian Simulation Functionality.......................... 122 5.5.4 Socio-Spatial Pedestrian Simulation Experiments........................... 123 5.5.4.1 Pedestrian Simulation Experiment 01......................................... 124 5.5.4.2 Pedestrian Simulation Experiment 02......................................... 126 Discussion...................................................................................................... 128

06 Design Process....................................................................... 130

6.1 M.Sc. Revised Experiments...................................................................... 134 6.1.1 Co-Evolutionary Algorithm: Tower, Structure, Public-Private Distribution............................................................................................ 134 6.1.2 Co-Evolutionary Algorithm: Tower, Structure, Public-Private Distribution Post-Analysis......................................................................................... 140 6.2 Micro-Urban Network.............................................................................. 142 6.2.1 Micro-Urban Pathways.................................................................. 142 6.2.2 Micro-Urban Scale: Network Pedestrian Simulation Analysis......... 146 6.3 Macro-Urban Network............................................................................. 148 6.3.1 Urban Network Relationships........................................................ 148 6.3.2 Urban Network Paths.................................................................... 150 6.3.3 Urban Network Paths - Temporal Shifts......................................... 150 6.4 Pathway Architectural Design.................................................................. 152 6.4.1 Pathway Catalog Experiment......................................................... 152 6.4.2 Pathway Catalog............................................................................ 156 6.4.2 Pathway Segment: Spatial............................................................. 158 Pedestrian Simulation Analysis............................................................... 158 Discussion...................................................................................................... 160

07 Case Study.............................................................................. 162 Design Narratives.......................................................................................... 165 Site Selection................................................................................................. 166 Tower Morphology......................................................................................... 170 Structural System.......................................................................................... 172 Tower Detail Section............................................................................... 174 Public-Private Distribution............................................................................. 176 Component Design......................................................................................... 178 Component Exploded Axon..................................................................... 180 Adaptation: 1 Year.................................................................................. 182 Adaptation: 3 Years................................................................................ 183 Adaptation: 5 Years................................................................................ 184 Adaptation: 10 Years.............................................................................. 185 Tower Vertical Section.................................................................................... 186 Pedestrian Walkways..................................................................................... 188 Pedestrian Walkway Detailed Section..................................................... 190 Multimodal Corridors..................................................................................... 192 Multimodal Corridor Street Section......................................................... 194 Tower Rendering............................................................................................ 196 The P2 Tower................................................................................................. 198 Multiscalar Adaptation................................................................................... 200

08 Discussion............................................................................... 208 M.Sc. Phase to M.Arch. Phase........................................................................ 210 Computational Workflow................................................................................ 210 Case Study..................................................................................................... 211 Conclusion...................................................................................................... 211

09 Appendix................................................................................ 212 A.01 Public-Private Evaluation Method.......................................................... 214 Parameter Calculations........................................................................... 214 A.02 Bamboo Node Studies............................................................................ 215 Scaled Equation Results.......................................................................... 215 A.03 Tower Morphology................................................................................. 216 A.04 Structural System.................................................................................. 218 A.05 Co-Evolutionary Studies........................................................................ 220 Parasitism Co-Evolutionary Experiment.................................................. 221 Commensalism Co-Evolutionary Experiment........................................... 222 Mutualism Co-Evolutionary Experiment.................................................. 223 A.06 Private-Public Distribution.................................................................... 224 A.07 Programmatic Topology........................................................................ 226 A.08 Programmatic Organization................................................................... 228 A.09 Variable Control Studies........................................................................ 230 Gaussian Curvature................................................................................. 230 Strip Width/Depth Ratio........................................................................ 231 Weave Density for 3D Printing: Sagging and Material Deformation........ 232 Digital to Physical Translation................................................................ 233 A.10 Material Fabrication System.................................................................. 234 Component Weaving Pattern................................................................... 235 Component Structural Analysis............................................................... 237 A.11 Artificial Neural Network Data Set........................................................ 238 A.12 Bridge Selection Matrix......................................................................... 242 A.13 Pedestrian Simulation Sample Code....................................................... 244 A.14 Co-Evolutionary Algorithm Sample Code............................................... 248

List of Figures Figure 02: Shek Kip Mei Fire 1953......................................................................... 18 Figure 03: Le Corbusier’s Ville Radieuse................................................................. 19 Figure 04: Map of Unauthorized Built Works across Hong Kong.............................. 20 Figure 05: Evolution of the Tower Block.................................................................. 20 Figure 06: Unauthorized Built Works Collage.......................................................... 21 Figure 07: Hong Kong Quality of Life Collage.......................................................... 23 Figure 08: Spectrum of Sociability........................................................................... 24 Figure 09: Kohn’s Two Dimensions of Publicness.................................................... 25 Figure 10: Four Models for Evaluating Publicness................................................... 26 Figure 11: Tower Block Case Study......................................................................... 27 Figure 12: Nakagin Capsule Tower by Kisho Kurokawa (1972)............................... 31 Figure 13: Plug-In City by Peter Cook (1964)......................................................... 31 Figure 14: Tower Layers and Timescales................................................................. 33 Figure 15: Robotic 3D Concrete Printing (Photo Puja Bhagat and Jonathan Wong). 35 Figure 16: Broadacre City (Photo by Skot Weidemann)........................................... 36 Figure 17: 15-Minute City (Drawing by Hassell Studio).......................................... 37 Figure 18: Urban Density Timeline......................................................................... 39 Figure 19: Cellular Autonoma (CA) Model............................................................... 41 Figure 20: Physics-Based Model.............................................................................. 41 Figure 21: Sociability Spectrum............................................................................... 49 Figure 22: Sociability Parameter Calculation Method............................................... 51 Figure 23: Sociability Spectrum Score Calculation Method....................................... 52 Figure 24: Temporal Graph Network Timeline......................................................... 54 Figure 25: Temporal Graph Network....................................................................... 55 Figure 26: Dijkstra’s Algorithm Pseudocode........................................................... 57 Figure 27: Network-Based Pedestrian Simulation.................................................... 58 Figure 28: Socio-Spatial Pedestrian Simulation....................................................... 58 Figure 29: Mathematical Expression of Bamboo Nodes............................................ 60 Figure 30: Bamboo’s Continuous Fibre Wall Principles............................................ 60 Figure 31: Evolutionary Algorithm Workflow.......................................................... 61 Figure 32: Co-Evolutionary Algorithm Workflow.................................................... 61 Figure 33: Small-World Network............................................................................. 62 Figure 34: Small-World Network Equations............................................................ 62 Figure 35: Small-World Network in Architecture..................................................... 63 Figure 36: Fabrication System................................................................................. 64 Figure 37: Concrete Life cycle................................................................................. 65 Figure 38: Fiber-Reinforced Cementitious Composites Life cycle............................. 65 Figure 39: Bamboo Growth Regions........................................................................ 66 Figure 40: Bamboo Growth Rate............................................................................. 66 Figure 41: Bamboo Weaving.................................................................................... 67 Figure 42: Artificial Neural Network (ANN)............................................................ 69 Figure 43: Scope of M.Sc. Phase Experiments......................................................... 74 Figure 44: Tower Design Workflow......................................................................... 75 Figure 45: M.Sc. Phase Resultant Tower Morphologies............................................ 77 Figure 46: M.Sc. Phase Resultant Structural Systems............................................. 79 Figure 47: M.Sc. Phase Resultant Public-Private Distributions................................ 81 Figure 48: M.Sc. Phase Resultant Small-World Networks........................................ 84 Figure 49: M.Sc. Phase Resultant Programmatic Organizations............................... 85 Figure 50: Component Design and Material Fabrication System............................... 87

Figure 51: Digital to Physical Translation Experiment............................................ 88 Figure 52: Digital to Physical Translation Experiment (cont.)................................. 89 Figure 53: Final 1:5 Scale Mock-Up Model.............................................................. 91 Figure 54: Wind Pressure Artificial Neural Network Setup...................................... 98 Figure 55: Generator and Discriminator ANN Workflow......................................... 99 Figure 56: Temporal Graph Experiment Workflow................................................... 100 Figure 57: Temporal Graph Evolutionary Algorithm Setup...................................... 101 Figure 58: Average Temporal Graph Parameters Comparison.................................. 102 Figure 59: Representative Temporal Graph Pareto Front Members.......................... 103 Figure 60: Temporal Graph Experiment Workflow................................................... 104 Figure 61: Open-Source Data Weightings................................................................ 105 Figure 62: Influence of Weighted Shortest Path....................................................... 107 Figure 64: M.Sc. Computational Workflow............................................................... 108 Figure 63: M.Arch. Computational Workflow........................................................... 108 Figure 65: Co-Evolutionary Algorithm Pseudocode................................................. 109 Figure 66: CoEA Design Space............................................................................... 111 Figure 67: CoEA Parallel Coordinates Plot - Population 01..................................... 112 Figure 68: CoEA Mean Value Graph - Population 01............................................... 112 Figure 69: CoEA Standard Deviation Graph - Population 01................................... 112 Figure 70: CoEA Parallel Coordinates Plot - Population 02..................................... 113 Figure 71: CoEA Mean Value Graph - Population 02............................................... 113 Figure 72: CoEA Standard Deviation Graph - Population 02................................... 113 Figure 73: CoEA Standard Deviation Graph - Post-Analysis with Wallacei............. 114 Figure 74: CoEA Parallel Coordinate Plot - Post-Analysis with Wallacei................. 115 Figure 75: CoEA Mean Graph - Post-Analysis with Wallacei................................... 115 Figure 76: Network-Based Pedestrian Simulation.................................................... 117 Figure 77: Network-Based Pedestrian Simulation Experiment 01............................ 119 Figure 78: Network-Based Pedestrian Simulation Experiment 02............................ 121 Figure 79: Socio-Spatial Pedestrian Simulation Workflow........................................ 122 Figure 80: Socio-Spatial Pedestrian Simulation Setup.............................................. 123 Figure 81: Socio-Spatial Pedestrian Simulation Experiment 01................................ 125 Figure 82: Socio-Spatial Pedestrian Simulation Experiment 02................................ 127 Figure 83: Co-Evolutionary Algorithm Setup........................................................... 135 Figure 84: Full Tower CoEA Design Space.............................................................. 137 Figure 85: Full Tower CoEA Parallel Coordinates Plot - Population 01.................... 138 Figure 86: Full Tower CoEA Mean Value Graph - Population 01.............................. 138 Figure 87: Full Tower CoEA Standard Deviation Graph - Population 01.................. 138 Figure 90: Full Tower CoEA Mean Value Graph - Population 02.............................. 139 Figure 89: Full Tower CoEA Standard Deviation Graph - Population 02.................. 139 Figure 88: Full Tower CoEA Parallel Coordinates Plot - Population 02.................... 139 Figure 91: Full Tower CoEA Standard Deviation Graph - Post-Analysis.................. 141 Figure 92: Micro-Urban Network EA Set-up........................................................... 143 Figure 93: Micro-Urban Network EA Results.......................................................... 144 Figure 94: Micro-Urban Network Post-Analysis...................................................... 147 Figure 95: Urban Network Data Comparison........................................................... 148 Figure 96: Urban Network EA Results.................................................................... 149 Figure 97: Multimodal Corridors - Initial State........................................................ 151 Figure 98: Multimodal Corridors - Days Shift.......................................................... 151 Figure 99: Multimodal Corridors - Years Shift......................................................... 151 Figure 100: Pathway Architectural Design EA Set-up............................................. 153 Figure 101: Pathway Architectural Design EA Results............................................ 154 Figure 102: Pathway Architectural Catalog............................................................. 156 Figure 103: Pathway Pedestrian Simulation Experiment......................................... 159 Figure 104: Exploded View of Component System................................................... 181

00 Abstract

Abstract Over time, people’s sociability changes, yet the buildings and spaces they occupy do not change to accommodate their new needs. Densification has increased this problem, particularly in Hong Kong. In Hong Kong, rapid densification focused solely on private spaces, leading to the proliferation of the Hong Kong tower block. Yet, the rigidity of the tower block prevented spaces from meeting people’s sociability needs as they changed over time and inhibited the emergence of organic interactions between people. Thus, the P2 Tower operated in this gap between the social affordance of the Hong Kong tower block and the people’s sociability needs. Through its research and experimentation, the P2 Tower called for the idea of an evolving architecture, one where people determine the past, present, and future of the spaces they inhabit. The P2 Tower engaged the concepts of private and public narrowly through a lens of how naturally people interact with one another to develop a system for quantifying the sociability of a space. Such a system underpinned the development of a novel computational framework which employs biomimetic principles alongside algorithmic processes. During the M.Sc. phase, the framework deconstructed the tower into its component parts, developing them as individual parts of a whole. It employed evolutionary algorithms, abstracted principles of a bamboo stem, and an advanced material fabrication system that combined bamboo weaving techniques and robotic concrete 3D printing, enabling the P2 Tower to continuously adapt at varying scales of time and space in response to people’s shifting sentiments around sociability. Extending beyond the tower, the M.Arch phase expanded the framework to the micro-urban and urban network scales, empowering the P2 Tower to engage and influence its context. At the micro-urban scale, a three-dimensional pedestrian simulation, driven by people’s social interactions, developed a pathway network that served as a bridge between the tower and its local context. Such a system allowed the social affordances of the P2 Tower to enhance the sociability of its local context. At the urban network scale, a resilient network of multimodal corridors connected multiple towers by considering their relationship as a temporal graph network, and a sociospatial pedestrian simulation drove the design of programmed spaces along these corridors. Coupled together, this dynamic, multiscalar framework offered a new housing solution and urban design strategy that meets the density needs of cities while also facilitating continuous spatial changes to match the sociability demands of people over time.

INTRODUCTION

01 Introduction

This thesis addresses the dual but interrelated domains of densification and ever-changing sociability by redefining the design and construction of the tower block and its urban context in Hong Kong. This is achieved by proposing a new model for evaluating a space along the public-private spectrum and subsequently using this methodology as a driving force to develop a new tower system workflow focused on its occupants’ sociability over time. During the M.Arch. phase, this method extends the social capabilities of the tower block into the urban environment through a series of micro-urban and urban interventions. The importance of this work is supported by the existing research and theoretical ideas within the field, but expands beyond the present domain by implementing novel methods and techniques which facilitate a more socially adaptive system, allowing it to exhibit contextspecific functionalities and performances over time. While this thesis applies its framework to Hong Kong as a case study, there is potential to implement its roots to other dense cities around the globe. As such, the research challenges the traditional notion of the tower block as a permanent, unchanging structure in the built environment and discovers its potential to become a temporal system which evolves alongside its occupants, meeting their needs and improving urban livability. Only in this way, can architecture begin to address the complex challenges of densification.

Bhagat | Wong

DOMAIN

02 Domain

2.1 Rise of the Tower Block 2.2 Which Public? Which Private? 2.3 The Private Tower Block 2.4 Visions for an Adaptable Architecture 2.5 Towers and Timescales 2.6 Adaptability through Fabrication 2.7 Towards an Urban System 2.8 Simulating Sociability

In order to comprehensively address the dual issues of densification and ever-changing sociability, it was imperative for the authors to deeply understand the existing discourse and research within these two realms. In doing so, the thesis could situate itself within a strong grounding, while simultaneously identifying gaps which have not thoroughly been explored. This research began with an investigation of the tower block typology and its rise in architecture which led to its significant prominence around the world and its permanence in Hong Kong. This inquiry was framed through the lens of the tower block’s rise in extreme privateness and how such a mentality became misaligned with the requirements of the tower’s occupants over time. In parallel with this research, the authors deeply explored the terms public and private in a social setting, understanding their positions on a spectrum and the capabilities of quantifying such concepts. Once both issues were thoroughly studied, the authors uncovered their significance when placed within the same domain by investigating the impact of socially adaptive systems. Such a concept was explored through the lens of adaptability in architecture, adaptability across timescales, and adaptability through making. Finally, the domain research concluded by understanding how simulating such social behaviors can become a driver for the design of dense architectural systems. In doing so, the thesis can operate within the identified gaps to purposefully address the dual issues of densification and everchanging sociability.

Bhagat | Wong

Rise of the Tower Block The Shek Kip Mei fire of 1953 marked a significant paradigm shift in the way the Hong Kong government approached the redevelopment of land and public housing. As tens of thousands of residents were abruptly homeless, the government raced to meet their immediate needs and provide basic shelter. Yet, the government also viewed this moment as an opportunity to revolutionize the land usage of its ‘barren rock’ and sharply alter government policy.1 Where sprawling squatter huts once hugged the earth, multi-story tower blocks were constructed that soared towards the sky. Thus, the seeds of the world’s largest housing program were planted, and the tower block typology became synonymous with identity of Hong Kong. The newly constructed tower blocks housed 2,500 residents; five people lived in an apartment; and each apartment averaged 24 m2.2 Michael Suen Mingyeung, Secretary for Housing, Planning and Lands, described these tower blocks as “simple, low-cost shelters to a minimum standard to meet the emergency needs.”3 As fires in dense squatter settlements plagued Hong Kong throughout the 1950’s and 1960’s, the emergency response demanded the construction of more and more tower blocks across the city, culminating in the formulation of the Ten-Year Housing Program in 1973. The program aimed to provide 1.8 million Hong Kong residents with “adequate housing” which was permanent and self-contained.4 It was an ambitious program, but dense public housing was nothing innovative in 1973. Through this public housing program, the Hong Kong government tapped into a global trend for mass housing which emerged in response to mass

migration to urban areas and rose to prominence following the destruction of World War II. Modern mass migrations began in the late 1800’s and early 1900’s, causing cities to rapidly densify.5 Over time, rapid densification only became worse, creating a strain on urban environments, forcing architects and urban planners to develop a new housing typology: the mass housing tower block.6 The tower block was designed based upon two principles which emerged at the time: industrial standardization and housing as a basic human right.7 Through these principles, the tower block enabled urban cities to efficiently house as many individuals as possible in a small urban footprint. Many architects around the world,

Figure 02: Shek Kip Mei Fire 1953

such as Le Corbusier in France, Leonid Sabsovich in Russia, and Bruno Taut in Germany, adopted these principles and developed their own tower block morphologies in response to the particular urban density issues in their cities.8 Thus, the tower block took its place as the archetypal typology for rapidly densifying cities across the globe.

Fung Ping Yan, “Public Housing in Hong Kong Past, Present and Future” (Chartered Institute of Housing Asian Pacific Branch, 2006), 2. Ping Yan, “Public Housing in Hong Kong Past, Present and Future”, 3. 3 Alan Smart, The Shek Kip Mei Myth: Squatters, Fires and Colonial Rule in Hong Kong, 1950 - 1963 (Hong Kong: Hong Kong University Press, 2006), 1. 4 Ying Deng, Edwin H.W. Chan, and S.W. Poon. “Challenge-Driven Design for Public Housing: The Case of Hong Kong.” Frontiers of Architectural Research 5, no. 2 (2016): 213–224. https://doi.org/10.1016/j.foar.2016.05.001. 5 Charles More, Understanding the Industrial Revolution, (London: Routledge, 2000), 1. 6 Florian Urban, Tower and Slab: Histories of Global Mass Housing (London: Routledge, 2012): 10-11. 7 Urban, Tower and Slab, 2. 8 Urban, Tower and Slab, 7-8. 1 2

Domain Chapter

Figure 03: Le Corbusier’s Ville Radieuse

Surprisingly to some and less so to others, the housing block typology fell out of prominence in the United States and Europe as rapidly as it had risen to it due to its failures anthropologically. Unfulfilled promises for community and modernity gave way for realities of social isolation, class segregation, and inhumane infrastructure.9 In essence, the tower block typology failed to meet the immediate and future needs of its residents. These discontinuities were not the result of poor problem solving or lackluster ambitions, but instead due to an overemphasis of the architectural design on the private, as opposed to the public. Such a focus on the private was the result of the tower block being a mechanism for solving a problem as opposed to planning for the future. Mass migration required housing, so housing is what the government built, nothing more or less. Thus, these structures were unable to adapt to the changing needs of the residents and society over time. Yet, even as other cities sought new solutions to urban densification, the Hong Kong government embraced the tower block typology, resulting in its proliferation across Hong Kong. In 1997, the Hong Kong government pledged to construct “on average not less than 85,000 flats per year.”10 By 2013, the tower block encapsulated 46.7% of the total housing stock in the city, a figure which only continues to grow today due to persistent urban strain.11 Such a legacy created a fixation on the private individual, and Hong Kong’s regulatory frameworks for housing embodied such a notion. In the Long-Term Housing Strategy (LTHS), the

Hong Kong government defined “adequate housing” by five characteristics: 1. Built of permanent materials 2. Self-contained 3. Occupied on an unshared basis except in the case of very small households 4. Not overcrowded 5. At a rent or price within the household’s means.12 Such a definition failed to make any reference to public spaces and inherently focused on providing for the private individual by directly contradicting the idea that a person exists amongst others. These principles remained pillars of public housing throughout time, resulting in minimal changes to the ways in which the tower block addressed the relationship between private and public. As the tower block matured from the initial Mark I type to the modern Harmony model over 50 years, the Hong Kong government gradually acknowledged the significance of community services to housing, but these were simply relegated to the ground floor or detached within the surrounding site.13 Thus, the tower blocks remained as housing for housing instead of becoming housing for living, and the sociability needs of the residents remained unfulfilled in their daily lives. These unfulfilled needs forced residents to create their own spaces for sociability. Across Hong Kong, residents living in tower blocks attached appendages onto the facade to hold air conditioning units, built caged-in balconies to extend their living units, and constructed entire

Constance Smith and Saffron Woodcraft. “Tower Block ‘Failures’?: High-Rise Anthropology.” Focaal 2020, no. 86 (2020): 1–10. Ping Yan, “Public Housing in Hong Kong Past, Present and Future”, 5. 11 Deng et al., “Challenge-Driven Design for Public Housing: The Case of Hong Kong,” 213–224. 12 Lau, Kwok-yu. Housing In the Other Hong Kong Report. (Hong Kong, 1991), 347-348. 13 Deng et al., “Challenge-Driven Design for Public Housing: The Case of Hong Kong,” 213–224. 9

Bhagat | Wong

Figure 05: Evolution of the Tower Block

rooftop structures to gamble and congregate.14 The proliferation of these homemade structures, labeled unauthorized built works (UBW) by the Hong Kong Housing Authority, reflect an unmet demand by residents for spaces of sociability.15 In 2001, an estimated 800,000 unauthorized built works existed across Hong Kong which stood in contrast to the 810,468 public rental housing units built today.16,17 By mapping the locations of these unauthorized built works alongside the density of Hong Kong and the locations of the public housing

estates, the entwined relationship between the tower block typology and these structures becomes evident. Not only their existence, but also the widespread proliferation of these UBWs across Hong Kong point towards a major discrepancy between the permanence of the existing tower block typology and the shifting temporality of people’s lives. At its core, the tower block typology in Hong Kong failed to meet people’s sociability needs as they change over time by prioritizing the private individual over of the public collective.

Tower Blocks Unauthorized Building Works (UWB) >40,000p/km2 2

40,000p/km2

25,000p/km2

4 5

2 2

6 2

2 39 3

5 6

37 18 17 2

67 6

52 5

31 97

2 4

19 4

13 47 55

12 2

8 7

2 4 14

16 12

2 3

<4,000p/km2

10,000p/km2

10 15

55 3

12 4

9 9

2 3 8

Figure 04: Map of Unauthorized Built Works across Hong Kong

Francisco García Moro. “The Death and Life of Hong Kong’s Illegal Façades.” ARENA Journal of Architectural Research 5, no. 1 (2020): 2. Daniel Chi Wing Ho, Kwong Wing Chau, and Yung Yau. “Evaluating Unauthorized Appendages in Private Apartment Buildings.” Building Research & Information 36, no. 6 (2008): 568–579. https://doi.org/10.1080/09613210802386198. 16 Lawrence W.C. Lai and Daniel C.W. Ho. “Unauthorised Structures in a High‐rise High‐density Environment ‐ The Case of Hong Kong.” Property Management 19, no. 2 (2001): 112–23. https://doi.org/10.1108/02637470110387830. 17 Hong Kong Housing Authority, “Key Figures,” Hong Kong Housing Authority, Hong Kong Housing Authority, 31 March 2022 14 15

Domain Chapter

Figure 06: Unauthorized Built Works Collage

Bhagat | Wong

Such a failure resulted in the deterioration of people’s quality of life in Hong Kong. The World Health Organization (WHO) defines quality of life (QoL) as an “individual’s perception of his or her position in life in the context of the culture and value systems in relation to goals, expectations, standards and concerns.”18 This notion can further be broken down into three main aspects: individual, interpersonal, and contextual.19 Therefore, the role of architecture in affecting the sociability of people’s lives cannot be understated. According to a study by Sing at Hong Kong University of Science & Technology, Hong Kong residents identified attributes related to their living conditions as one of the main factors affecting their quality of life, where 38% of respondents claimed to

“rarely or never experienced enjoyment” and 59% pointed towards “having a comfortable home” as being a life-long goal.20 Similarly, another study highlighted that a majority of Hong Kong residents maintained a negative view of the public sphere and their living environments, particularly for those living in public housing. Residents of public housing scored their quality of life on average 10% lower than those living in private housing across four quality of life domains that constitute a person’s sociability needs: physical health, psychological health, social relations, and environment.21 Thus, it can be inferred that addressing the living conditions of Hong Kong residents is one of the most impactful means to improve people’s quality of life and address their sociability needs as they change over time.

The Whoqol Group. “The World Health Organization Quality of Life Assessment (WHOQOL): Development and General Psychometric Properties.” Social Science & Medicine 46, no. 12 (June 1998): 1569–85. 19 Omar Fassio, Chiara Rollero, and Norma De Piccoli. “Health, Quality of Life and Population Density: A Preliminary Study on ‘Contextualized’ Quality of Life.” Social Indicators Research 110, no. 2 (January 2013): 479. 20 Ming Sing, “The Quality of Life in Hong Kong.” Social Indicators Research 92, no. 2 (June 2009): 295. 21 Zhonghua Gou, Xiaohuan Xie, Yi Lu, and Maryam Khoshbakht. “Quality of Life (QoL) Survey in Hong Kong: Understanding the Importance of Housing Environment and Needs of Residents from Different Housing Sectors.” International Journal of Environmental Research and Public Health 15, no. 2 (January 27, 2018): 219. 18

Domain Chapter

Figure 07: Hong Kong Quality of Life Collage

Bhagat | Wong

Which Public? Which Private?

0.0

1.0

PRIVATE

PUBLIC

INDIVIDUAL

COLLECTIVE

STATIC

ACTIVE

ISOLATED

CONNECTED

Figure 08: Spectrum of Sociability

While the history of the tower block in Hong Kong presents strong evidence for characterizing the tower blocks of Hong Kong as an architecture of and for the private, the research would be remiss if it were to make such a bold assertion without acknowledging the pervasiveness of complexity and contradiction in the terms public and private. Therefore, it is imperative to first break down these terms and explore their evolution and divergence over time before being able to properly address how they might manifest architecturally. And so, the research narrowly examines these two terms through the lens of architecture while maintaining an awareness of the parallel conversations occurring in other disciplines such as sociology, philosophy, and political science. The concept of a public space or a private space is one often taken for granted and misused. Misused by architects, planners, and developers, the colloquial, idealization of these concepts is typically not reflective of reality. The Italian philosopher Noberto Bobbio declared in 1989 that the distinction between these two terms was one of the “grand dichotomies”

of Western philosophy.22 However, such a unitary division overlooked the lenses through which the terms were utilized. It assumed a strict political division.23 In reality, the relationship between these terms is neither political nor apolitical. It is instead dependent on the realm of discourse in which they are employed. Sociologist Jeff Weintraub identified in 1997 four overarching categories through which the terms adopt unique definitions, providing a framework for this research to define its scope. In particular, Weintraub’s dramaturgic approach reflects emerging, modern concepts of public and private in the realm of architecture. He explains that “the [dramaturgic] approach… sees the “public” realm as a sphere of fluid and polymorphous sociability and seeks to analyze the cultural and dramatic conventions that make it possible.”24 Such a definition defines space along a spectrum of sociability which is influenced by the ways in which people interact it. Sociability, as Jane Jacobs illustrates, is the result of the configuration of physical spaces. In The Death and Life of Great American Cities (1961), Jacobs

Norberto Bobbio, Democracy and Dictatorship: The Nature and Limits of State Power (Minneapolis, MN, 1989), 1. Jeff Weintraub, The Theory and Politics of the Public/Private Distinction: Perspectives on a Grand Dichotomy (New York, NY, 1997), 2. 24 Weintraub, The Theory and Politics of the Public/Private Distinction: Perspectives on a Grand Dichotomy, 7. 22 23

Domain Chapter

Figure 09: Kohn’s Two Dimensions of Publicness

describes how the “streets of great cities have builtin equipment allowing strangers to dwell in peace together on civilized but essentially dignified and reserved terms. Lowly, unpurposeful and random as they may appear, sidewalk contacts are the small change from which a city’s wealth of public life may grow.”25 Yet, such a strictly architectural perspective oversimplifies the discussion by ignoring the broader factors at play in a neighborhood, city, or society. Therein lies the intricacies of Weintraub’s dramaturgic approach. He acknowledges the multidimensionality of the public-private distinction, arguing that only through “the interplay between the spatial organization of cities and long-term sociohistorical processes” may a fuller understanding of public and private emerge.26 While architects cannot control all these external elements, it is imperative for them to have an awareness of these social relationships.

Quantifying the Publicness of Public Spaces Building out from Weintraub’s dramaturgic approach, the political scientist Margaret Kohn evoked a new idea by challenging the established, mono-dimensional definitions of public and private by architects and set a qualitative baseline for

distinguishing types of spaces along a spectrum between public and private.27 Kohn illustrated how one may begin to approach quantifying the publicness of a public space, hybridizing the physical, social, and political aspects of a space. While her approach to public space was novel, it lacked the specificity and rigor necessary to compare and evaluate the effectiveness of a space to be public or private. It was vague, ambiguous, and remained open to interpretation. Such characteristics continued to plague definitions by other researchers. Four models for publicness emerged over the following decade which achieved increasingly levels of specificity and rigor. In 2007, Van Melik, Van Aalst, and Van Weesep developed the cobweb model, which addressed public space indirectly by focusing on ‘themed space’ and ‘secured space’.28 The model utilized a series of six radial spokes and three concentric rings to visually represent the intensity for each dimension of themed and secured spaces: surveillance, restraints on loitering, regulation, events, funshopping, and pavement cafes.29 The strength of the cobweb model lied in its multidimensional visual representation of publicness. Building upon the cobweb model, Nemeth and Schmidt created the tri-axial model in 2010, which directly focused on establishing a distinction between public and private.30 The model utilized three intersecting axis, where each axis represented

Jane Jacobs, The Death and Life of Great American Cities (New York, NY, 1961), 72. Weintraub, The Theory and Politics of the Public/Private Distinction: Perspectives on a Grand Dichotomy, 24. 27 Kohn, Brave New Neighborhoods: The Privatization of Public Space, 11 28 Rianne Van Melik, Irina Van Aalst, and Jan Van Weesep. “Fear and Fantasy in the Public Domain: The Development of Secured and Themed Urban Space.” Journal of Urban Design 12, no. 1 (2007): 25–42. 29 Van Melik et al., “Fear and Fantasy in the Public Domain: The Development of Secured and Themed Urban Space,” 25. 30 Jeremy Németh and Stephen Schmidt. “The Privatization of Public Space: Modeling and Measuring Publicness.” Environment and Planning B: Planning and Design 38, no. 1 (2011): 5–23. 25 26

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Van Melik, Van Aalst, Van Weesep (2007) 2

In 2011, Varna and Tiesdell reconciled the cobweb and tri-axial models. The star model, as they called it, was arranged along five spokes extending out from a hexagon, each spoke representing a dimension of publicness: ownership, control, civility, physical configuration, animation.29 It was the first time that a model for publicness considered the physical characteristics of a space. Additionally, the model utilized a systematic process for quantifying the publicness of a space through identifying, weighting, and combining to create a single meta-dimensional score. In 2013, Langstraat and Van Melik developed the OMIA model to articulate the publicness of a public space as a result of privatization.30 It utilized concentric circles subdivided into four quadrants, each representing one dimension of publicness: ownership, management, accessibility, and inclusiveness. This model realigned with Weintraub’s original concept of sociability and broadened the applicability of a publicness evaluation model.

5 Secured public space Themed public space 1. Surveillance 1. Events 2. Restrains on lotering 2. Funshopping 3. Regulation 3. Pavement cafes

Németh and Schmidt (2010) Ownership

Uses/Users

Management

Space A More ‘public’ More ‘private’

Space B

Varna and Tiesdell (2011) Ownership

Physical Conﬁguration

Control

Animation

a different dimension of publicness: ownership, management, and use/users.31 Though this model, the publicness of each dimension is identified along a continuum, providing a more intuitive comparison.

Civility

Langstraat and Van Melik (2013)

As a whole, these four models offered a solid basis for understanding how the publicness of a space may be evaluated. Yet, they all lacked three critical elements. Firstly, they primarily relied on qualitative measurements and data, making comparisons between different spaces either unreliable or inconsistent. Secondly, each model was constructed as a methodology for post-analyzing an existing space as opposed to designing new spaces. Lastly, all of the models approached the distinction between public and private from a biased lens of publicness, relegating the concept of private to mean anything else but public. These missing elements constitute the foundation from which this research began to construct its own model for evaluating a space along a spectrum from private to public, from the individual to the collective, from the personal to the social.

Management

Ownership

More Public

More Private

Németh and Schmidt, “The Privatization of Public Space: Modeling and Measuring Publicness,” 5. 32 George Varna and Steve Tiesdell. “Assessing the Publicness of Public Space:The Star Model of Publicness.” Journal of Urban Design 15, no. 4 (November 2010): 575–598. 33 Florian Langstraat and Rianne Van Melik. “Challenging the ‘End of Public Space’: A Comparative Analysis of Publicness in British and Dutch Urban Spaces.” Journal of Urban Design 18, no. 3 (2013): 429–48. 31

Acessibility

Inclusiveness

Figure 10: Four Models for Evaluating Publicness

Domain Chapter

The Private Tower Block A Case Study of Three Hong Kong Towers The Sociability Spectrum, as the research has coined it, is an adaptive model for evaluating the publicness of a space through a set of quantifiable parameters which fall under the scope of an architect’s work as a designer. It builds upon the four previous models for publicness by specifically focusing on their three identified weakness. Without delving into too much detail about the model itself, which will be further articulated and explained in Chapter 03, the Sociability Spectrum evaluates a space by analyzing four dimensions of publicness: Ownership, Accessibility, Affordance, and Environment. Each dimension has its own unique set of quantifiable parameters which were chosen based on emerging trends derived from the existing evaluation models studied, such as those relating to transit, use, and accessibility, or were established by the team where gaps in the existing research were found, such as those relating to network centrality and environmental comfort. Each parameter’s domain was established based on local code requirements, information derived from existing models, or were inherently bounded by their calculation method.

(2000) tower block types were selected to explore the evolution of the tower block’s sociability throughout time. The study determined that the towers had sociability scores of 0.18, 0.17, and 0.20 respectively. Such low scores emphasized the privateness of these designs. Beyond that, it highlighted the fact that there was no significant change in the towers’ publicness, where scores differed by a mere 0.03, even though the design of the tower block changed. Upon further analysis, such a consistently private scores can be attributed to several major design pitfalls. Firstly, all three structures exhibited high occupant densities, resulting in only five or six square meters for each resident. Secondly, the high density also led to lengthy corridors, which drastically decreased each building’s spatial connectivity and interior daylighting. Lastly, each building lacked any program variety, meaning that occupants were required to venture out into the city to obtain daily necessities. As such, the case study revealed that while the Hong Kong Housing Authority did make form-based alterations to the tower block over time, these modifications had no evident effect on the publicness of the spaces, creating a discontinuity between the tower block and the sociability needs of the residents over time.

The research conducted a case study of three archetypal Hong Kong tower blocks to evaluate their score along the Sociability Spectrum and tune the system to the context of Hong Kong. The Mark I (1955), Linear I (1980), and Harmony I

LINEAR I

DENSE APARTMENT LAYOUT B.02 Occupant Density B.05 Average Area / Space

40m

LACK OF PROGRAM VARIETY

B.03 Spatial Connectivity

B.06 Function Density

PRIVATE

SA = 0.40

EN = 0.18

OW = 0.08

PUBLIC

BA = 0.12

40m

0.20

PRIVATE

SA = 0.36

OW = 0.08

PUBLIC

EN = 0.15

0.17

PRIVATE

SA = 0.41

LENGTHY CORRIDORS

0.18

BA = 0.12

2000

B.01 Threshold Condition

PUBLIC

EN = 0.21

HARMONY I

LIMITED ENTRY POINTS

1980

OW = 0.08

1955

BA = 0.15

MARK I

Figure 11: Tower Block Case Study

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Domain Chapter

Bhagat | Wong

Visions for an Adaptive Architecture While the tower block typology became a major vehicle for addressing modern challenges of densification in Hong Kong and around the globe, it was by no means the only means the only solution conceived and put forth by architects and urban planners during the 20th century. In fact, the practicality of the tower block stood in juxtaposition to the idealism of design proposals from the same period which envisioned an architecture which reflected the changing sociality of everyday life. Whereas one sought to solve an immediate problem, the others aimed to re-imagine the ways in which we live and interact with one another. The work of Archigram and Metabolism in the 1960’s proposed a radically new solution to the challenges of mass migration and densification in the United Kingdom and Japan, respectively. These groups viewed architecture not as static and permanent objects existing within an urban context but instead as ever-changing spaces integral to the urban vitality of a city.34 Through their proposals, Archigram and Metabolism experimented with architectural artifacts which were designed to change and adapt to the shifting lifestyles of its inhabitants. The Metabolists responded to the same urban conditions and densification challenges in Japan that existed in Hong Kong during the proliferation of tower block typology, yet this group looked towards the future of urban living instead of the present. The population of Tokyo tripled following World War II, raising from 2.78 million in 1945 to 8.31 million in 1960.35 The Metabolists viewed such challenges not as ones to be solved per say but instead as an opportunity to re imagine the relationship between humans and the built environment. In their manifesto, Metabolism – a Proposal for a New Urbanism (1960), the Metabolists declared that humans exist together as a continuously shifting, social entity.36 Additionally, it regarded the built

environment as an extension of this humanity.37 By intertwining these two groups and perceiving them as always in flux, the Metabolists proposed architectural artifacts which were structured to change throughout time. While a majority of the work by the Metabolist was relegated to speculative models and drawings, the Nakagin Capsule Tower by Kisho Kurokawa was realized as a built project. Conceptually, the building was designed as series of modular units attached to a central core. These modular units, or capsules, enabled continuous replicability and adaptability amongst different parts of the building as renovations were required, technology was updated, and spaces become obsolete.38 Unfortunately, such an idealism was never fully realized due to limitations of existing technology. In the United Kingdom, a similar housing crisis took place in the 1960’s, which prompted the government there to take a similar, impulsive response as the Hong Kong government. The government constructed dozens of public housing tower blocks across the country. The problem was solved but at the expense of urban livability. Rejecting the rigidity and inhumanity of the tower block, Archigram proposed an architectural system which re-imagined the ways in which humans interacted with one another. Adaptation sat at the heart of Archigram’s proposal Plug-In City (1964), which took inspiration from their avant-garde counterparts in Japan. Conceptually, the project proposed private, modular residential units which plugged into a public, central infrastructure, challenging the relationship between public and private spaces in an urban context.39 Through such a system, the Plug-In City had the ability to continuously evolve programmatically, functionally, and socially. Such an evolution, as Peter Cook intended, was driven by the users’ interactions with the architecture

Gizem Deniz Guneri, “Peter Cook Beyond Archigram: Towards a Critical Utopianism.” Prostor 28, no. 1 (59) (June 30, 2020): 130–41. Hein et al., Rebuilding Urban Japan After 1945, 55. 36 Kiyonori et al., Metabolism – A Proposal for a New Urbanism (Tokyo: Bijutsu Shūpansha, 1960), 1. 37 Kishō Kurokawa, Metabolism in Architecture (London: Studio Vista, 1977), 27. 38 Kishō Kurokawa, Metabolism in Architecture, 32. 39 Simon Sadler, Archigram: Architecture without Architecture, 37. 34 35

Domain Chapter

Figure 12: Nakagin Capsule Tower by Kisho Kurokawa (1972)

Figure 13: Plug-In City by Peter Cook (1964)

around them. Archigram understood “housing as a consumer project,” which propelled them to design in such a way that all residents participated in constructing the sociability of their spaces through their own efforts.36 Yet, in a similar manner to that of the Metabolists, Archigram’s design proposals were never realized due to limitations by the technologies available and the conventional orthodoxies of its time. When faced with similar housing crises and densification challenges as Hong Kong in their respective cities, both the Metabolists and Archigram presented a vision of architecture that

was organic, dynamic, and ever-changing, but both were also limited by their times. Therefore, the P2 Tower revisits these principles put forth by the Metabolists and Archigram specifically through a lens of cybernetics, where these ideas of adaptation and flexibility were embedded into a computational design workflow and took advantage of emerging technologies and theories in the 21st century, such as artificial intelligence, parametricism, digital fabrication, and emergence. The computational workflow developed by this research leveraged these emerging technologies and theories in order to create a feedback system that continuously responds to dynamic variables.

Simon Sadler, Archigram: Architecture without Architecture, 37.

Bhagat | Wong

Towers and Timescales The visions put forth by Archigram and the Metabolists for the past, present, and future of urban living surely pushed the boundaries on how architects and urban planners may begin to understand high-rise housing in the modern era. The stark contrast of their designs with the rigidity and inhumanity of the tower block typology presents an opportunity for this thesis to propose a new housing tower that meets the immediate density needs of a city while also enabling the continuous adaptation to the changing needs of its residents over time. Before such an endeavor can be undertaken, it would be important to first investigate the layers and organization strategies of tall buildings, recognizing their unique architectural, mechanical, and structural requirements. Such a foundational understanding of towers would enable this thesis to reasonably reconcile the idealism of Archigram and the Metabolists’ megastructures and the practicality of the tower block. While tall buildings afford ample opportunity to address modern challenges of densification and urban living, the complexity of their programmatic organization and environmental conditions give rise to new challenges. Technologically, the design of a tower can be organized into five subsystems: the structural systems, the floor systems, the vertical circulation system, the façade system, and the environmental system.41 The structural system refers to the elements of the tower which are primarily responsible for resisting the vertical and lateral loads acting upon the building. Critical design aspects of a tower’s structural system to resist to wind, gravity, seismic loads include the dynamic properties, aerodynamic characteristics, location of structural members on the floor plate, the floor-to-floor heights, and the slenderness.42 The floor system refers to the elements of the building which handle horizontally transferring live and dead loads to the primary structural system for vertical transfer to the ground. The vertical circulation system refers to elements of the building which move people and

goods throughout the height of the tower. It plays a critical role particularly in mixed-use towers as a means to efficiently control the movement of people throughout the tower for their intended purposes.43 The façade system refers to the delineation between the inside and the outside and plays a major role in defining the visual aesthetics of the tower per the design intent. Additionally, the façade system is integrally connected to the structural system as it deals with high wind loads, which typically results in the façade being divided into different zones to respond to varying wind loads.44 Lastly, the environmental system refers to the ways in which the building form and the building envelope regulate the interior environmental conditions by managing the wind, rain, sunlight, etc. This includes design considerations such as the morphology, orientation, and façade elements.45 These five layers work together as independent parts of the same whole, but from a broader perspective, each layer also operates on its own timescale. Whereas the structural system of a building may be expected to operate on the timescale of centuries, the façade system only acts on the timescale of decades. Such variation brings about different influences on the design of a space such as functional requirements, spatial needs, or social perceptions. Therefore, it is critical to breakdown the timescales of each tower layer as a means to respond appropriately to its specific public and private influences. In doing so, this thesis begins to understand the ways in which architectural responses to change over time affect the sociability of a space at varying timescales. From a social perspective, the timescales of these tower layers correspond directly to the timescales of the residents, whether that is an individual, a group, or a population. For example, an individual timescale corresponds to the different stages of life. When a person is growing up, their spatial needs and connections vary drastically. Therefore, the interplay between the timescales of the tower layers and the lives of its residents is inherently intertwined.

Elif Erdine. “Generative Processes in Tower Design: Algorithms for the Integration of Tower Subsystems.” (PhD, Architectural Association School of Architecture, 2014), 39. 42 Elif Erdine. “Generative Processes in Tower Design: Algorithms for the Integration of Tower Subsystems,” 45. 43 Elif Erdine. “Generative Processes in Tower Design: Algorithms for the Integration of Tower Subsystems,” 59. 44 Elif Erdine. “Generative Processes in Tower Design: Algorithms for the Integration of Tower Subsystems,” 62. 45 Elif Erdine. “Generative Processes in Tower Design: Algorithms for the Integration of Tower Subsystems,” 69. 41

Domain Chapter

FIXED SYSTEMS

TOWER MORPHOLOGY

STRUCTURE

ADAPTABLE SYSTEMS DECADES PUBLIC-PRIVATE SEGMENTS

YEARS PROGRAM TOPOLOGY

MONTHS SPATIAL ORGANIZATION

Figure 14: Tower Layers and Timescales

Bhagat | Wong

Adaptability through Digital Fabrication In order to enable an architectural system to adapt at these different timescales and in response to people’s changing lifestyles, the research must revisit and challenge traditional construction methods and technologies for tall buildings, which are commonly permanent and immutable. Emerging digital fabrication techniques and material systems offer the opportunity to create an architecture of adaptability envisioned by the Metabolists and Archigram. In particular, robotic additive manufacturing allows for the seamless manufacturing of bespoke geometries without the need for hundreds of unique formworks or jigs, significantly reducing the time, material, and manpower for fabrication. Such a process would enable the on-demand, rapid fabrication of customized parts necessary for an adaptable architectural system. Recent advancements in robotic additive manufacturing have steadily increased interest amongst the construction industry to incorporate this fabrication technique into their practices. In 2005, the Chinese company WinSUN invented the spray nozzle and developed the first continuous 3D printer for construction, creating ten, off-site houses.46 Following 12 years later, the first 3D printed building in Europe was constructed in Copenhagen by the Dutch company 3D Printhuset. The morphology of the building was entirely curvilinear as to emphasize the technology’s lack of geometric constraints. In 2019, the world’s longest 3D-printed concrete bridge was printed by a team at Tsinghua University School of Architecture which spanned 86m and cost 33% less.47 As robotic additive manufacturing continues to advance, particularly in terms of efficiency and cost, its ability to facilitate adaptable systems increases. Yet,

several limitations continue to block its widespread adoption, specifically as it relates to material. Concrete additive manufacturing is well advanced as compared to other metal or polymer printing, but its material constraints create several fundamental drawbacks.42 Firstly, the composition of the concrete must be balanced such that it is pumpable and printable, severely minimizing the range of usable mixtures and limiting the potential to lower the embodied carbon of concrete.43 Additionally, printed concrete displays both isotropic and anisotropic properties, whereas poured concrete only exhibits isotropic properties.44 Such a change in material properties, makes it difficult to predict its structural performance and thus, scalability becomes an issue. These limitations prohibit concrete additive manufacturing from being fully embraced by the construction industry. Additionally, concrete often has a high embodied carbon, which makes it a difficult material to use as sustainability factors continue to rise, necessitating the use of low carbon materials globally. In order to address these material-related challenges, different researchers investigated the use of fiber-reinforced cementitious composites as alternative materials to traditional concrete mixtures.45 These material compositions aimed to optimize four factors related to printability and buildability: easy-extrusiveness, easy-flow, wellbuildable, and proper setting time. Of these factors, the research found that prioritizing extrudability and flowability by selecting raw materials with maximum particle size of about one tenth of nozzle diameter and adjusting the water to binder ratio ensured an easier optimization of the remaining

S. El-Sayegh, L. Romdhane, and S. Manjikian. “A Critical Review of 3D Printing in Construction: Benefits, Challenges, and Risks.” Archives of Civil and Mechanical Engineering 20, no. 2 (June 2020): 44. 41 S. El-Sayegh, L. Romdhane, and S. Manjikian. “A Critical Review of 3D Printing in Construction: Benefits, Challenges, and Risks,” 44. 42 Baigarina, Akerke, Essam Shehab, and Md. Hazrat Ali. “Construction 3D Printing: A Critical Review and Future Research Directions.” Progress in Additive Manufacturing 8, no. 6 (December 2023): 1397. 43 S.El-Sayegh, L. Romdhane, and S. Manjikian. “A Critical Review of 3D Printing in Construction: Benefits, Challenges, and Risks,” 47. 44 Akerke Baigarina, Essam Shehab, and Md. Hazrat Ali. “Construction 3D Printing: A Critical Review and Future Research Directions,” 1397. 45 GuoWei Ma, Li Wang, and Yang Ju. “State-of-the-Art of 3D Printing Technology of Cementitious Material—An Emerging Technique for Construction.” Science China Technological Sciences 61, no. 4 (April 2018): 475. 45 GuoWei Ma, Li Wang, and Yang Ju. “State-of-the-Art of 3D Printing echnology of Cementitious Material—An Emerging Technique for Construction,” 485. 41

Domain Chapter

Figure 15: Robotic 3D Concrete Printing (Photo Puja Bhagat and Jonathan Wong)

factors.46 Additionally, these types of materials have the ability to lower embodied carbon of concrete mixtures, particularly when a portion of concrete is replaced with fly ash or other lowcarbon materials. While cementitious composites are relatively new, they provide a promising, more sustainable alternative for robotic manufacturing that maintains a level of flexibility and adaptability, while improving upon material-related challenges.

and fabricate a wider range of morphologies using this technique.47 This type of localized control and formation enables a level of adaptability which is difficult to achieve with traditional concrete systems. Thus, combining woven bamboo with fiber-reinforced cementitious composite 3D printing both reaches the necessary structural performance of large scale forms and increases the range of achievable and adaptable morphologies.

To further improve upon these challenges, rebar is often introduced to concrete assemblies. However, rebar also has a high embodied carbon. As such, bamboo strip weaving offers a low-carbon alternative to rebar that can act as integrated formwork and reinforcement. Bamboo strip weaving is a traditional Chinese artform which uses thin strips of bamboo to achieve self-standing morphologies without the need for additional joinery or attachment systems. Particularly, the Kagome weave is a triaxial pattern which can produce highly complex three-dimensional surfaces due to its self-bracing capacity and high shear resistance.46 Additionally, it enables a high degree of geometrical control, high redundancy, and local reparability, allowing designers to generate

These techniques can be further combined with the notion of individual modular components which is strongly present in the works of Archigram, the Metabolists and others of the time. Modular components, combined with the capabilities of robotic printing and low-carbon material systems, can achieve an adaptable architecture which works within the requirements of 21st century cities. Therefore, this research explored the use of robotic 3D printing on bamboo strip formwork in a modular component assembly as a method to improve upon existing challenges within the industry and facilitate a level of adaptation sought by that of the P2 Tower’s predecessors.

Phil Ayres, Alison Grace Martin, and Mateusz Zwierzycki, “Beyond the Basket Case: A Principled Approach to the Modelling of Kagome Weave Patterns for the Fabrication of Interlaced Lattice Structures Using Straight Strips.,” 75. 47 Martin Ayres and Zwierzycki, “Beyond the Basket Case: A Principled Approach to the Modelling of Kagome Weave Patterns for the Fabrication of Interlaced Lattice Structures Using Straight Strips,” 75. 46

Bhagat | Wong

Towards An Urban System Although the evolution of a person’s life can be reflected in their immediate living environment, it cannot be forgotten that towers do not exist in isolation but instead as an element of a complex urban environment. Therefore, it is important to extend beyond the confines of a single tower and consider its role in the micro-urban environment as well as the macro-urban system. The design proposals by Archigram and Metabolist, which were discussed previously, began to speculate about how towers may impact their urban environments, but for the most part, these design proposals limited to a inward-looking vacuum. On the other hand urban design proposals such as Frank Lloyd Wright’s Broadacre City and Carlos Moreno’s

The Broadacre City

Frank Lloyd Wright, in April of 1935, introduced the Broadacre City as a urban design rooted in urban decentralization, economic self-sufficiency, and individualism with the goal of leveraging the potential brought about by the Machine Age and returning American cities to their roots of “democratically formed village life.”48 Wright was rallying against what he described as the plights of modern cities which sat in the forefront to depression-laden times. The Broadacre City stepped outside of mainstream urban theories and practices by proposing scattered, independent villages throughout the rural landscape, each containing all of the necessary modern institutions, and connecting them by a single, horizontal road network. Thus, the decentralized nature of the Broadacre City emphasized the role and influence of each public institution as crucial to the workings of the overall urban system by breaking down their differences and mering them into a singular, interconnected network. 49Yet, the rural sprawl of the Broadacre City only had the potential Figure 16: Broadacre City (Photo by Skot Weidemann) to be realized in the United States seeing as many other 15-Minute City examined how simple architectural countries lacked the available land and thus, failed components may combine, interact, and connect to to address the reality of the existing disconnected construct a complex urban system. These urban urban environments by instead proposing an escape planning proposals addressed modern challenges to Wright’s so-called “middle landscape.”50 of densification by re-imagining the city as a singular, interconnected network. In doing so, they envisioned urban environments which expanded the influences of a single, architectural artifact and were responsive to the changing sociability needs of its On the other hand, Carlos Moreno’s 15-Minute inhabitants. City, which emerged from the consequences of

The 15-Minute City

Arthur C. Nelson, “The Planning of Exurban America: Lessons from Frank Lloyd Wright’s Broadacre City.” Journal of Architectural and Planning Research 12, no. 4 (1995): 339 49 Mark B. Lapping, “Toward A Social Theory of the Built Environment: Frank Lloyd Wright and Broadacre City.” Environmental Review 3, no. 3 (March 1, 1979): 16 50 Mark B. Lapping, “Toward A Social Theory of the Built Environment: Frank Lloyd Wright and Broadacre City,” 21. 48

Domain Chapter

Figure 17: 15-Minute City (Drawing by Hassell Studio)

the COVID-19 pandemic lock downs, proposed a methodology for re-designing existing cities and addressing the specific culture of its own urban context. The 15-Minute City built upon a legacy of an understanding of the city as a collection of localized neighborhoods which operated together as part of an overall urban system. Thus, Moreno’s proposal argued that localized interventions in these neighborhood would positively impact other interconnected neighborhood as well as the entire system.51 The idea nearly all of a person’s needs are met within a short walk or bike ride from their home sits at the core of the 15-Minute City. This was achieved by not focusing on the development of transportation to bring people to their programmatic needs, but instead bringing those same amenities to the places people live and focusing on ten factors: proximity, density, diversity, mixed-use, modularity, adaptability, flexibility, human-scale design, connectivity, and digitalization.52 In doing so, Moreno proposal aims to revitalize the neighborhood by ensuring that people’s immediate needs are met, even as they change over time. While such an ideal is difficult

to challenge from a practical point of view, it can be argued the 15-Minute City is rooted in a notion that the physicality of architecture is a pseudopanacea for all the plights of modern urbanization and densification and disregards the socio-spatial aspects of living and working as a member of a neighborhood. The Broadacre City and the 15-Minute City both expanded the domain of a single architectural artifact by considering them as elements within an overarching urban system. Building out from these models for urban, the P2 Tower extended its sociability influence onto its localized urban environment through a series of pedestrian pathways and also considered the ways in which a collection of P2 Towers may interact with one another to develop an overall urban network through a series of multi-modal corridors. Thus, the computational workflow developed by this research generated an urban system driven by the socio-spatial elements of everyday life and sociability needs of people which integrates into the existing urban fabric of densely populated cities.

Georgia Pozoukidou, and Zoi Chatziyiannaki. “15-Minute City: Decomposing the New Urban Planning Eutopia.” Sustainability 13, no. 2 (January 18, 2021): 931. 52 Amir Reza Khavarian-Garmsir, Ayyoob Sharifi, Mohammad Hajian Hossein Abadi, and Zahra Moradi. “From Garden City to 15-Minute City: A Historical Perspective and Critical Assessment.” Land 12, no. 2 (February 20, 2023): 522 51

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FRENCH REVOLUTION

rise of technology

Global

rise of pollution

rise of tec downfall of cities

1920-1930

1853-1870 Georges Haussmann Paris, France

1882

1850-1920

PARIS BOULEVARDS

Ebenezer Howard Great Britain

Glob

1929 - 1939

rise of poor health in cities rise of political uprisings

THE GARDEN CITY

WORLD

Global

1914 - 1918

1789 / 1830 1848 / 1871

Paris, France

1820 - 1840

Great Britain

GREAT DEPRESSION

WORLD WAR I

RADIANT CITY

1931

INDUSTRIAL REVOLUTION

BROADACRE CITY Frank Llyod Wright United States

Le Corbusier Paris, France

THE LINEAR CITY Arturo Soria y Mata Madrid, Spain

THE DEATH AND AMERICA

Jan Unit

Domain Chapter

United States

chnology

2001

1959 - 1975

China

COVID-19 PANDEMIC Global

2021 - 2022

9/11 TERRORIST ATTACK

CULTURAL REVOLUTION

Global

1950 - 1953

Global

1938 - 1945

bal

VIETNAM WAR

1966 - 1976

WAR II KOREAN WAR

rise of security and surveillance rise of social distancing

1960-70

1970

rise of communal living

PLUG-IN CITY

1961

2015-2023

ne Jacobs ted States

Archigram United Kingdom

1960-70

D LIFE OF AN CITIES

SERPENTONE Mario Florentino Rome, Italy

CAPSULE TOWER

15 MINUTE CITY

The Metabolists Ginza, Japan

Carlos Moreno Paris, France

Figure 18: Urban Density Timeline

Bhagat | Wong

Simulating Sociability In a similar manner to how a single tower exists as part of an urban system, people cannot be considered as individuals at these larger scales but instead as members of a collective system. Therefore, this research may not simply claim to have designed spaces of private and public without full consideration to people’s social behaviors in these spaces as a unified entity. Pedestrian simulations, such as Peng Wang’s PedSim and Arup’s MassMotion, afford architects and urban designers the opportunity to predict, analyze, and evaluate the ways in which occupant may potentially utilize a space. While pedestrian simulations imitate people’s movements, the data extracted from these simulations is highly dependent on a wide host of parameters, including the granularity of the model, the level of individualism of the agents, the agents’ behaviors, etc. 53 Therefore, the effectiveness of a pedestrian simulation is determined by the attunement of these parameters to the scale of the simulation and the context of its application.

a variety of environmental factors. The Cellular Automation (CA) model discretized the environment into a grid of cells, where pedestrians were free to move to their neighboring cells based upon a given probability and rules.56 Such a model enabled the analysis of emergent crowd behaviors due to the dynamic interactions between each pedestrians with one another and their respective rules. The last model for pedestrian simulations relied on emerging research around artificial intelligence, following a data-driven approach. Here, the machine learning algorithm predicted the movement and patterns of the pedestrians based upon their previous behaviors. Each of these models for pedestrian simulation afforded different benefits of analysis at varying scales and situations.

Types of Pedestrian Simulations

However, these models and existing pedestrian simulations lacked key functionalities and behaviors which were critical to the goals of the research. First, most pedestrian simulations existed solely on small, two dimensional surfaces, lacking any ability for vertical movements or network-based paths. This proved to be a challenge due to the size and spatial organization of urban networks which require large-scale, three dimensional simulations. Second, and most importantly, existing pedestrian simulations lacked any mechanism for socialization between pedestrians. This behavior was essential for understanding how the designed urban networks facilitate sociability between occupants and cater to their specific social needs over time. As such, it was necessary for this research to develop a novel pedestrian simulation which enabled social interaction behaviors and accepted large-scale, three dimensional networks.

Existing research in pedestrian simulations categorized these models into four buckets based upon the ways in which the pedestrian behaviors were modeled. The simplest model considered the spatial environment as a non-metric graph, where the edges represented pathways such as roads or hallways and the nodes represented the intersections of the pathways.54 By simplifying the environment, the pedestrian behaviors at larger scales were more easily modeled and observed, particularly in terms of understanding which paths a pedestrian may take between two points of interest. Another model, the physical-based model, simulated the behavior of pedestrians based upon the laws of physics, where attraction and repulsion forces by other pedestrians or the context influenced their movements.55 This methodology operated well at smaller scales and provided more detailed pedestrian movements as it simultaneously balanced

Pitfalls of Existing Pedestrian Simulations

Amir Rasouli, “Pedestrian Simulation: A Review,” 2021: 2-7. Amir Rasouli, “Pedestrian Simulation: A Review,” 10. 55 Amir Rasouli, “Pedestrian Simulation: A Review,” 10. 56 Victor J. Blue and Jeffrey L. Adler. “Cellular Automata Microsimulation for Modeling Bi-Directional Pedestrian Walkways.” Transportation Research Part B: Methodological 35, no. 3 (March 2001): 294. 53 54

Domain Chapter

Current Pedestrian

M-1,1

M0,1

M-1,0

M0,0

M0,-1

M1,1

Potential Movements Other Pedestrians

M1,-1

Figure 19: Cellular Autonoma (CA) Model

Architectural Element Repellent Forces

Current Pedestrian Destination Attraction Force Other Pedestrian Attraction Forces Figure 20: Physics-Based Model

Bhagat | Wong

Discussion The current context of the Hong Kong tower block reveals a large discrepancy between the permanence of the built environment and the temporality of people’s lives. At its core, the tower block typology in Hong Kong has failed to meet people’s sociability needs as they change over time by emphasizing the private individual over of the public collective. Therefore, this thesis investigated this gap between the social affordance of the Hong Kong tower block and the people’s sociability needs. It aimed to create a new design for public housing towers that meets the density needs of Hong Kong while also facilitating continuous spatial changes to match the needs of people over time. This was achieved by first constructing a new model for evaluating a space along the public-private spectrum. This model was then utilized as a driving force to design a new tower system workflow focused specifically on the sociability needs of its occupants. Finally, a level of adaptation was integrated into the system following the logic of this methodology, allowing towers to exhibit different functionalities and performances over time. When expanded to the urban scale, this notion can influence larger populations and timescales, driven by the socio-spatial elements of urban life and the sociability needs of a collective which were integrated into the existing urban fabric of Hong Kong. In doing so, this thesis celebrated the social intricacies of each local context by designing new corridors which facilitated their specific lifestyles. This was achieved through a series of local and urban scale pedestrian pathways which spanned multiple contexts and communities across Hong Kong. This thesis also deeply investigated the use

Domain Chapter

of novel social pedestrian simulations to drive the design of the social urban fabric within dense cities. This thesis adds to the existing discourse surrounding sociability and adaptability in architecture by leveraging the power of both unique but interconnected fields to address the emerging challenges of densification and people’s changing sociability needs in Hong Kong. The research addressed the following questions: 1. How can a novel computational framework and material fabrication system address the constant flux of people’s sociability along the public-private spectrum in Hong Kong over time? 2. How can adaptable architecture improve the quality of life in Hong Kong? 3. Can challenging conventional tower organizations in terms of public and private redefine the ways in which people live? 4. How can temporal urban systems socially adapt to and bridge multiple communities across a dense city? 5. How can understanding pedestrian behavior drive the design of a social urban space? As such, the research aimed to challenge the traditional notion of the tower block as a permanent, unchanging structure in the built environment and discover its potential to become a temporal system which evolves alongside its occupants, meeting their needs and improving urban livability. Only in this way, can architecture begin to address the complex challenges of densification.

Bhagat | Wong

Bibliography Ayres, Phil, Alison Grace Martin, and Mateusz Zwierzycki. “Beyond the Basket Case: A Principled Approach to the Modelling of Kagome Weave Patterns for the Fabrication of Interlaced Lattice Structures Using Straight Strips.,” n.d., 75. Baigarina, Akerke, Essam Shehab, and Md. Hazrat Ali. “Construction 3D Printing: A Critical Review and Future Research Directions.” Progress in Additive Manufacturing 8, no. 6 (December 2023): 1393–1421. https://doi.org/10.1007/s40964-023-00409-8. Blue, Victor J., and Jeffrey L. Adler. “Cellular Automata Microsimulation for Modeling Bi-Directional Pedestrian Walkways.” Transportation Research Part B: Methodological 35, no. 3 (March 2001): 293–312. https://doi.org/10.1016/S0191-2615(99)00052-1. Caldeira, Teresa, and Michael Sorkin. “Variations on a Theme Park: The New American City and the End of Public Space.” Journal of Architectural Education (1984-) 48, no. 1 (September 1994): 65. https://doi.org/10.2307/1425310. Deng, Ying, Edwin H.W. Chan, and S.W. Poon. “Challenge-Driven Design for Public Housing: The Case of Hong Kong.” Frontiers of Architectural Research 5, no. 2 (June 2016): 213–224. https://doi.org/10.1016/j.foar.2016.05.001. Di Palma, Vittoria, Diana Periton, and Marina Lathouri, eds. Intimate Metropolis. London: Routledge, 2008. El-Sayegh, S., L. Romdhane, and S. Manjikian. “A Critical Review of 3D Printing in Construction: Benefits, Challenges, and Risks.” Archives of Civil and Mechanical Engineering 20, no. 2 (June 2020): 34-59. https://doi.org/10.1007/s43452-020-00038-w. Erdine, Elif. “Generative Processes in Tower Design: Algorithms for the Integration of Tower Subsystems” PhD, Architectural Association School of Architecture, 2014. Fassio, Omar, Chiara Rollero, and Norma De Piccoli. “Health, Quality of Life and Population Density: A Preliminary Study on ‘Contextualized’ Quality of Life.” Social Indicators Research 110, no. 2 (January 2013): 479–88. https://doi.org/10.1007/s11205-011-9940-4. García Moro, Francisco. “The Death and Life of Hong Kong’s Illegal Façades.” ARENA Journal of Architectural Research 5, no. 1 (July 20, 2020): 2. https://doi.org/10.5334/ajar.231. Guneri, Gizem Deniz. “Peter Cook Beyond Archigram: Towards a Critical Utopianism.” Prostor 28, no. 1 (59) (June 30, 2020): 130–41. https:// doi.org/10.31522/p.28.1(59).8. Harris, Jose. “War and Social History: Britain and the Home Front during the Second World War.” Contemporary European History 1, no. 1 (March 1992): 17–35. https://doi.org/10.1017/S096077730000504X. Hein, Carola, Jeffery Diefendorf, and Ishida Yorifusa. Rebuilding Urban Japan After 1945. 1st ed. 2003. New York, NY: Palgrave Macmillan, 2014. Ho, Daniel Chi Wing, Kwong Wing Chau, and Yung Yau. “Evaluating Unauthorized Appendages in Private Apartment Buildings.” Building Research & Information 36, no. 6 (December 2008): 568–79. https://doi.org/10.1080/09613210802386198. Hong Kong Housing Authority, “Key Figures,” Hong Kong Housing Authority, Hong Kong Housing Authority, 31 March 2022, https://www. housingauthority.gov.hk/mini-site/haar2122/en/index.html Kelly, G., Robert Schmidt, A. Dainty, and Victoria Story. “Improving the Design of Adaptable Buildings Though Effective Feedback in Use,” 2011. https://hdl.handle.net/2134/26294. Khavarian-Garmsir, Amir Reza, Ayyoob Sharifi, Mohammad Hajian Hossein Abadi, and Zahra Moradi. “From Garden City to 15-Minute City: A Historical Perspective and Critical Assessment.” Land 12, no. 2 (February 20, 2023): 512. https://doi.org/10.3390/land12020512. Kiyonori et al. Metabolism – A Proposal for a New Urbanism. Tokyo: Bijutsu Shūpansha, 1960. Kurokawa, Kishō. Metabolism in Architecture. London: Studio Vista, 1977. Kohn, Margaret. Brave New Neighborhoods: The Privatization of Public Space. New York, NY: Routledge, 2004. Lai, Lawrence W.C., and Daniel C.W. Ho. “Unauthorised Structures in a High‐rise High‐density Environment ‐ The Case of Hong Kong.” Property Management 19, no. 2 (May 1, 2001): 112–23. https://doi.org/10.1108/02637470110387830. Langstraat, Florian, and Rianne Van Melik. “Challenging the ‘End of Public Space’: A Comparative Analysis of Publicness in British and Dutch Urban Spaces.” Journal of Urban Design 18, no. 3 (August 2013): 429–48. https://doi.org/10.1080/13574809.2013.800451. Lau, Kwok-yu. Housing In the Other Hong Kong Report. Hong Kong: Chinese University Press, 1991. Ma, GuoWei, Li Wang, and Yang Ju. “State-of-the-Art of 3D Printing Technology of Cementitious Material—An Emerging Technique for Construction.” Science China Technological Sciences 61, no. 4 (April 2018): 475–95. https://doi.org/10.1007/s11431-016-9077-7. Mark B. Lapping, “Toward A Social Theory of the Built Environment: Frank Lloyd Wright and Broadacre City.” Environmental Review 3, no. 3 (March 1, 1979): 11–23. https://doi.org/10.2307/3984040. Marsillo, Laura, Nawapan Suntorachai, Keshava Narayan Karthikeyan, Nataliya Voinova, Lea Khairallah, and Angelos Chronis. “Context Decoder - Measuring Urban Quality through Artificial Intelligence,” 237–46. Ghent, Belgium, 2022. https://doi.org/10.52842/conf. ecaade.2022.2.237. Mehta, Vikas. “Evaluating Public Space.” Journal of Urban Design 19, no. 1 (January 1, 2014): 53–88. https://doi.org/10.1080/13574809 .2013.854698. Ming Sing, “The Quality of Life in Hong Kong.” Social Indicators Research 92, no. 2 (June 2009): 295–335. https://doi.org/10.1007/s11205008-9349-x.

Domain Chapter

Nelson, Arthur C. “The Planning of Exurban America: Lessons from Frank Lloyd Wright’s Broadacre City.” Journal of Architectural and Planning Research 12, no. 4 (1995): 337–56. http://www.jstor.org/stable/43029176. Németh, Jeremy, and Stephen Schmidt. “The Privatization of Public Space: Modeling and Measuring Publicness.” Environment and Planning B: Planning and Design 38, no. 1 (2011): 5–23. https://doi.org/10.1068/b36057. Németh, Jeremy, and Stephan Schmidt. “Toward a Methodology for Measuring the Security of Publicly Accessible Spaces.” Journal of the American Planning Association 73, no. 3 (September 30, 2007): 283–97. https://doi.org/10.1080/01944360708977978. Ping Yan, Fung. “Public Housing in Hong Kong Past, Present and Future.” Chartered Institute of Housing Asian Pacific Branch, 2006. Pozoukidou, Georgia, and Zoi Chatziyiannaki. “15-Minute City: Decomposing the New Urban Planning Eutopia.” Sustainability 13, no. 2 (January 18, 2021): 928-953. https://doi.org/10.3390/su13020928. Rasouli, Amir. “Pedestrian Simulation: A Review,” 2021, 1-18. https://doi.org/10.48550/ARXIV.2102.03289. Sadler, Simon. Archigram: Architecture without Architecture. Cambridge, Mass: MIT Press, 2005. Sarkisian, Mark. Designing Tall Buildings: Structure as Architecture. New York, NY: Routledge, 2012. Seng, Eunice. “The City in a Building: A Brief Social History of Urban Hong Kong.” SITA 2017, no. 5 (2017). https://doi.org/10.54508/ sITA.5.07. Shelton, Barrie, Justyna Karakiewicz, and Thomas Kvan. The Making of Hong Kong: From Vertical to Volumetric. London: Routledge, 2011. Smart, Alan. The Shek Kip Mei Myth: Squatters, Fires and Colonial Rule in Hong Kong, 1950 - 1963. Aberdeen, Hong Kong: Hong Kong Univ. Press, 2006. Schmidt III, Robert, and Simon Austin. Adaptable Architecture: Theory and Practice. Routledge, 2016. Smith, Constance, and Saffron Woodcraft. “Tower Block ‘Failures’?: High-Rise Anthropology.” Focaal 2020, no. 86 (2020): 1–10. https://doi. org/10.3167/fcl.2020.860101. Tang, Bo-sin, and Siu-wai Wong. “A Longitudinal Study of Open Space Zoning and Development in Hong Kong.” Landscape and Urban Planning 87, no. 4 (September 2008): 258–68. https://doi.org/10.1016/j.landurbplan.2008.06.009. Urban, Florian. Tower and Slab: Histories of Global Mass Housing. London: Routledge, 2012. Van Melik, Rianne, Irina Van Aalst, and Jan Van Weesep. “Fear and Fantasy in the Public Domain: The Development of Secured and Themed Urban Space.” Journal of Urban Design 12, no. 1 (February 2007): 25–42. https://doi.org/10.1080/13574800601071170. Varna, George, and Steve Tiesdell. “Assessing the Publicness of Public Space:The Star Model of Publicness.” Journal of Urban Design 15, no. 4 (November 2010): 575–98. https://doi.org/10.1080/13574809.2010.502350. Weintraub, Jeff Alan, and Krishan Kumar, eds. Public and Private in Thought and Practice: Perspectives on a Grand Dichotomy. Morality and Society. Chicago: University of Chicago Press, 1997. The Whoqol Group. “The World Health Organization Quality of Life Assessment (WHOQOL): Development and General Psychometric Properties.” Social Science & Medicine 46, no. 12 (June 1998): 1569–85. https://doi.org/10.1016/S0277-9536(98)00009-4. Xue, Charlie Q. L., and Kevin K. K. Manuel. “The Quest for Better Public Space: A Critical Review of Urban Hong Kong.” In Public Places in Asia Pacific Cities, edited by Pu Miao, 60:171–90. The GeoJournal Library. Dordrecht: Springer Netherlands, 2001. https://doi. org/10.1007/978-94-017-2815-7_9. Zamanifard, Hadi, Tooran Alizadeh, Caryl Bosman, and Eddo Coiacetto. “Measuring Experiential Qualities of Urban Public Spaces: Users’ Perspective.” Journal of Urban Design 24, no. 3 (May 4, 2019): 340–64. https://doi.org/10.1080/13574809.2018.1484664. Zhonghua Gou, Xiaohuan Xie, Yi Lu, and Maryam Khoshbakht. “Quality of Life (QoL) Survey in Hong Kong: Understanding the Importance of Housing Environment and Needs of Residents from Different Housing Sectors.” International Journal of Environmental Research and Public Health 15, no. 2 (January 27, 2018): 219. https://doi.org/10.3390/ijerph15020219.

Bhagat | Wong

METHODS

03 Methods

3.1 Public-Private Evaluation Method 3.2 Urban Network 3.3 Pedestrian Simulations 3.4 Tower Organization 3.5 Program Relationships 3.6 Fabrication and Material Systems 3.7 Analysis Tools

The workflows and processes developed during this stage deeply investigated innovative methodologies, algorithms, and material fabrication systems which facilitated the creation of a socially temporal design and fabrication workflow in the subsequent research. In order to create such a system, the authors first developed an evaluation method which could quantify and analyze sociability across a spectrum. This created a framework and lens which would guide the domain of the research. Within this domain, the research developed two novel social pedestrian simulations which would leverage such a notion of sociability and implement its corresponding behaviors as a driver of design. Within the framework of the design workflow, the use of co-evolutionary algorithms enabled collaborative systems to temporally evolve together to address unique, yet interconnected social needs. When paired with the small world network algorithm, this system facilitated the required growth, while maintaining a level of robustness which was required for adaptable systems. Physically, this system was realized through a comprehensive material fabrication system, which implemented bamboo weaving and concrete 3D printing. By leveraging the properties and methods associated with these systems, the research developed adaptable, yet easily fabricatable forms, while resurfacing dying cultural material systems. Such novel methods worked within the gaps of the developed domain to investigate the relevance of socially and temporally adaptive architectural systems to address the challenges of densification in Hong Kong.

Bhagat | Wong

3.1 Public-Private Evaluation Method Over time, as the sociability needs of people change, the form and functionality of the built space around them should change as well. In order to create such an adaptation system, it was first necessary to devise a systematic method to quantify a space’s sociability, namely the Sociability Spectrum. The team developed a series of parameters which constitute the sociability of a space along a spectrum, building upon the existing models for measuring publicness.

The team improved upon these models by directly address their shortcomings, ensuring each one was quantifiable, directly related to a space’s sociability, and existed within an architect’s domain. In doing so, the devised sociability evaluation method aimed to measure a space’s sociability such that this data can be utilized to inform the design and adaptation of an architectural artifact as the social needs of its occupants change.

The Parameters and Sociability Calculation Method M.Arch. Phase | M.Sc. Phase The parameters within the evaluation method existed in four dimensions: Ownership, Site Accessibility, Building Affordance, and Environment. Each category aimed to encompass one major portion of the architectural domain. The specific realm and definition of each dimension is as follows: Ownership: What is the legal status and program functionality of the building? Site Accessibility: How to occupants find, view, and enter the site? Building Affordance: How do occupants use, circulate, and occupy the building? Environment: What is the spatial quality of the building’s interior? Within each dimension, a series of parameters were devised which worked to quantify the relevant sociability metrics (Fig. 21). These parameters were chosen based on emerging trends derived from all existing evaluation models studied, such as those relating to transit, use, and accessibility. Additional parameters were also established by the team where gaps in the existing research were found, such as those relating to network centrality and environmental comfort. Each parameter was calculated in a quantifiable manner and incorporated domain boundaries which limited their scope to a relevant range. Some domain boundaries were derived from local code requirements. For example, the minimum domain (most private) for the Spatial Proportions parameter was defined by Hong Kong’s minimum allowable room area and height. Other domains were defined based on information from the existing models for determining sociability. For example, the Connectedness to Amenities parameter was 48

Methodology

created by compiling the major relevant programs mentioned in the existing research and crafting a quantifiable metric for analysis based on the distance and number of these amenity types within walking distance of the architectural artifact. Furthermore, some parameters contained embedded domains, as they were ratios or percentages, such as Thermal Comfort (TCP) and Visual Site Connection. Please see Figure 22 for a diagram visualizing all parameter calculations or the Appendix (A.01) for a comprehensive table describing the calculations for each parameter. The resultant values from all parameters were then remapped between 0 and 1 to normalize their values within an appropriate and comparable domain. Once each individual parameter was calculated and normalized, the values were systemically combined to create one comprehensive value for a space’s sociability. To do this, each value was first summed within each dimension to create a combined score. Then, each combined score was weighted in accordance with its relevance to the sociability needs of the occupants. Finally, all weighted values were summed and remapped between 0 and 1 to achieve a single, inclusive value for a space’s sociability (Fig. 23). The public-private evaluation method was used throughout the research during both the M.Arch. and M.Sc. phases as a tool to drive the design and adaptation of the tower morphology over time. As the sociability needs of the occupants changed, the design needs of the tower spaces changed, and the evaluation system was utilized to determine which changes were required.

PRIVATE

Visual Site Connections

OWNERSHIP

individual

Daylighting

Threshold Conditions

Ownership (Public/Private)

Access Points to the Site

architectural artifact

Density of People

Physical Accessibility Spatial Connectivity

SITE ACCESSIBILITY

Thermal Comfort

Spatial Proportions

quantiﬁable parameters

dimensions of publicness

BUILDING AFFORDANCE

Modes of Transit to the Site

Average Area Per Space Density of Function

Function (Public/Private)

Noise Protection

Centrality to Context Area of Outdoor Space

Use (Public/Private)

PUBLIC

ENVIRONMENT

Connectedness to Amenities

Area of Social Space

collective

Figure 21: Sociability Spectrum

Bhagat | Wong

0.0 to 1.0 = Private to Public

B.02 (430m * 18 Flrs) / (140 ppl * 18 Flrs) = 3.07sqm/pers. = 0.00

B.01 (1 Entrance / 430m Ground Floor) * 100 = 0.23

OCCUPANT DENSITY

THRESHOLD CONDITION

How do people use, circulate and occupy the building?

BUILDING AFFORDANCE

ENTRANCE

B.03 Node Values / Nodes = 0.29 SPATIAL CONNECTIVITY

Analyzed Element Base Condition

APT A 5 PEOPLE APT B 7 PEOPLE

B.04 2.5m Room Height = 0.00

B.05 (430m * 18 Flrs)/ (40 Spaces * 18 Flrs) = 10m / Space = 0.00 AVERAGE AREA PER SPACE

SPATIAL PROPORTIONS

B.06 2 Functions / (40 Spaces * 18 Flrs) * 25 = 0.07 FUNCTION DENSITY

2.5m

LOBBY APARTMENT

B.07 (1 Accessible / 40 Spaces) * 2.5 = 0.06

B.08 50m Social Space / 430m = 0.11

PHYSICAL ACCESSIBILITY

AREA OF SOCIAL SPACE 2

B.09 1100m Site Area / (430m Building Area * 18 Flrs) = 0.14 AREA OF OUTDOOR SPACE

ACCESSIBLE SPACE NON-ACCESSIBLE SPACE

0.0 to 1.0 = Private to Public Analyzed Element

E.01

E.02 THERMAL COMFORT

DAYLIGHTING

OWNERSHIP Public Ownership = 1.0

1.0

Methodology

Average Noise Absorption of Materials = 0.03

0.99

0.56

0.01

0.37

OW.02

OWNERSHIP

What is the legal status and programmatic function of the building?

OW.01

E.03 NOISE CONDITION

Average Yearly PMV = 0.45

Average Yearly PMV = 0.79

ENVIRONMENT

What is the spatial quality of the building’s interior?

Base Condition

FUNCTION Private Function = 0.0

Public Ownership

OW.03

0.0 to 1.0 = Private to Public

USE

Analyzed Element

Private Use = 0.0

Base Condition

0.3

Public Function

Public Ownership Public Function Private Use

Private Function Private Use

Public Use

0.6

Public Ownership

0.0

Private Ownership Private Function Private Use

0.0 to 1.0 = Private to Public Analyzed Element

S.01

73m Visible Boundary / 223m Site Boundary = 0.32

0.5 ACCESS POINTS TO SITE

US DI RA

S.02

Base Condition

VISUAL SITE CONNECTIONS

(1 Access Point / 1100m Site) * 200 = 0.18 2

How do people ﬁnd, enter and view the site?

S.03 S.04

POST OFFICE

20 Bus Stops, No Other Modes = 0.4

HOSPITAL

CONNECTEDNESS TO AMENITIES 1KM Min. Average Distance = 1296m = 0.14 BUS STOPS

S.05

CENTRALITY TO CONTEXT 2KM

RESTURAUNT

SIT EC O

Site Node Centrality Value = 0.54

PARK

T EX NT

SITE ACCESSIBILITY

SCHOOL

MODES OF TRANSIT TO SITE 1KM

SUPERMARKET

S.01 VISUAL ACCESS BANK

S.02 SITE ACCESS

LIBRARY

SCHOOL

100m

100

250m

0.0 to 1.0 = Priv

Analyzed Eleme

L SITE CONNECTIONS

ble Boundary / 223m Site Boundary = 0.32

Base Conditi

SS POINTS TO SITE

s Point / 1100m2 Site) * 200 = 0.18

2K M

US DI RA

S OF TRANSIT TO SITE 1KM

Stops, No Other Modes = 0.4

ECTEDNESS TO AMENITIES 1KM

rage Distance = 1296m = 0.14

RALITY TO CONTEXT 2KM

e Centrality Value = 0.54

S.05 SITE CENTRALITY VALUE: 0.54

100

200

500m

Figure 22: Sociability Parameter Calculation Method

Bhagat | Wong

DIMENSIONS

SITE ACCESSIBILITY How do people ﬁnd, enter, and view the site?

BUILDING AFFORDANCE How do people use, circulate, and occupy the building?

ENVIRONMENT What is the spatial quality of the building’s interior?

OWNERSHIP What is the legal status and programmatic function of the building?

Figure 23: Sociability Spectrum Score Calculation Method

Methodology

QUANTIFIED PARAMETERS

PARAMETER CAL

S.01 VISUAL SITE CONNECTIONS

0.32

S.02 ACCESS POINTS TO SITE

0.18

S.03 MODES OF TRANSIT TO SITE

0.40

S.04 CONNECTEDNESS TO AMENITIES

0.14

S.05 CENTRALITY TO CONTEXT

0.54

B.01 THRESHOLD CONDITION

0.23

B.02 OCCUPANT DENSITY

0.00

B.03 SPATIAL CONNECTIVITY

0.29

B.04 SPATIAL PROPORTIONS

0.00

B.05 AVERAGE AREA PER SPACE

0.00

B.06 FUNCTION DENSITY

0.07

B.07 PHYSICAL ACCESSIBILITY

0.06

B.08 AREA OF SOCIAL SPACE

0.11

B.09 AREA OF OUTDOOR SPACE

0.14

E.01 DAYLIGHTING

0.79

E.02 THERMAL COMFORT

0.45

E.03 NOISE CONDITION

0.03

B.01 OWNERSHIP

1.0

B.02 FUNCTION

0.0

B.03 PROGRAMMATIC USE

0.0

LCULATION

SUM = 1.58

WEIGHTING

FINAL RESULT

x 1.0 = 1.58

0.0 - 1.0 Private - Public SUM = 0.90

x 1.25 = 1.12 4.24

SUM = 1.27

x 1.0 = 1.29

SUM = 1.0

x 0.25 = 0.25

0.21

Bhagat | Wong

Systems

3.2 Urban NetworkT 1

12 Network 3.2.1 Temporal Graph

M.Arch. Phase Static graphs are effective methods for abstractly representing T11the relationships between distinct but connected elements, represented by nodes and edges respectively. By reducing these relationships to a series of nodes and edges, a static graph allows one to more easily understand the behavior of complex, real-world networks and predict their behaviors. They are typically utilized to represent social connections, transportation networks, and T10 systems, but a static graph disregards the biological dimension of time, which minimizes their real-world application.

may be understood as a collection of static graphs over the same nodes. By considering T3 a real-world system as a temporal graph, notions of centrality and shortest-path as well as other graph properties shift to also consider the added dimension of time. This enables what may have been a poor performing static graph to be a strong performing temporal graph across time.

Therefore, by considering a collection ofTP2 4 Towers as a temporal graph, where the nodes represented the P2 tower at varying stages of time and the edges represented multimodal corridors connecting them, the research could conceptually connect the existing networks of each P2 Tower to one another at the urban scale as well as understand the relationship of the entire urban network acrossTthree timescales, 5 days, months, and years. Such an approach allowed the P2 Tower and its urban network to adapt to the shifting sociability of its residents and perform to the same standard over time.

On the other hand, a temporal graph provides a more accurate and detailed representation of complex, real-world networks by considering the added dimension of time. A temporal graph T9 represents the relationships between distinct elements as they shift over time, allowing one to better understand the underlying processes of their topological properties.1 Thus, a temporal graph

T7 0

T1 T2

...

T3 Tn

Figure 24: Temporal Graph Network Timeline

Shubham Gupta and Srikanta Bedathur, A Survey on Temporal Graph Representation Learning and Generative Modeling, 2022.

Methodology

Programmatic Topology

Constructed, Active Tower

Public Space

Constructed, Inactive Tower Unconstructed Tower Constructed, Active Path

P2 Tower

Tower Morphology

Constructed, Inactive Path Unconstructed Path

Private Spaces

Structural Systems

T1 T12

T11

T10

T5 T8

T6 T7

0 T1 T2

Figure 25: Temporal Graph Network

Bhagat | Wong

Weighted Shortest Path M.Arch. Phase Dijkstra’s Algorithm identifies the shortest path of edges between a set of nodes in a graph, where the edges connecting nodes maintain a weighting which corresponds to a relational distance but not necessarily a metric one. The shortest path is an efficient methodology for translating the properties and performance of a graph onto a real-world network, such as roadways or social connections, particularly if the weightings correspond to realworld parameters such as elevation, daylighting, or distance. Additionally, bias can be introduced into the weightings to prioritize particular site-specific parameters depending on the design goals. At the micro-urban scale, the weighted shortest path was utilized in the pedestrian simulation to select the travel path for each pedestrian based upon their desired programmatic destinations, where the weightings corresponded to the metric

Dijkstra’s Algorithm 1) Identify the start and end node of the path while maintaining a table of each node with is corresponding distance to the start node. On initialization, set each distance is set to infinity. Additionally, maintain an array of visited nodes and unvisited nodes to keep track of the algorithm’s progress. 2) On the first iteration, identify all the connected edges to the start node and add their edge distances to their corresponding entries in the table. Then, shift the start node from the unvisited node array to the visited node array. 3) On the next iteration, select the unvisited node with the smallest distance in the table as the current node. Then, identify all of the connected edges to the current node and add their distances to their corresponding entries in the table. Lastly, shift the current node to the visited node array. 4) Continue looping Step 3 until the current node equals the end node. 5) After exiting the loop, identify the shortest path by progressing backwards from the end node using the nodes of smallest distance in the table.

Methodology

distances between the programmatic nodes. The use of the shortest path algorithm ensured that the pedestrians’ movements followed a logical route, which in turn, allowed the simulation to more effectively evaluate the underlying principles of the network’s performance. At the urban scale, the weighted shortest path translated the temporal graph of the connected P2 Towers to the site-specific conditions of Hong Kong by identifying the locations of the multimodal corridors. By setting the edge weightings of the temporal graph to site-specific parameters, the shortest path algorithm ensured that the performance of the temporal graph was maintained as it translated to the complex urban environment of Hong Kong.

Current Node Edge

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Figure 26: Dijkstra’s Algorithm Pseudocode

Bhagat | Wong

3.3 Pedestrian Simulations The team understood the existing pitfalls in existing pedestrian simulations, namely the lack of social interaction and lack of large scale urbanbased simulations. As such, it was necessary to develop a new pedestrian simulation which enabled social interaction behaviors and accepted largescale, three-dimensional networks. Through this research, the team developed two similar types of social pedestrian simulations. Both employed the same social interaction behaviors but were tailored to work well for two unique functionalities CONSTRUCTORS

INPUTS

and scales. The first was a network-based social pedestrian simulation which utilized network lines and shortest path algorithms to enable pedestrian behaviors. This will be used to analyze full urban networks on a large scale. The second was a sociospatial pedestrian simulation which utilized a threedimensional mesh surface and spatial movements to enable pedestrian behaviors. This will be used to analyze spatial sections of networks at a smaller scale in relation to program and surrounding context.

INITIALIZATION

ALGORITHM

wait time adjustment person type

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destination list

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starting point

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count for each type

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travel along designated path

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heat map of network utilization destination type access type

DESTINATION PROFILE

location typical wait time

stop at target destinations

map of individual pedestrian travels

ALGORITHM

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capacity

Figure 27: Network-Based Pedestrian Simulation

CONSTRUCTORS

INPUTS

INITIALIZATION

person type

PEDESTRIAN PROFILE

social interaction level count for each type

MESH SURFACE PROFILE

pedestrian start locations

interact with other pedestrians

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refinment level

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building locations

ENVIRONMENT PROFILE

tranverse mesh towards similar face weightings

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program type

heat map of mesh utilization

program social level

PROGRAM PROFILE

sphere of influence

program placement

program area program count

Figure 28: Socio-Spatial Pedestrian Simulation

Methodology

stop at programs

map of individual pedestrian travels

3.3.1 Network-Based Social Pedestrian Simulation M.Arch. Phase The network-based social pedestrian simulation is designed for large-scale network analyses. It requires inputs of the context, destinations, and pedestrians. The simulation operates by generating pedestrians and calculating shortest walk paths to their desired destinations based on input parameters. Once all information is compiled, the algorithm will run with three major behaviors. Pedestrians can move towards their destinations along their shortest walk paths, stop at destinations for designated amounts of time, and stop to socialize with others. The socialization behavior can take place if both pedestrians are within a user-specified distance from each other and if their social levels are within

3.3.2 Socio-Spatial Pedestrian Simulation M.Arch. Phase The socio-spatial pedestrian simulation employs similar behaviors to the network-based social pedestrian simulation, but operates on a much smaller scale, studying a spatial portion of a network. This simulation requires inputs of a mesh surface for the pedestrians to walk on, which can be two dimensional or three dimensional, as well as inputs of context, pedestrians, and programs. Each mesh face is then given a sociability weighting based on the social scores of the surrounding buildings and nearby programs. To begin the simulation, pedestrians are spawned randomly on the mesh and move from mesh face to mesh face based on a combined weighting of three considerations: towards a neighboring mesh face which has the most similar sociability score, towards

a particular range of one another. The chance of socialization is scaled based on how similar their social levels are. Global social perception and global randomness factors are also introduced to the algorithm to further mediate social interactions in a way which may more closely represent how individuals interact. Once the simulation is finished, the network can be analyzed in terms of pedestrian movements and socialization behaviors. Further detail on the functionalities of this simulation will be discussed in Chapter 05. This developed pedestrian simulation enables similar functionalities to existing pedestrian simulations, but provides the opportunity for large-scale network based simulations that understand and analyze how people might socialize within a network. It will be used to analyze and select pedestrian networks which are generated during the thesis.

a nearby pedestrian with a similar sociability score, and towards a randomly selected neighboring mesh face. Socialization can occur when two pedestrians are nearby one another in a similar manner to the network-based pedestrian simulation. Once the simulation is finished, the mesh surface can be analyzed by producing a heat map of pedestrian movements, both collective and individual, and by calculating the time each pedestrian spends socializing or moving. Further detail on the functionalities of this simulation will be discussed in Chapter 05. This developed pedestrian simulation provides similar abilities to other spatial pedestrian simulations, but enables a unique social interaction behavior which guides pedestrian movements. This simulation will be used during the thesis to analyze program locations and usage on local portions of the designed network and can generate zones for new program spaces in the future based on how pedestrians might use the analyzed space.

Bhagat | Wong

3.4 Tower Organization 3.4.1 The Principles of Bamboo Stems as a Structural System M.Sc. Phase | M.Arch. Phase

The bamboo stem’s internal organization has evolved over time to create a highly efficient structural system for resisting bending, buckling, and uplifts. In particular, the spacing of nodes and internodes are mathematically arranged and proportioned in accordance with their location along the entire stem, where the base employs a denser spacing and thicker node to resist high lateral loads and the upper portions sequentially decrease in size as the loads decrease vertically to minimize weight and material. These principles of node distribution can be abstracted through mathematical equations to an architectural domain and serve as the basis for a stable and materially efficient structural system of a tall tower. Empirical research by Mulyana et al. translated the node spacing of various bamboo species into a third-order mathematical expression.3 Through these equations, an initial guide for a tower design was achieved, where nodes translated to major horizontal structure such as floor systems, culm walls became major vertical structure, and internodes became large, segmented spatial zones.

In addition to its structural capabilities, the organization strategy of this biological system affords a tall tower the ability to adapt and reconfigure, because all of the major structure lies on the perimeter of the form, providing free interior spans. Additionally, the optimized material usage and geometry in bamboo stems minimizes the area and locations of fixed structural elements in the proposed system, while maintaining maximum structural capacity. Such an organization strategy provides the freedom and flexibility to employ an adaptable architectural system. These principles were used during the M.Sc. phase to develop the tower’s structural system. During the M.Arch. phase, the team extended the use of bamboo stem principles to include the stem’s continuous fibre wall. The continuous fibre wall provides structural stiffness due to the orientation of its fibres parallel to load paths and its doublelayered skin whose layers are transversely oriented to one another. Combining both the principles of internode spacing and continuous fibre walls more holistically integrates bamboo stem principles into tall tower design. As such, the structural system was revised during the M.Arch. phase to facilitate both mechanisms.

1.0

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0.8

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-2.043x³ + 2.115x² + 0.852x + 0.001

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Mulyana et al. Bamboo Node Equation

-1.566x³ + 1.8261x² + 0.7468x - 0.033

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Figure 29: Mathematical Expression of Bamboo Nodes

Figure 30: Bamboo’s Continuous Fibre Wall Principles

Mulyana, B., and R. Reorita. “Mathematical Expression of Internode Characteristics of Yellow Ampel Bamboo (‘Bambusa Vulgaris’ Var. Striata).” Series II: Forestry Wood Industry Agricultural Food Engineering, June 28, 2022, 43–56. https://doi.org/10.31926/but.fwiafe.2022.15.64.1.4. 3

Methodology

3.4.2 Co-Evolutionary Algorithms for Private-Public Distribution M.Sc. Phase | M.Arch. Phase Charles Darwin’s Theory of Evolution introduced the notion that through natural selection, populations in nature will adapt over time in response to specific environmental conditions. Such a notion inspired the development of evolutionary algorithms (EA), which computationally mimic this process by ‘evolving’ a population over time based upon a series of fitness criteria. Architecturally, an EA provides an efficient methodology for reconciling the complexity of numerous design factors. Yet, these algorithms break down under particular environmental conditions. Firstly, EAs find difficulty in cases of extremely large search spaces. Additionally, the absence of inherent, objective procedures for quantifying an individual’s fitness greatly limits the outcomes of EAs. Lastly, EAs

struggle to optimize when the complexity of the search space exceeds a limit of rationality. In such cases, co-evolutionary algorithms (CoEA) offer a potential solution to these limitations by decomposing a complex and high-dimensional problem into simpler parts. In nature, co-evolution refers to the evolution of “two major groups of organisms with a close and evident ecological relationship.” Translating such a notion into a computational framework, a CoEA evolves two or more interconnected populations in tandem such that the evolutionary growth of one population influences the other to adapt, and vice-versa. A CoEA differs from a typical EA in that the fitness of any individual is subjective. The algorithm is less concerned with any one individual but instead, the interactions of an individual with an individual of the other population. These interactions can be cooperative or competitive. Such a system uniquely situates these individuals within a specific environment of quantified relationships.

body plan gene

gene gene

gene

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gene B

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evaluation

design objectives

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selection

pareto front memebers

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Figure 31: Evolutionary Algorithm Workflow

design objectives

ﬁtness criteria

constraints

body plan gene gene gene

gene gene

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gene

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Figure 32: Co-Evolutionary Algorithm Workflow

Bhagat | Wong

3.5 Program Relationships

Figure 33: Small-World Network

3.5.1 Small-world Network as a Spatial Relationship System M.Sc. Phase In the real world, social networks and brain neuron networks efficiently accomplish the transfer of information, exhibiting the qualities of small-world networks (SWN). A SWN exhibits properties of high clustering and low path length between nodes. These properties make node-to-node connections more efficient in the system, seeing as the short average path length allows for fast information dissemination between nodes and the high clustering ensures that points are quickly connected in their localized zones. These principles can be abstracted into an architectural domain as spatial relationships throughout the horizontal and vertical planes of an architectural system. SWN can simulate the connections between spaces, where the nodes behave as abstracted locations of different spaces or functions and the network connections act as the relationships between these programs. Thus, the node relationships and connection logics of a SWN offer a highly efficient methodology for

interweaving public and private spaces throughout a tall building, strengthening their interaction and cooperation. Additionally, such a system is highly adaptable, enabling the tower to easily shift these programmatic relationships as the sociability of the people change seeing as it is a robust network with safeguards for random failures of nodes and connections. Even if some nodes or connections fail or disappear, the network still remains connected, and paths will persist to other nodes in the network, providing a flexible system for an adaptable architecture.

Figure 34: Small-World Network Equations

Qawi K. Telesford et al., ‘The Ubiquity of Small-World Networks’, Brain Connectivity 1, no. 5 (2011): 367–75, https://doi.org/10.1089/ brain.2011.0038. 5 Duncan J. Watts and Steven H. Strogatz, ‘Collective Dynamics of “Small-World” Networks’, Nature 393, no. 6684 (June 1998): 440–42, https://doi.org/10.1038/30918. 6 Duncan S. Callaway et al., ‘Network Robustness and Fragility: Percolation on Random Graphs’, Physical Review Letters 85, no. 25 (18 December 2000): 5468–71, https://doi.org/10.1103/PhysRevLett.85.5468. 4

Methodology

SEGMENT 05 vertical connection SEGMENT 04 vertical connection SEGMENT 03 vertical connection SEGMENT 02 vertical connection SEGMENT 01

TOPOLOGICAL RELATIONSHIPS

ARCHITECTURAL TRANSLATION

Figure 35: Small-World Network in Architecture

Bhagat | Wong

3.6 Fabrication and Material System

Rice Husk

+ Robotic 3D Printing

Recycle Aggregate

Concrete Material Natural Fiber Reinforcements

Figure 36: Fabrication System

3.6.1 Additive Manufacturing: Robotic 3D Printing M.Sc. Phase Additive manufacturing is a process where material is deposited layer by layer to create a given object or form.7 Robotic 3D printing is situated within this broad category, defining a more specific manufacturing process which utilizes a 6-axis robotic arm to maneuver space and integrates an end effector tool to deposit material in layers.8 Such a process allows for the creation of bespoke morphologies, which are often difficult to hand craft, and minimizes material wastage. The robotic

arm itself also affords the ability to move through space in all six axes and print with a wide variety of materials systems, providing a higher degree of customizability and range of form capabilities.9 These advantages proved highly pertinent for an adaptable building system. Robotic 3D printing can seamlessly manufacture the bespoke geometries from the research without the need for hundreds of unique formworks or jigs, significantly reducing the time, material, and manpower for fabrication. Therefore, the research explored the possibilities of robotic 3D printing within its range of limitations during the M.Sc. phase to maximize its potential in the context of an adaptable architecture.

Rebecca Linke, “Additive Manufacturing, Explained | MIT Sloan,” MIT Sloan, December 7, 2017, https://mitsloan.mit.edu/ideas-made-tomatter/additive-manufacturing-explained. 8 “Automation and Additive Manufacturing,” KUKA AG, accessed June 29, 2023, https://www.kuka.com/en-gb/products/processtechnologies/3d-printing. 9 Linke, “Additive Manufacturing, Explained | MIT Sloan.” 7

Methodology

3.6.2 Material Systems: Fiber-Reinforced Cementitious Composites M.Sc. Phase Concrete is one of the few materials that can be used to 3D print structurally stable architectural components at a large scale, due to its high flow state and consistency when printing and its high structural capacity when fully hardened. However, concrete is also a highly unsustainable material. Thus, there has been a recent shift towards creating new mixtures of concrete with less embodied carbon. CO2 Sources

Fiber-reinforced cementitious composites are one potential solution, where a portion of cement is replaced by another low carbon material such as fly ash. These composites not only reduce the embodied carbon of the material system but are also shown to improve upon the ductility of standard concrete mixtures due to the integration of fiber elements.10 Additionally, these materials are obtainable from local contexts, further decreasing the carbon related to transportation. Thus, this research explored the use of these composites as the material system for the adaptable components during the M.Sc. phase. Specifically, the thesis utilized a cementitious composite of rice husk and recycled aggregate, which are local to Hong Kong.

Emissions

Pollution Transportation Energy Auxillary Materials

Electricity Raw Materials Auxilary Materials

Electricity

Admixture

Water

Auxilary Materials Water Waste

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Emissions Waste Waste

Auxilary Materials

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Figure 37: Concrete Life cycle

CO2 Sources

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Electricity Raw Materials Auxilary Materials

Electricity

Admixture

Water

Auxilary Materials Water Waste

Electricity

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Waste Emissions

Figure 38: Fiber-Reinforced Cementitious Composites Life cycle H. Tian and Y. X. Zhang, “Tensile Behaviour of a Sustainable Fibre Reinforced Cementitious Composite under Different Strain Rates,” in Recent Advances in Structural Integrity Analysis - Proceedings of the International Congress (APCF/SIF-2014), ed. Lin Ye (Oxford: Woodhead Publishing, 2014), 316–20, https://doi.org/10.1533/9780081002254.316. 10

Bhagat | Wong

3.6.3 Material Systems: Bamboo Strip Weaving as Rebar Reinforcement and Formwork M.Sc. Phase Rebar reinforcement and formwork can be integrated into concrete 3D printing to extend the range of structural capabilities and morphologies that are possible to fabricate, but rebar itself also has a high embodied carbon. Bamboo strip weaving offers a low-carbon alternative to rebar that can act as integrated formwork and reinforcement. Bamboo strip weaving is a traditional Chinese artform which

utilizes thin strips of bamboo to achieve self-standing morphologies without the need for additional joinery or attachment systems. Particularly, the Kagome weave is a triaxial pattern which can produce highly complex three-dimensional surfaces due to its self-bracing capacity and high shear resistance.11 Additionally, it enables a high degree of geometrical control, high redundancy, and local reparability, allowing designers to generate and fabricate a wider range of morphologies using this technique.12 Thus, combining woven bamboo with concrete 3D printing both reaches the necessary structural performance of large scale forms and increases the range of achievable morphologies.

Figure 39: Bamboo Growth Regions

12m 8m 5m

1 year

2 years

3 years

4 years

5 years

Figure 40: Bamboo Growth Rate

Phil Ayres, Alison Grace Martin, and Mateusz Zwierzycki, “Beyond the Basket Case: A Principled Approach to the Modelling of Kagome Weave Patterns for the Fabrication of Interlaced Lattice Structures Using Straight Strips.,” n.d., 75. 12 Ayres, Martin, and Zwierzycki, “Beyond the Basket Case: A Principled Approach to the Modelling of Kagome Weave Patterns for the Fabrication of Interlaced Lattice Structures Using Straight Strips.”, 75. 11

Methodology

Figure 41: Bamboo Weaving

3.7 Analysis Tools 3.7.1 Finite Element Analysis (FEA) M.Sc. Phase | M. Arch Phase Finite Element Analysis (FEA) is used to evaluate the structural performance of a digital model by subdividing the input geometry into simplified, discrete elements and applying loads to these simplified elements through the use of a physics engine and mathematical calculations in order to approximate the structural performance of the design.13 FEA specifically provides numerical data and digital visualizations on a model’s deformation, mechanical stresses, and utilization, among others.14 Karamba3D was used as the FEA software to evaluate and compare the structural performance of design candidates. Its ability to seamlessly integrate with Grasshopper enabled the design process to maintain a continuous feedback loop with other Grasshopper-based analysis software as different design options were evaluated, enabling a holistically informed design decision.

3.7.2 Computational Fluid Dynamics (CFD) M.Sc. Phase | M. Arch Phase Computational Fluid Dynamics (CFD) is the numerical modeling of fluid behavior, typically wind or water, around and within an object through mathematical equations and analytical techniques.15 To conduct this analysis, fluid particles are generated at one end of the determined field and are then continuously recalculated and tracked over a given number of iterations throughout the simulation process. Computational Fluid Dynamics enables designers to properly understand fluid patterns and movements as critical data during the design process.

The research utilized Ladybug Tool’s CFD plugin for Grasshopper, Dragonfly, to predict wind pressure loads on the building, which was critically important due to the context of Hong Kong and the variable and high wind loads present on tall building for the design of the structural system. Additionally, since the tower morphology adapted over time, it was important to continuously reevaluate the tower’s reaction to wind flows and forces at each iteration.

3.7.3 Artificial Neural Network (ANN) M.Sc. Phase | M. Arch Phase An artificial neural network (ANN) is a machine learning model whose principles are extracted from biological neurons in the brain. It consists of three main layers of neurons: the input layer, multiple hidden layers, and the output layer.16 Information is passed forward through each layer, where each neuron is connected to one another by an associate weight and threshold value. By continuously activating and deactivating different combinations of neurons, the model is trained to predict output values more accurately. The research trained an ANN using the plugin LunchboxML for Grasshopper to predict the wind pressure on a building for any tower morphology, site context, and wind conditions. The use of an ANN afforded the workflow a high degree of flexibility and applicability for new and changing scenarios.

“Introduction to Finite Element Analysis,” Introduction to finite element analysis, accessed June 29, 2023, https://www.open.edu/openlearn/ science-maths-technology/introduction-finite-element-analysis/science-maths-technology/introduction-finite-element-analysis. 14 “Finite Element Analysis Software | Autodesk,” accessed June 29, 2023, https://www.autodesk.co.uk/solutions/finite-element-analysis. 15 H. Lomax, Thomas H. Pulliam, and David W. Zingg, “Introduction,” in Fundamentals of Computational Fluid Dynamics, ed. H. Lomax, Thomas H. Pulliam, and David W. Zingg, Scientific Computation (Berlin, Heidelberg: Springer, 2001), 1–5, https://doi.org/10.1007/978-3662-04654-8_1. 16 MIT News | Massachusetts Institute of Technology. “Explained: Neural Networks,” April 14, 2017. https://news.mit.edu/2017/explainedneural-networks-deep-learning-0414. 13

Methodology

input layer

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Figure 42: Artificial Neural Network (ANN)

Bhagat | Wong

Bibliography Ayres, Phil, Alison Grace Martin, and Mateusz Zwierzycki. “Beyond the Basket Case: A Principled Approach to the Modelling of Kagome Weave Patterns for the Fabrication of Interlaced Lattice Structures Using Straight Strips.,” n.d. Ehrich, Paul and Peter Raven. “Butterflies and Plants: A Study in Coevolution.” Evolution 18, no. 4 (1964): 586-608. https://doi. org/10.2307/2406212 “Finite Element Analysis Software | Autodesk.” Accessed June 29, 2023. https://www.autodesk.co.uk/solutions/finite-element-analysis. Heschong, Lisa, and Kevin Van Den Wymelenberg. “IES Spatial Daylight Autonomy (SDA) and Annual Sunlight Exposure (ASE).” Illuminating Engineers Society, 2022. Introduction to finite element analysis. “Introduction to Finite Element Analysis.” Accessed June 29, 2023. https://www.open.edu/openlearn/ science-maths-technology/introduction-finite-element-analysis/science-maths-technology/introduction-finite-element-analysis. Janssen, Jules J. A. Mechanical Properties of Bamboo. Vol. 37. Forestry Sciences. Dordrecht: Springer Netherlands, 1991. https://doi. org/10.1007/978-94-011-3236-7. KUKA AG. “Automation and Additive Manufacturing.” Accessed June 29, 2023. https://www.kuka.com/en-gb/products/processtechnologies/3d-printing. Linke, Rebecca. “Additive Manufacturing, Explained | MIT Sloan.” MIT Sloan, December 7, 2017. https://mitsloan.mit.edu/ideas-made-tomatter/additive-manufacturing-explained. Lomax, H., Thomas H. Pulliam, and David W. Zingg. “Introduction.” In Fundamentals of Computational Fluid Dynamics, edited by H. Lomax, Thomas H. Pulliam, and David W. Zingg, 1–5. Scientific Computation. Berlin, Heidelberg: Springer, 2001. https://doi.org/10.1007/9783-662-04654-8_1. MIT News | Massachusetts Institute of Technology. “Explained: Neural Networks,” April 14, 2017. https://news.mit.edu/2017/explainedneural-networks-deep-learning-0414. Oldroyd, David R. “Charles Darwin’s Theory of Evolution: A Review of Our Present Understanding.” Biology and Philosophy 1, no. 2 (June 1, 1986): 133–68. https://doi.org/10.1007/BF00142899. Potter, Mitchell A., and Kenneth A. De Jong. “Cooperative Coevolution: An Architecture for Evolving Coadapted Subcomponents.” Evolutionary Computation 8, no. 1 (March 2000): 1–29. https://doi.org/10.1162/106365600568086. Sarkisian, Mark, P Lee, E Long, and David Shook. “Organic and Natural Forms in Building Design,” 2010. https://www.researchgate.net/ publication/328782547_Organic_and_Natural_Forms_in_Building_Design. Showkatbakhsh, Milad, and Mohammed Makki. “Multi-Objective Optimisation of Urban Form: A Framework for Selecting the Optimal Solution.” Buildings 12, no. 9 (September 17, 2022): 1473. https://doi.org/10.3390/buildings12091473. Tian, H., and Y. X. Zhang. “Tensile Behaviour of a Sustainable Fibre Reinforced Cementitious Composite under Different Strain Rates.” In Recent Advances in Structural Integrity Analysis - Proceedings of the International Congress (APCF/SIF-2014), edited by Lin Ye, 316–20. Oxford: Woodhead Publishing, 2014. https://doi.org/10.1533/9780081002254.316. Vellei, Marika, Richard de Dear, Christian Inard, and Ollie Jay. “Dynamic Thermal Perception: A Review and Agenda for Future Experimental Research.” Building and Environment 205 (November 1, 2021): 108269. https://doi.org/10.1016/j.buildenv.2021.108269.

Methodology

Bhagat | Wong

M.SC. RECAP

04 M.Sc. Recap

4.1 Tower Morphology 4.2 Structural System 4.3 Public-Private Distribution 4.4 Programmatic Topology and Organization 4.5 Material and Fabrication System

The M.Sc. phase of the thesis developed a framework which deconstructed the tower into its component parts, developing them as individual parts of a whole. Each element considered a particular scale and time frame of design, and sequentially built on the concepts and morphologies of the others to create a holistic and comprehensive design workflow. Certain elements, such as the tower and structure, were developed as static portions in the workflow, whose forms were designed for context-responsive and performance-based criteria to ground the tower within its existing environment in Hong Kong. The remaining portions of the tower, such as the public-private distribution, programmatic topology, and spatial organization, were developed as temporal systems, which could facilitate spatial change in accordance to everchanging social drivers across unique, yet interconnected time scales. Finally, these elements were physically realized through the development of a comprehensive material fabrication system which leveraged bamboo weaving and concrete 3D printing techniques to enable such a dynamic and adaptable system. Each portion of the tower workflow employed novel methods and processes, such as abstracted principles of a bamboo stem, evolutionary algorithms, and robotic fabrication, to enable the P2 Tower to continuously adapt at varying scales of time and space in response to people’s shifting sentiments around sociability.

Bhagat | Wong

M.Sc. Experiments Recap RESEARCH DEVELOPMENT

DESIGN DEVELOPMENT

DESIGN PROPOSAL

BAMBOO INTERNODE EXPERIMENT

TOWER EVOLUTIONARY ALGORITHM

TOWER MORPHOLOGY

CFD NEURAL NETWORK EXPERIMENT

STRUCTURE EVOLUTIONARY ALGORITHM

STRUCTURAL SYSTEM

CO-EVOLUTIONARY EXPERIMENTS

PUBLIC PRIVATE EVOLUTIONARY ALGORITHM

PRIVATE-PUBLIC DISTRIBUTION

TOPOLOGICAL RELATIONSHIPS EXPERIMENTS

VERTICAL TOPOLOGICAL RELATIONSHIPS EVOLUTIONARY ALGORITHM

PROGRAMMATIC TOPOLOGY

SPACE ORGANIZATION EVOLUTIONARY ALGORITHM

SPATIAL ORGANIZATION

VARIABLE CONTROL EXPERIMENTS

COMPONENT WEAVING PATTERN EXPERIMENT

STRUCTURAL ANALYSIS EXPERIMENT

PHYSICAL MODEL EXPERIMENTS

Figure 43: Scope of M.Sc. Phase Experiments

M.Sc. Recap

MATERIAL FABRICATION SYSTEM

YEARS

SOCIABILITY SCORE

VATE-PUBLIC DIST PRI RIB U DECADES

MATIC TOPO RAM LOG OG Y PR

MONTHS

N TIO

STRUCTURAL SYSTEM

FABRICATION SYSTEM

Figure 44: Tower Design Workflow

TOWER MORPHOLOGY

AL ORGANIZATION ATI SP

Bhagat | Wong

4.1 Tower Morphology Design Research Phase Description: To develop appropriate tower morphologies, it was necessary to understand how a tower’s design can mitigate the impacts of wind, a crucial force acting upon tall structures. The authors studied the design of a bamboo stem’s internode spacing as a key mechanism to resist wind loads. However, this mechanism could not be directly applied to the scale of a tower. As such, the Bamboo Internode experiment was conducted to translate this internode spacing into the scale of an architectural tower system. Design Research Experiment: The experiment applied the following mathematical expression from Mulyana et al. to establish the internodal, lateral bracing of a tall tower.1

RIL = 2.8312(RIN)3 - 8.926(RIN)2 + 5.2101(RIN) - 0.0062 RIL = Relative Internode Length | RIN = Relative Internode Number

The co-efficients for this equation were optimized for the scale of architectural tower systems using an evolutionary algorithm. Experiment Results: The experiment found that the translated equation for bamboo internode placement principles at a tower scale is: -1.566x3 + 1.8261x2 + 0.7468x -0.033. Post analysis was conducted to confirm the relevance of the equation. Please see the Appendix (A.02) for details on this experiment. Experiment Relevance and Use: This experiment was directly utilized in the M.Sc Design Development phase to generate the internode heights for the tower morphology.

Design Development Phase Description: This experiment developed a workflow to generate various tower design options which morphologically responded to the environmental conditions of Hong Kong while meeting local density requirements and occupant sociability needs. Design Development Experiment: To create the final tower morphology, an evolutionary algorithm was used to generate towers optimized towards four fitness objectives: max. daylighting during the winter, max. surface area-to-volume ratio, min. wind vector angle deflection, and max. floor-to-area ratio. The primitive tower design was grounded in the existing Harmony tower. The bamboo internode equation was used to place internode heights.

Experiment Results: The evolutionary algorithm results demonstrated a diversity of design options, verifying its ability to provide a range of solutions to address the local climate, density needs, and sociability needs of the occupants (Fig. 45). Please see the Appendix (A.03) for details on this experiment. Experiment Relevance and Use: This morphology generation process developed site specific tower forms which responded to local environmental conditions and sociability needs. During the M.Sc. phase, the morphologies gained from these experiments fed into a sequential simulation to generate the structural system.

M.Arch. Phase Next Steps During the M.Sc. phase, the tower morphology, structural system, and public-private distribution scales occurred as sequential simulations. However, the authors re-evaluated their relationships during the M.Arch. phase, understanding the structural

system and public-private distribution as concurrent systems rather than as consecutive ones. As such, the authors revised and combined these experiments as a co-evolutionary algorithm, rather than as sequential simulations, to facilitate this relationship.

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4.2 Structural System Design Research Phase Description: As established, wind forces are crucial to the design of tall tower and structural systems. However, since the proposed workflow is applicable to multiple locations and CFD is highly time intensive and computationally heavy, this experiment aimed to introduce variable site flexibility by training an artificial neural network (ANN) to accurately predict the wind pressure for any similar tower system. Design Research Experiment: The experiment used data from the towers generated during the tower morphology experiments as the training data set for the ANN, consisting of seven unique inputs: the deconstructed xyz-coordinate of the node point on the tower, the deconstructed normal vector of the surface at the node point, the wind speed (m/s), and the proximity count of the node to other nodes

within a 5m radius. From these inputs, the training output data for the ANN was the wind pressure (kN) on the tower at the node. A single-objective optimization was used to reduce the ANN error. The ANN was validated using 30% of the original data set which was not used for training. Experiment Results: The experiment successfully created an ANN based on similar tower morphologies in various site conditions. Upon validation, it was shown to achieve an average percent error around 50%, but when corrected for outlying data points, the error dropped to 10-15% on average. Experiment Relevance and Use: This experiment was used in the M.Sc. Design Development phase to predict wind loads on various tower morphologies.

Design Development Phase Description: This experiment developed a workflow to generate a structural system which responded to the dynamic wind loads in Hong Kong. It utilized a sequential simulation on top of the previous tower morphology evolutionary algorithm. It integrated both the bamboo node equation and ANN developed previously to more accurately calculate and respond to wind loads on a tower. Design Development Experiment: The experiment utilized a sequential, multi-objective evolutionary algorithm to generate an exoskeleton structural system optimized for two fitness objectives: minimized deformation and minimized embodied carbon. The structure’s form was developed by generating the tower’s principle stress lines,

rationalizing them, and extracting their medial skeletons to maintain their topological connections. Experiment Results: The structural systems generated were minimally optimized for both objectives and the individuals produced lacked variety. As such, a revision of this experiment was required during the M.Arch. phase. Please see Appendix (A.04) for details on this experiment. Experiment Relevance and Use: This workflow was used to generate context-specific structural systems. During the M.Sc. phase, the morphologies gained from this experiment fed into a sequential simulation to create the public-private distribution.

M.Arch. Phase Next Steps During the M.Sc. phase, the structural system used principles of bamboo stems to develop its form. However, bamboo’s continuous fibre wall was not considered. This may explain why the M.Sc. phase structural system’s evolutionary algorithm optimized poorly. As such, this experiment was revised during the M.Arch. phase to integrate 78

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these principles. Since the structural system was revised, it was also necessary to revise the ANN, since the formal logic was altered. This was done as a generator-discriminator set-up to potentially reduce error. Additionally, the tower, structure, and public-private distribution were revised as a co-evolutionary algorithm, as described previously.

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Figure 46: M.Sc. Phase Resultant Structural Systems

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4.3 Public-Private Distribution Design Research Phase Description: Since the tower integrated both public and private programs, it was necessary to explore co-evolutionary algorithms (Co-EA) as a means to evolve both spaces simultaneously and meet their specific objectives. Three types of Co-EAs were studied (parasitism, commensalism, and mutualism) using simplified geometries to understand the algorithm clearly. Design Research Experiment: One experiment was conducted for each type of Co-EA. Each one used a multi-objective optimization on the same primitive but with different fitness objectives to simulate the three types of co-evolution found in nature. The primitive consisted of two towers sharing the same site which evolved simultaneously. Before each CoEA experiment was conducted, each tower was individually optimized using a traditional EA to identify their optimal gene ranges. The conducted CoEA used these optimized gene ranges in its simulation. In doing so, the optimization focused

more on the relationship between the fitness objective as opposed to each individual one. Their advantages and disadvantages were noted, and one method was selected for use. Experiment Results: The results demonstrated a shift in the optimization results from traditional EAs in that the optimized phenotypes and their respective performances are interrelated, which showed the benefits of Co-EAs. Among the three types of Co-EAs, mutualism proved to be the most applicable for this research, since the public-private distribution is inherently a cooperative system. Please see Appendix (A.05) for details on this experiment. Experiment Relevance and Use: The mutualism Co-EA type was used during the M.Sc. Design Development phase to simultaneously grow the public and private spaces in the tower.

Design Development Phase Description: This experiment developed a workflow to distribute the tower’s private and public zones throughout the tower, such that each responded appropriately to the sociability needs of the residents. The mutualism Co-EA method was selected for this experiment, as noted previously. Design Development Experiment: This experiment was a sequential simulation on top of the previously generated tower and structural system EAs. The private-public distribution Co-EA optimized for maximized public distribution, maximized public segment connections, maximized housing density, and maximized private program proximity. The distribution was generated through a voxel growth system. Genes controlling the starting seed locations

and growth parameters dictated the aggregation of the voxels, enabling them to compete with one another over the finite space. Experiment Results: All fitness criteria mildly optimized. This showcased the “ideal team” mindset which allowed for two systems to improve in conjunction. Please see Appendix (A.06) for details on this experiment. Experiment Relevance and Use: This workflow was used to generate co-evolved public-private distributions. During the M.Sc. phase, the distributions from this study fed into the program topology and spatial organization experiments.

M.Arch. Phase Next Steps During the M.Sc. phase, only public and private spaces were distributed. However, when considering the tower’s urban connection during the M.Arch. phase, a third, transitional zone was required in the 80

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distribution as a mediator between the tower and its context. Additionally, the tower, structure, and public-private distribution were revised as a coevolutionary algorithm, as described previously.

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4.4 Programmatic Topology and Organization Design Research Phase Description: To place specific program within the tower’s public and private zones, it was necessary to consider their topological relationships to efficiently locate them based on their sociability factors and allow for redundancy when the tower adapts. To do this, a small world network (SWN) algorithm was used to create connections between a series of weighted nodes, representing the program center points. An EA was used in this process to minimize the effect of the inherent randomness of the SWN. Design Research Experiment: This experiment created a logic of connectivity between architectural functions to achieve a well-connected, yet efficient, network. An EA was used with goals to achieve a maximized clustering of points, a minimized path count, a maximized path weighting, and a node weighting closest to the required program sociability

score. The connectivity rules were bounded by each program’s sociability score, where program only connect with others who have similar values. As such, a gradient of public and private spaces could be achieved in the tower. Experiment Results: This experiment showcased the SWN’s ability to create highly efficient topological relationships when optimized through an EA. By modifying the conditions and weights, designers can easily obtain program relationships which are efficient, diversified, and interconnected. This is ideal for an adaptable tower system. Experiment Relevance and Use: The small world network was used during the M.Sc. Design Development phase to create topological relationships between program types in the tower.

Design Development Phase: Topological Relationships Description: This experiment developed a workflow to create program relationships within the tower which respond to residents’ sociability needs. The optimized public-private distributions developed in Experiment 4.3 served as a basis for this stage. The SWN algorithm studied during the Design Research phase was also integrated, but was expanded upon to introduce a vertical connection logic between multiple networks. As such, a SWN is generated for each tower segment and vertical connections were created to unify each network. Design Development Experiment: To obtain optimized small-world networks, this experiment used an evolutionary algorithm with following goals: a maximized clustering of points, a minimized path count, a maximized path weighting, and a node weighting closest to the required program sociability score. As seen in the previous study, the rules of connectivity were bounded by each program’s sociability score, where program can only connect with others who have similar values. This logic was 82

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used for all vertical connections between networks as well. As such, a gradient of public and private spaces could be achieved throughout all networks in the tower. Experiment Results: This experiment showcased the benefits of using SWN to create relationships between programs in a complex tower system. Generating several localized networks with vertical connections allowed for clear optimizations within each tower segment, yet provided strong relationships throughout the system. This is beneficial for a complex, ever-changing tower. Please see Appendix (A.07) for details on this experiment. Experiment Relevance and Use: This workflow was used to generate topological relationships between programs in a tower. During the M.Sc. phase, the relationships from this study fed into the spatial organization experiment which placed programs based on these connections.

Design Development Phase: Programmatic Organization Description: This experiment was a continuation of the topological relationships experiment, aiming to translate the developed small world networks into spatial program locations within the tower while also meeting the desired program area and program count requirements. The optimized public-private distributions developed in Experiment 4.3 and the aforementioned topological relationship experiment results served as a basis for this stage. Design Development Experiment: To create an appropriate program organization from the nonspatial topological relationships, the optimized public-private distributions from Experiment 4.3 served as a base primitive for this experiment. A voxel growth algorithm was then used to grow each program simultaneously. Since this process was inherently random, an evolutionary algorithm was used to optimize its performance towards the following goals: minimize topological relationships discrepancies, minimize program area difference, and minimize program count difference. In doing so, this workflow can both facilitate the required programmatic connections while still providing

adequate program areas and distributions throughout the tower. Experiment Results: The results of the EA showed the generated individuals achieved the desired relationships and spatial organizations as each fitness criteria optimized well. As such, this process proved to be an acceptable method for generating program layouts which both provided the connectivity and redundancy of a small-world network and facilitated the required programmatic needs. Please see Appendix (A.08) for details on this experiment. Experiment Relevance and Use: This workflow was used to translate the previously developed topological relationships into spatial programmatic organizations within the tower. During the M.Sc. phase, these spatial organizations were used as the locations for each program component, creating usable spaces within the tower design. The fabrication method for these components was explored during the experiments which follow this stage.

M.Arch. Phase Next Steps The authors found that the programmatic topology and spatial organization workflow developed during the M.Sc. phase was sufficient and did not require any revisions when considering the tower in relation

to its urban context. As such, this developed process was utilized as designed during the Design Proposal phase.

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Figure 49: M.Sc. Phase Resultant Programmatic Organizations

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4.5 Material Fabrication System Component Design and Material Fabrication System A component was designed to formalize the voxelized program areas within the tower from Experiment 4.4. One component occupied the space of one voxel and attached to the tower’s substructure. The rhombic dodecahedron was selected as the geometry for the component due to its space-filling nature, large usable floor area, and feasible print and weave angles. The component dimensions were 5m x 5m x 3.5m, which were determined by considering both the minimum area required for usable program and the minimum dimensions required to physically weave the component. However, a component of this

size is out of range for a robotic arm to feasibly 3D concrete print on, so the geometry was sub-divided for ease of fabrication. The component was made of bamboo weaving and 3D printed concrete. The bamboo acted as formwork and rebar to minimize material usage, while maintaining structural stability. A second layer of bamboo was integrated within the structural studs on the inside, as a base to weave in interior panels. This created a seamless, single material joinery system.

Design Research Phase Description: Several experiments were conducted to gain control over the parameters of the weaving process. This was necessary because several variations of the component design were employed depending on the component’s location within a specific program (e.g. corner, edge, top, bottom), and each one contained specific angle and corner conditions to achieve their forms. Additionally, these components would be aggregated hundreds of times across the scale of a tower. As such, it was necessary to gain comprehensive control over the weaving process to create all component variations and maintain a level of accuracy during aggregation.

sagging, weaving density for minimal deformation, and joint system tests. Each experiment provided data on one parameter of the weaving and 3D printing fabrication, which collectively combined to create a comprehensive dataset. This knowledge was then translated into the digital realm through an additional digital to physical translation experiment.

Design Research Experiments: Five experiments were conducted to gain control over the weaving and 3D printing process: polygon Gaussian curvature, strip width/depth ratio, weaving density for material

Experiment Relevance and Use: The variable control and digital to physical translation developed from these experiments will be used to create the weaving pattern for all component variations.

Experiment Results: These experiments showcased a thorough knowledge of the bamboo weaving process, gaining the ability to create accurate, variable curvatures and consistent forms. Please see Appendix (A.09) for details on these experiments.

Design Development Phase Description: To test the results from the Design Research phase and create a suitable component weaving pattern and fabrication system, the authors conducted four key experiments: a component weaving pattern experiment, a component structural analysis, a component slab section fabrication test, and large-scale mock-up fabrication test. Component Weaving Pattern Test: This experiment created the component’s weaving pattern using the 86

M.Sc. Recap

established computational workflow and knowledge gained from the initial variable control experiments. The weaving pattern was tested through the creation of a physical prototype. The prototype was scanned and compared to the digital model to determine the accuracy of the computational workflow. The results showcased an acceptable level of accuracy throughout the entire model. However, some larger areas of deviation were found towards

the outer edges of the component due to the digital workflow’s inability to account for the inherent error in the weaving process, uneven material widths, and variable Young’s moduli for each bamboo strip. Component Structural Analysis Test: To analyze the feasibility of the component, its structural performance was tested against a simple concrete shell using Finite Element Analysis. This experiment aimed to understand if the proposed fabrication system worked similarly to a standard concrete system under a gravity and wind load (0.5kN/m2). The experiment results showcased the thinner concrete shell and bamboo system had a similar maximum deformation to the standard concrete shell. As such, it was feasible to use the bamboo and concrete system for the component design. Component Slab Section: This experiment tested the feasibility of creating the proposed multi-layer concrete and bamboo system through the fabrication of a simple section. This model tested concrete’s ability to bond with bamboo and the critical stud to

bamboo condition. Casted concrete was used instead of 3D printed concrete due to limited facilities. The experiment results showcased a strong connection between the concrete and bamboo. The concrete flowed between the woven cells, which locked the bamboo in place. As such, this experiment proved the viability of the proposed system, allowing the team to move forward to a large-scale mock-up. Large-Scale Mock-Up: Using the data and results from all the fabrication experiments, the authors created a 1:5 scale mock-up of the component’s most critical conditions. The model showcased the viability of the designed component and material fabrication system. Experiment Relevance and Use: All weaving and 3D printing experiments showcased a comprehensive understanding of the proposed material fabrication system. As such, this system was utilized to fabricate each component within the tower design. Please see Appendix (A.10) for details on these experiments.

M.Arch. Phase Next Steps The authors found the material fabrication system developed during the M.Sc. phase was sufficient and did not require any revisions when considering the

tower in relation to its urban context. As such, this developed process was utilized as designed during the Design Proposal phase.

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Figure 50: Component Design and Material Fabrication System

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Figure 52: Digital to Physical Translation Experiment (cont.)

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Figure 53: Final 1:5 Scale Mock-Up Model

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Discussion The M.Sc. phase of the research developed a comprehensive workflow for the design and construction of a housing tower block which met the density needs of Hong Kong while also facilitating continuous spatial changes to match the needs of people over time. In doing so, the research addressed the dual issues of densification and everchanging sociability in Hong Kong. The workflows and processes developed during this stage deeply investigated innovative methodologies, algorithms, and material fabrication systems which facilitated such a temporal, context-specific solution. The use of co-evolutionary algorithms enabled collaborative systems to evolve together over time to address unique, yet interconnected social requirements. When paired with the use of the small world network algorithm, this system facilitated such growth, while maintaining a level of redundancy and robustness which was required for temporal systems. Physically, this system was realized through a comprehensive fabrication system, which utilized bamboo weaving and concrete 3D printing. By leveraging the properties and methodologies associated with these systems, the research developed adaptable, yet easily fabricatable modular forms, while resurfacing dying cultural material systems. While the M.Sc. phase was shown to be successful, there were some elements which required improvement when considering the scope of the M.Arch. phase. This phase extended the social capabilities of the tower block into the urban environment. As such, the tower workflow required local redevelopments in order to facilitate this urban connection. Most prominently, the largest three scales, the tower morphology, structure, and private-public distribution, were re-established to involve a more context-responsive form, a more reasonable structural logic, and a new transitional space type which bridged the tower to its local context. These changes enabled a more intuitive and functional connection to the urban environment, which allowed the M.Arch. phase developments to more easily address the issues of densification and sociability on a larger scale.

M.Sc. Recap

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Bibliography Mulyana, B., and R. Reorita. “Mathematical Expression of Internode Characteristics of Yellow Ampel Bamboo (‘Bambusa Vulgaris’ Var. Striata).” Series II: Forestry Wood Industry Agricultural Food Engineering, June 28, 2022, 43–56. https://doi.org/10.31926/but. fwiafe.2022.15.64.1.4.

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5.1 Revised Artificial Neural Network 5.2 Temporal Graph Network 5.3 Weighted Shortest Walk Algorithm 5.4 Co-Evolutionary Algorithm 5.5 Pedestrian Simulations

RESEARCH

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Expanding the social affordances of the P2 Tower into the urban environment required introductory experiments to determine their applicability on such a large, network scale within the developed workflow. Temporal graph networks were investigated as a method to introduce social adaptability on an urban network level. This algorithm facilitated urban scale changes in accordance to particular events on three major timescales. Additionally, the thesis’ specific application of this method alongside evolutionary algorithms enabled these adaptations to be quantified and evaluated together, ensuring that each time shift individually and jointly provided appropriate functionalities to meet the social needs of the urban residents at any time. Furthermore, since the M.Arch phase’s urban domain expanded the notion of sociability to the level of a collective population, it was necessary to implement pedestrian simulations as a tool to analyze mass behaviors. However, since this research required the development of new simulation tools, several experiments were conducted to develop and test their functionalities using a simplified environment. Finally, since the M.Arch. phase required the implementation of the M.Sc. tower workflow in multiple locations across an urban environment, it was necessary to revisit certain experiments to correct pitfalls from the previous phase. As previously discussed, the tower, structure, and public-private distribution required reevaluation as concurrent systems, rather than sequential ones, through the use of co-evolutionary algorithms. As such, the authors reconsidered their previous use of coevolutionary algorithms and revised their approach to more closely align with true co-evolution in nature. Such a redevelopment of the tower’s structural system also caused the authors to revise the previously developed ANN, since the formal logic was altered. Since this tower would be applied to multiple locations across the urban environment, this ANN was conducted as a generatordiscriminator set-up to potentially reduce error.

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5.1 Revised Artificial Neural Network During the M.Sc. phase, an artificial neural network (ANN) was trained to predict the wind pressure on the tower based upon the tower morphology and wind speed (See Appendix A.11) in order to increase the applicability and flexibility of the computation workflow developed by this research. Yet, validation of the trained artificial neural network showed an average percent error around 50%, which dropped to 10-15% on average when corrected for outlying data points. Therefore, the experiment sought to use a generator and discriminator methodology to train the ANN as a way to improve the performance and accuracy of the ANN. The generator and discriminator methodology for training an ANN utilized two sequential neural networks, where the first ANN generated a series of predicted wind pressure values. These ‘fake’ values were then combined with a collection of ‘real’ wind pressure values obtained through computational

fluid dynamic analysis. The mixed set of ‘real’ and ‘fake’ values were used to train the second ANN, which aimed to predict whether a value was ‘real’ or ‘fake’. Through such a process, the generator and discriminator were in conflict with one another, where the generator sought to produce more and more realistic ‘fake’ values and the discriminator aimed to better differentiate between ‘real’ and ‘fake’ values. In order to tune the hyper-parameters of each neural network and leverage this conflict to iteratively improve their performance, a multiobjective, evolutionary algorithm was employed to minimize the error rate of both the generator and the discriminator. The conflicting nature of these objectives generated a much stronger performance for the ANN than the simple training of it from the M.Sc. phase.

Wind Speed Normal Vector

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Figure 54: Wind Pressure Artificial Neural Network Setup

Research Development

Experiment Description: The experiment revisited the experiment from the M.Sc. phase, which sought to train an artificial neural network to predict the wind pressure on a tower. In utilizing a generator and discriminator methodology to train the artificial neural network, the experiment aimed to improve the performance of the artificial neural network by taking advantage of the conflicting nature of these two mechanisms.

then trained on this combined data set, where the output was either 0 or 1 to identify ‘fake’ and ‘real’ values respectively.

Experiment Set-Up: The experiment employed two consecutive ANNs using the LunchBoxML plugin for Grasshopper. The first ANN, or the generator, was trained on a data set of tower morphologies created during the M.Sc. phase. The training input data for the ANN consisted of the deconstructed xyz-coordinate of the node point on the tower, the deconstructed normal vector of the surface at the node point, the wind speed (m/s), and the proximity count of the node to other nodes within a 5m radius. From these inputs, the training output data for the ANN was the wind pressure (kN) on the tower at the node, which was obtained through computational fluid dynamic (CFD) analysis using the Butterfly plugin for Grasshopper. The CFD utilized wind speeds ranging from 5 m/s to 15 m/s, a mesh resolution of 3.0, and ran for 200 iterations. 10 random tower morphologies were tested, generating a training set of 67,000 inputs.

Experiment Results: The trained ANN was postanalyzed for accuracy and performance using 30% of the original data set as validation, which was not utilized for training. From these predicted wind pressure values, the percentage error was calculated and averaged across the entire data set. The results of the experiment showed the generator and discriminator methodology reduced the ANNs error by 30% as compared to that of the M.Sc. phase (9.776x103 to 7.501x103) Yet, the runtime for the evolutionary algorithm increased by 250% (12 hours to 30 hours).

After the generator was trained, it was used to create a set of 30,000 ‘fake’ wind pressure values, which was combined with a set of 30,000 ‘real’ wind pressure values from CFD analysis. The second artificial neural network, or the discriminator, was

Once both ANNs were trained with their respective data sets, an evolutionary algorithm was utilized to minimize the error of each one. The evolutionary algorithm ran for 15 generations with 10 individuals in each generation.

Experiment Relevance: While it may be argued the time required to train the neural network outweighed the time required for a traditional CFD analysis, the use of an ANN in the computational workflow developed through this research enabled its widespread applicability and adaptability to different scenarios. In particular, the accuracy improvement of the ANN through this experiment ensured the workflow developed during the M.Sc. phase continued to perform to a high standard as the research expanded to consider the urban context and other external factors during the M.Arch. phase.

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Figure 55: Generator and Discriminator ANN Workflow

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5.2 Temporal Graph Network INITIAL CONDITION

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Figure 56: Temporal Graph Experiment Workflow

With the development of the localized, microurban networks of independent P2 Towers during the M.Arch phase, the research explored how to interconnect these P2 Towers scattered across an urban landscape through the use of a temporal graph. Differently from a static graph, here the nodes represented the P2 Tower at varying stages of time and the edges represented multimodal corridors physically linking them. The use of a temporal graph enabled the research to understand the relationship of the entire urban network across three timescales, days, months, and years. To create a robust network that performed to the same standard even as it changed over time, the experiment conducted a multi-objective optimization using an evolutionary algorithm on the temporal graph, where three temporal shifts were applied to the initial state of the graph on a specified timescale that altered it according to the architectural implication of that timescale. The initial state of the temporal graph was evaluated 100

Research Development

on three performance criteria, while the state of the graph after each temporal shift was evaluated collectively for the same fitness criteria to develop a robust graph with redundancies and flexibility. The experiments applied the evolutionary algorithm to each timescale shifts independently in order to understand the effects of each timescale on the urban network. Additionally, the evolutionary algorithm was applied to a static variant of the graph as a baseline comparison to highlight the architectural impact of considering the added dimension of time. Lastly, the three timescales were applied concurrently during a multi-objective optimization in order to develop a robust, multiscalar urban network. Such an approach allowed the P2 Tower and its urban network to adapt to the shifting sociability of its residents and perform to the same standard over time.

LOCAL PEDESTRIAN NETWORK

EXISTING CONTEXT

FC01 | Min. Path Count (Initial)

INITIAL CONDITION

FIRST TIME SHIFT

SECOND TIME SHIFT

THIRD TIME SHIFT

FC02 | Max. Closeness Centrality (Initial)

FC03 | Max. Mean Clustering (Initial)

FC04 | Min. Path Count (Shifted)

FC05 | Max. Closeness Centrality (Shifted)

FC06 | Max. Mean Clustering (Shifted) SPATIAL URBAN LAYOUT

Figure 57: Temporal Graph Evolutionary Algorithm Setup

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5.2.1 Temporal Urban Graph Optimization Independent Shifts Experiment Description: The experiment conducted four independent multi-objective optimizations, one for each timescale, to balance performance of the initial state of the temporal graph with that of the proceeding temporal graph for each temporal shift. Experiment Set-Up: For each timescale, a separate experiment and optimization was conducted, but the setup remained consistent, and the difference between the experiments existed in the architectural implications of the temporal shifts. Firstly, an initial state of the temporal graph was randomly generated, where the nodes represented the P2 Tower at varying stages of time and the edges represented multimodal corridors physically linking them, also at varying stages of time. These varying stages of time existed in three architectural states: Constructed, Activated, and Deactivated. If a node or edge did not exist in the temporal graph, then architecturally, it was considered unbuilt. The random generation of the initial state, temporal graph was controlled by five genes: the total node count, the construction percentage, the node activation rate, the edge activation rate, and a random seed. The initial state, temporal graph was evaluated based upon three fitness criteria: minimized edge count, maximized closeness centrality, and maximized mean clustering. After the initial state was generated, three consecutive temporal shifts were applied to this graph, representing architectural changes that may occur Experiment 01 No Shift

Experiment 02 Days Shift

Experiment 03 Months Shift

Experiment 04 Years Shift

FC1 | Min Path Count

39.09

42.28

55.04

58.00

FC2 | Closeness Centrality

0.97

1.02

0.99

FC3 | Clustering Coefficient

1.38

1.69

2.05

2.02

Constructed Node Count

10.96

11.03

12.12

12.22

Active Node Count

5.81

6.67

6.60

6.82

Active Edge Count

39.09

42.28

55.04

58.00

Construction Percentage

0.80

0.82

0.78

0.80

Active Node Percentage

0.73

0.80

0.74

0.73

Active Edge Percentage

0.79

0.80

0.76

0.79

Figure 58: Average Temporal Graph Parameters Comparison

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at each timescale. For example, the three shifts at the days timescale corresponded to the morning, afternoon and evening, where access to the public for the P2 Tower or a multimodal pathway may open or close depending on the time of day. Similarly, the three shifts at the months timescale correspond to the summer, fall/spring, and winter, where entirely new multimodal pathways may be constructed or the P2 Tower opened or closed seasonally due to its ability to meet the immediate sociability needs of its residents versus the general public. After each shift, the graph was re-evaluated for the same three fitness criteria as the initial state graph, and the values were averaged across all three shifts to create three conflicting fitness criteria, challenging the performance of the initial state graph with that of the shifted state graphs. The evolutionary algorithm for each timescale ran for 100 generations with 100 individuals in each generation. Experiment Results: By comparing the average values from all of the Pareto Front members across all of the fitness criteria as well as other parameters related to the initial graph, the experiment independently contrasted the impact of shifting the state at the timescale of days, months, and year as compared to one another and a static graph. The results showed each timescale required additional nodes and edges to accommodate the temporal shifts and maintain a similar performance in terms of closeness centrality and clustering coefficient. In particular, the results showed that the timescale of years had the greatest impact on the initial state graph. Experiment Relevance: Architecturally, the results of this experiment highlighted the importance of redundancy in networks in order to account for change over time. By introducing auxiliary P2 Towers and multimodal pathways during the initial development of the urban network, it ensured the entire network continued to maintain a strong performance, even as conditions changed. Additionally, the experiment showcased the degree of impact and the type of impact that each timescale had on the initial state, temporal graph, which would be later used to develop other experiments that concurrently apply these three timescales to an initial state, temporal graph and create one which considers all three timescales simultaneously.

Experiment 01 No Shift

Experiment 02 Days Shift

Experiment 03 Months Shift

Experiment 04 Years Shift

Experiment 05 Concurrent Shift

Figure 59: Representative Temporal Graph Pareto Front Members

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5.3 Weighted Shortest Walk Algorithm INPUTS

WEIGHTING

ALGORITHM

Building Nodes Relationships

TEMPORAL GRAPH Building Connection Relationships

OPEN SOURCE INFORMATION

CLIMATE DATA

Topography

Normalize

Apply Bias Weighting

Building Locations

Normalize

Apply Bias Weighting

Road Locations

Normalize

Apply Bias Weighting

Building Types

Normalize

Apply Bias Weighting

Road Types

Normalize

Apply Bias Weighting

Daylighting

Normalize

Apply Bias Weighting

Wind

Normalize

Apply Bias Weighting

Calculate Weighted Shortest Path

Figure 60: Temporal Graph Experiment Workflow

The use of the temporal graphs to generate the urban network of P2 Tower in Experiment 5.2.1 created a robust network which was responsive to shifts at different timescales, but simply superimposing this non-metric graph on the complex urban environment of Hong Kong would have been quite naive. Therefore, the experiment utilized a weighted shortest path algorithm, specifically Dijkstra’s Algorithm, to translate the temporal graph into multimodal corridors linking different P2 Towers throughout Hong Kong. Open-source data provided by the government of Hong Kong was utilized to obtain the site-specific urban conditions for the experiment as a means to generalize the results of the experiment and the computational workflow developed through this research such that it may be easily applied to other 104

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urban conditions as a solution to densification. The open-source data included topography, building footprints, building heights, building program, road centerlines, road lane counts, and climate information. By analyzing this open-source data, the experiment utilized five weightings, closeness centrality, daylight hours, distance, visibility, and elevation, to weight the graph edges and create a context specific path connection between the specified towers. Additionally, the experiment introduced biases to these weighting to align the generated paths with specific design goals. In doing so, the shortest path algorithm reconciled the site-specific urban conditions of Hong Kong with the robust performance of the temporal graph network from Experiment 5.2.1.

Closeness Centrality 0.5295

0.2785

Total Daylight Hours 1241 hours

0 hours

Isovist Visable Area

Distance 198.85 m

14.56 m

Elevation 35.29 mPD

-5.76 mPD

Figure 61: Open-Source Data Weightings

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5.3.1 Weighted Shortest Path Experiment Experiment Description: The experiment translated the temporal graphs generated from Experiment 5.2.1 to the urban context of Hong Kong by applying Dijkstra’s Algorithm to identify the weighted shortest path, where the edge weightings of the graph corresponded to open-source data about the site-specific urban conditions. Experiment Set-Up: Open-source data, including the topography, building footprints, building heights, road centerlines, and weather conditions, were obtained from the government of Hong Kong. This open-source data was utilized to construct an accurate digital model of the urban context which also stored additional metadata. Then, the existing road network was simplified to a graph network, where the nodes represented road intersections, and the edges represented the roads connecting these intersections. After the model was constructed, each edge in the graph was analyzed for five conditions: its closeness centrality in the overall network, the total daylight hours it receives during the winter, the metric length of the edge, the average visibility range from any given point on the edge, and the average elevation of edge. These values were then normalized from 0 to 1, and a bias was introduced to each of these conditions in order to prioritize certain design goals over others. Then, all of these values were summed

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together for each edge, becoming their associated weighting. Once the graph network with its appropriate edge weightings was generated, a temporal graph from Experiment 5.2.1 was selected amongst the Pareto Front members, specifically, the Pareto Front member with the lowest average of fitness rankings in order to maintain a generalization of the workflow developed as part of this research. The temporal graph identified which P2 Towers or open lots needed to be connected physically, so Dijkstra’s Algorithm was applied to the graph network of the urban context to identify a context-specific path connecting all of the open lots. Experiment Results: The results of the experiment highlighted the ability for the weighted shortest path algorithm to properly translate the temporal graph to context-specific urban conditions. Additionally, the experiment showcased how different design goals, whether that was a prioritization for walkability in terms of distance or accessibility in terms of daylighting, altered the path between two open lots within the urban context. Experiment Relevance: The weighted shortest path provided a strong mechanism for translating the generated temporal graph to the urban context and providing a framework to begin designing the multimodal corridors or the entire urban network.

10x Bias

DAYLIGHTING

10x Bias

ISOVIST

10x Bias

DISTANCE

10x Bias

ELEVATION

10x Bias

CLOSENESS CENTRALITY UNBIASED

Open Lot Weighted Path Unweighted Path End

Figure 62: Influence of Weighted Shortest Path

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5.4 Co-Evolutionary Algorithms SOCIABILITY SCORE

MONTHS

DECADES

N TIO

TOWER MORPHOLOGY

STRUCTURAL SYSTEM

VATE-PUBLIC DIST PRI RIB U

AL ORGANIZATION ATI SP

YEARS

MATIC TOPO RAM LOG OG Y PR

FABRICATION SYSTEM

Figure 64: M.Sc. Computational Workflow

AL ORGANIZATION ATI SP

YEARS

MATIC TOPO RAM LOG OG Y PR

MONTHS

STRUCTURAL SYSTEM

SOCIABILITY SCORE

TOWER MORPHOLOGY

DECADES

FABRICATION SYSTEM PRIVATE-PUBLIC DISTRIBUTION

Figure 63: M.Arch. Computational Workflow

During the M.Sc. phase, the computational workflow developed assumed a sequential evolution of the tower morphology, structural system, and public-private distribution. Yet, such an approach disregarded the inherently connected nature of these tower layers. While sequential evolutionary algorithms build upon one another by consecutively shortening the range of optimal genes, undesirable gene values may still exist within these shortened domains. Therefore, it was necessary to re-evaluate their positions in the workflow as concurrently developed systems, rather than consecutive elements. To facilitate this, the M.Arch phased utilized a coevolutionary algorithm, where separate populations of the structural system and the public-private distribution evolved independently but also in parallel. Throughout this process, the two systems shared data to inform their own optimizations, which in turn, created a stronger collective which was balanced across all performance objectives. Conducting a CoEA, as opposed to simultaneously evolving the structural system and the publicprivate distribution in a single evolutionary 108

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algorithm, was required because the high number of fitness criteria from combining the two systems prevented a traditional evolutionary algorithm from adequately optimizing. Initial experiments with the CoEA explored its application on a single segment of the tower where the structural system and public-private distribution were simplified but represented a microcosm of the entire system. Such a approach enabled the experiment to better explore, in detail, the behavior of both these systems in relationship to one another as well as evaluate the CoEA as a tool for the multiobjective optimization of complex and interrelated systems. A custom plug-in for Grasshopper3D was written using C# to implement the cooperative coevolutionary algorithm. Please see the Appendix (A.14) for a sample of the code. The results of this experiment were later applied across the entire tower, where the full structural system and the public-private distribution evolved in parallel to develop a synergistic relationship between all of the systems throughout the tower.

5.4.1 Co-Evolutionary Algorithm - Exploration Experiment Description: The experiment explored the cooperative co-evolutionary algorithm as a tool for simultaneously optimizing interconnected parts of a complex system. In the terms of the research, the experiment specifically co-evolved the structural system and the public-private distribution of a single, shared segment of the tower, where each optimized towards their own, independent fitness criteria and the shared fitness criteria were periodically reevaluated to realign the optimization. Experiment Set-Up: The co-evolutionary algorithm simultaneously optimized two populations. For both populations, a box controlled by three genes, which determined the length, width, and height, represented a segment of the tower. As a shared element between both populations, it was evaluated for its surface area-to-volume ratio and gross floor area, fitness criteria which impacted both systems. In the first population, a simplified structural system on the exterior of the box was controlled by five genes which determined the shell thickness, the curve division distance, the curve connection type, the beam diameter, and the beam thickness. This population aimed to optimize for two fitness criteria unique to the structural system: minimized embodied carbon and minimized deformation. For the second population, a simplified publicprivate distribution was generated on the interior of the box using a random walk algorithm, where INDIVIDUAL MULTI-OBJECTIVE OPTIMIZATION

the public and private voxels incrementally grew to fill out the interior space. This was controlled by four genes, which determined the start seed of the public distribution, the start seed of the private distribution, the public growth rate, and the private growth rate. This population aimed to optimize two fitness criteria unique to the public-private distribution: maximized public space percentage and maximized private space density. Each of these separate populations optimized independently through a traditional evolutionary algorithm for five generations with ten individuals in each generation. After the fifth generation, the populations were brought together to be evaluated and ranked collectively based upon the shared fitness criteria of the box. Then, this combined population optimized towards these shared fitness criteria through a traditional evolutionary algorithm for five generations in order to realign the independent optimizations to the results of the other. After these five generations, the shared population separated back into two populations and optimized independently for their own fitness criteria for another five generations before coming back together again. This back-and-forth between optimizing separately for independent fitness criteria and optimizing collectively for shared fitness criteria continued for five cycles before the co-evolutionary algorithm terminated, and the Pareto Front members were identified for further evaluation of the workflow.

SHARED EVALUATION

SHARED RANKING

SHARED MULTI-OBJECTIVE OPTIMIZATION

Total Top 50% Proceed

Shared_FC 01 Shared_FC 02

Shared Gene 01

POPULATION 01 (P1)

P1_FC 01 P1_FC 02 P1 Genes

P1 Gene xx

Shared Gene 01 Shared Gene 02 P2 Gene 01

POPULATION 02 (P2)

P2_FC 01 P2_FC 02

Shared_FC 01 Shared_FC 02

OPTIMIZED P1

Shared Genes

P2 Genes

P2 Gene xx

Five Optimization Cycles

P1 Gene 01

Five Optimization Cycles

Shared Gene 02

OPTIMIZED P2

REPEAT CYCLE terminates after five cycles

Figure 65: Co-Evolutionary Algorithm Pseudocode

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Experiment Results: Examining the optimization results of the experiment, the co-evolutionary algorithm showed the potential to be a powerful tool for optimizing complex systems. While the results did not show an ideal optimization, it was observed that the two independent populations began to converge alongside the shared fitness criteria. The convergent individuals in the last few generations were by no means the best performing individuals for any one fitness criteria, but they, on average, performed well across both their independent fitness criteria in addition to their shared fitness criteria. Such results were observed when looking at the parallel coordinate graphs and the mean value graph for both populations. In addition, the standard deviation graphs for each fitness criteria of both populations showcased how the shared parameters converged for both populations, even though the optimal combination of shared elements for one population may not be the ideal scenario for the other. Such a phenomenon can most likely be attributed to the collective evolutionary generations of the algorithm, which realigned both populations shared genes and shared fitness values. Experiment Relevance: While statistically, the experiment highlighted the ability for the coevolutionary algorithm to handle complex problem environments, the architectural implications of the

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algorithm are less apparent from observing the phenotypes. Much of this may be attributed to the simplistic nature of the experiment and the type of evolutionary algorithm employed. By applying the methodology to a larger scale, the capabilities of the co-evolutionary algorithm may become more apparent. Therefore, the research took the lessons learned from this experiment, improved upon the nuances of the co-evolutionary algorithm, and applied it to revise the development of the structural system and public-private distribution across the entire tower. In doing so, the computational workflow became better attuned to the interconnected nature of its discrete elements.

BEST RANK P1 FC01 Gen 06;06

Shared Gene 01: 8 Shared Gene 02: 10 Shared Gene 03: 5

BEST RANK P1 FC02 Gen 01;01

Shared Gene 01: 8 Shared Gene 02: 6 Shared Gene 03: 5

BEST BALANCED P1 Gen 00;04

Shared Gene 01: 10 Shared Gene 02: 13 Shared Gene 03: 5

BEST RANK P2 FC01 Gen 04;00

Shared Gene 01: 8 Shared Gene 02: 10 Shared Gene 03: 5

BEST RANK P2 FC02 Gen 02;04

Shared Gene 01: 12 Shared Gene 02: 11 Shared Gene 03: 14

BEST BALANCED P2 Gen 02;01

Shared Gene 01: 12 Shared Gene 02: 09 Shared Gene 03: 11

P1 Ind. Gene 01: 4 P1 Ind. Gene 02: 9 P1 Ind. Gene 03: 6 P1 Ind. Gene 04: 9 P1 Ind. Gene 05: 5.24 P1 Ind. Gene 06: 0.89

P1 Ind. Gene 01: 4 P1 Ind. Gene 02: 5 P1 Ind. Gene 03: 6 P1 Ind. Gene 04: 9 P1 Ind. Gene 05: 5.24 P1 Ind. Gene 06: 0.34

P1 Ind. Gene 01: 4 P1 Ind. Gene 02: 5 P1 Ind. Gene 03: 5 P1 Ind. Gene 04: 7 P1 Ind. Gene 05: 10.8 P1 Ind. Gene 06: 0.44

P2 Ind. Gene 01: 5.24 P2 Ind. Gene 02: 6.43 P2 Ind. Gene 03: 4 P2 Ind. Gene 04: 73 P2 Ind. Gene 05: 2 P2 Ind. Gene 06: 324 P2 Ind. Gene 07: 1 P2 Ind. Gene 08: 1

P2 Ind. Gene 01: 4.47 P2 Ind. Gene 02: 6.11 P2 Ind. Gene 03: 3 P2 Ind. Gene 04: 395 P2 Ind. Gene 05: 1 P2 Ind. Gene 06: 226 P2 Ind. Gene 07: 2 P2 Ind. Gene 08: 2

P2 Ind. Gene 01: 6.43 P2 Ind. Gene 02: 9.69 P2 Ind. Gene 03: 4 P2 Ind. Gene 04: 73 P2 Ind. Gene 05: 2 P2 Ind. Gene 06: 324 P2 Ind. Gene 07: 1 P2 Ind. Gene 08: 1

Figure 66: CoEA Design Space

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Increased Performance

Gen50

Gen0

Shared FC1

Shared FC2

Shared FC3

Population 01 FC1

Population 01 FC2

Figure 67: CoEA Parallel Coordinates Plot - Population 01

Shared FC1 Mean Generation Fitness Value

Shared FC2 Shared FC3 Population 01 FC1

Generation Figure 68: CoEA Mean Value Graph - Population 01

Shared FC1

Shared FC2

Population 01 FC1

Population 01 FC2 Figure 69: CoEA Standard Deviation Graph - Population 01

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Shared FC3

Population 01 FC2

Increased Performance

Gen50

Gen0

Shared FC1

Shared FC2

Shared FC3

Population 02 FC1

Population 02 FC2

Figure 70: CoEA Parallel Coordinates Plot - Population 02

Shared FC1 Mean Generation Fitness Value

Shared FC2 Shared FC3 Population 01 FC1

Population 01 FC2

Generation Figure 71: CoEA Mean Value Graph - Population 02

Shared FC1

Shared FC2

Population 02 FC1

Population 02 FC2

Shared FC3

Figure 72: CoEA Standard Deviation Graph - Population 02

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5.4.2 Co-Evolutionary Algorithm - Post-Analysis Experiment Description: The experiment aimed to post-analyze the results of Experiment 5.4.1 by comparing them to a multi-objective optimization of the same scenario using a traditional evolutionary algorithm, where the fitness criteria for both populations as well as the shared ones are optimized simultaneously. Experiment Set-Up: The set-up for the experiment is identical to that of Experiment 5.4.1, where the optimization is tested upon a generic box that represented a segment of the tower, a simplified structural system on the exterior of the box, and a public-private distribution. The difference between this experiment and the previous one lies in the optimization algorithm employed. While Experiment 5.4.1 utilized a cooperative co-evolutionary algorithm to simultaneously, this experiment employed a traditional evolutionary algorithm to simultaneously evolve all of the fitness criteria together. These fitness criteria were maximized surface area-to-volume ratio, maximized gross floor area, minimized deformation, minimized embodied carbon, maximized public space percentage and maximized private space density, seven in total. The evolutionary algorithm ran for 55 generations with 10 individuals per generation, the same as Experiment 5.4.1, and the plugin Wallacei for Grasshopper was used to conduct the optimization.

Experiment Results: The results of the experiment highlight the results of experiment 5.4.1 and upon comparison, showcased the way in which the coevolutionary algorithm is better suited to optimizing complex systems of interrelated elements. Looking at the parallel coordinate plot and standard deviation graphs, it was observed that very few of the fitness criteria were able to optimize over the same number of generations and individuals as Experiment 5.4.1. In particular, the mean value graph highlighted how fitness criteria related to the structural system and the public-private distribution were antithetical to those of the tower morphology. While such an occurrence was noticed in Experiment 5.4.1, the impact of the conflict was mitigated through the cyclical nature of the algorithm. Experiment Relevance: This experiment supported the results of Experiment 5.4.1 and justified the continued use of the cooperative co-evolutionary algorithm for other aspects of the research. While these two experiments were not directly comparable due to clear and technical difference is the tools used to employ the algorithms, the results emphasized a high-level challenge of traditional evolutionary algorithms and showcased how a cooperative coevolutionary algorithm affords the opportunity to remedy these pitfalls.

Tower FC1

Tower FC2

Structure FC1

Structure FC2

PP Distribution FC1

PP Distribution FC2

Figure 73: CoEA Standard Deviation Graph - Post-Analysis with Wallacei

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Shared FC3

Increased Performance

Gen50

Gen0

Tower FC1

Tower FC2

Tower FC3

Structure FC1

Structure FC2

PP Distribution FC1

PP Distribution FC2

Figure 74: CoEA Parallel Coordinate Plot - Post-Analysis with Wallacei

Tower FC1

Mean Generation Fitness Value

Tower FC2 Tower FC3 Structure FC1 Structure FC2 PP Distribution FC1

PP Distribution FC2

Generation Figure 75: CoEA Mean Graph - Post-Analysis with Wallacei

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5.5 Pedestrian Simulations Since the M.Arch. phase was heavily focused on connecting the tower to its context and bridging the sociabilities of the local communities, it was crucial to understand how occupants would interact with the proposed urban system and with each other. This was primarily achieved by using pedestrian simulations to more closely understand social behaviors at this scale. However, as previously noted, no existing pedestrian simulations integrated such behaviors as core mechanisms. Knowing this, the authors developed a new plug-in which could enable this social functionality within the realm of a pedestrian simulation at a large urban network

scale. Through this research, the authors developed two similar types of social pedestrian simulations which work well for two unique functionalities and scales. The first is a network-based social pedestrian simulation which utilizes network lines and shortest path algorithms to enable pedestrian behaviors. This will be used to analyze full urban networks at a large scale. The second is a sociospatial pedestrian simulation which utilizes a threedimensional mesh surface and spatial movements to enable pedestrian behaviors. This will be used to analyze spatial sections of networks at a smaller scale in relation to program and surrounding context.

5.5.1 Network-Based Social Pedestrian Simulation Functionality The network-based social pedestrian simulation is designed for large-scale network analyses. This simulation enables similar behaviors to those in existing simulations but introduces socialization as an additional core mechanism of pedestrian behavior. The developed pedestrian simulation requires the following inputs: Network Curves: curve geometry, curve capacity Destinations: destination type, accepted pedestrian types, point location, capacity, and wait time Pedestrians: pedestrian type, journey type, social level, count This information is then initialized by constructing pedestrian, destination, and network curve classes. This initialization process also constructs pedestrian start locations based on a series of input start curves and a seed value. At this stage, pedestrian destination lists are generated as well, based on a pedestrian’s journey type and each destination’s access type. A shortest walk algorithm is used to obtain the most efficient path towards each destination. Once all information is compiled, the algorithm runs with three major behaviors. Pedestrians move 116

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towards their destinations along their shortest walk paths, stop at destinations for designated amounts of time, and stop to socialize with others. The socialization behavior can take place if both pedestrians are within a user-specified distance from each other and if their social levels are within a particular range of one another. The chance of socialization is scaled based on the difference of social level, where those with more similar values have a higher chance of interaction. Global social perception and global randomness factors are also introduced to the algorithm to further mediate social interactions in a way which may more closely represent how individuals interact. Once the simulation is finished, the network can be analyzed by producing a heat map of pedestrian movements on the network, a map of pedestrians’ individual movements, and data on pedestrian travel times and interactions. Please see Appendix (A.13) for a sample of the code. While this pedestrian simulation does not yet enable all types of social behaviors, such as an agent’s ability to wander, cue, or change goals, it does create the groundwork for understanding and analyzing how people might move and socialize within a network.

5.5.2 Network-Based Social Pedestrian Simulation Experiments To test the functionalities of the developed pedestrian simulation, the authors conducted two small-scale experiments on a simplified network. The first experiment aimed to understand how the implemented social factors impact the behaviors of the pedestrians. This experiment was conducted by maintaining a constant network environment, parameter set, and pedestrian types, and solely altering the sociability values within the system. Each network was then analyzed based on several fitness criteria relating to movement efficiency and socialization to understand how the varied social settings impacted the pedestrian movements.

CONSTRUCTORS

INPUTS

Once the authors understood the base mechanisms of the pedestrian simulation, a second experiment was conducted to leverage this tool to select a high performing network system from a catalog of possible solutions. This experiment was conducted by maintaining constant pedestrian types, parameters, and sociability factors, and solely altering the network environment. Each network was then analyzed based on several fitness criteria relating to movement efficiency and socialization to understand which system performed better.

INITIALIZATION

ALGORITHM

OUTPUT

wait time adjustment person type

PEDESTRIAN PROFILE

journey type

travel speed adjustment destination list

shortest path

social interaction

interact with other pedestrians

social interaction level spawning zones

starting point

pedestrian travel times

count for each type

NETWORK PATH PROFILE

travel paths capacity

travel along designated path heat map of network utilization

destination type access type

DESTINATION PROFILE

location typical wait time

map of individual pedestrian travels

stop at target destinations

capacity

Figure 76: Network-Based Pedestrian Simulation

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5.5.2.1 Pedestrian Simulation Experiment 01 Experiment Description: This experiment focused on altering the social behavior settings of the pedestrian simulation to understand how these factors affected the algorithm’s functionality. Experiment Set-Up: This experiment was conducted by maintaining a constant network environment, destination locations, seed parameter values, and pedestrian types, and solely altering the sociability values within the system. The algorithm ran for 100 iterations with a total of 12 pedestrians (3 of each type: young adult, single adult, family, and elderly). Four identical networks were tested, where each was given a unique sociability setting for the both the global environment and individual pedestrian social values, where 0.0 is no social interaction and 1.0 is the highest level of social interaction. Test 01 (No Sociability): Global Factor: 0.0 Pedestrian Factors: 0.0 Test 02 (Low Sociability): Global Factor: 0.1 Pedestrian Factors: 0.2-0.3 Test 03 (Med. Sociability): Global Factor: 0.5 Pedestrian Factors: 0.4-0.7 Test 04 (High Sociability): Global Factor: 0.9 Pedestrian Factors: 0.7-0.9

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Each network was analyzed based on three fitness objectives: maximized percentage of iterations socializing (number of iterations socializing / total iterations), maximized travel efficiency (number of iterations moving / total iterations) and minimized number of total movements. As such, the best performing network would be efficient for movement, yet provide opportunities for socializing. Experiment Results: The experiment showcased that the social functionality greatly affected the algorithm’s results. As seen in Figure 77, the networks with the higher sociability settings saw a larger number of social interactions and a higher number of visits to the network nodes, as more individuals were stopping to interact at those locations. However, it should be noted that as more interactions occurred the number of movement iterations increased, meaning that it took longer for individuals to complete their itineraries across the network. As such, a balance is required between social interaction and network efficiency. Experiment Relevance: This experiment built the foundation for the pedestrian simulation, ensuring that its social functionality worked as expected. As such, the authors could confidently use the pedestrian simulation moving forward.

TEST 01 (NO SOCIABILITY)

Max. % Social Iterations

Max. Travel Efficiency

Min. Total Movements

TEST 02 (LOW SOCIABILITY)

Max. % Social Iterations

Max. Travel Efficiency

Min. Total Movements

TEST 03 (MED. SOCIABILITY)

Max. % Social Iterations

Max. Travel Efficiency

Min. Total Movements

Max. % Social Iterations

TEST 04 (HIGH SOCIABILITY)

8 Pedestrians

Max. Travel Efficiency

Min. Total Movements

0 Pedestrians

Figure 77: Network-Based Pedestrian Simulation Experiment 01

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5.5.2.2 Pedestrian Simulation Experiment 02 Experiment Description: Once the authors understood the base mechanisms of the pedestrian simulation, a second experiment was conducted to leverage this tool to select a high performing network system from a catalog of possible solutions. Experiment Set-Up: This experiment was conducted by maintaining constant pedestrian types, seed parameter values, and sociability factors, and solely altering the network environment (network curves and destinations). The algorithm ran for 100 iterations with a total of 12 pedestrians with varying social levels from 0.3 to 0.8 (3 of each type: young adult, single adult, family, and elderly). The global social level remained at 0.5. Four different networks were tested, where the same number of destinations were maintained, but the placement and pathways of the network environment were altered, as seen in Figure 78. Once the algorithm was complete, each network was analyzed based on three fitness objectives: maximized percentage of iterations socializing (number of iterations socializing / total iterations), maximized travel efficiency (number of iterations moving / total iterations), and maximized network usage (average number of pedestrian visits to each node in the network). As such, the best performing network would be efficient for movement with the most utilized paths, while providing opportunities for socialization. Experiment Results: The experiment showcased that pedestrian sociability could be used alongside pathway efficiency as a suitable analysis tool and selection method. As seen in Figure 78, when solely considering the non-social fitness criteria

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(maximum travel efficiency and maximum network usage), Test 01’s network may be perceived as the most fit selection. However, when considering how individuals may socialize along this network, it was clear that Test 01 is no longer ideal. While this network may be efficient for travel purposes, the locations of the pathways and destinations did not enable pedestrians with similar sociability levels to regularly pass by one another and interact. As such, very little interaction occurred. However, when considering both travel criteria and social interaction needs, another network, such as the system in Test 02 or Test 03, became more fit. These networks balanced all needs, allowing for efficiency in movement in terms of path usage and travel distance, while still affording opportunities for similarly social individuals to interact and communicate. As such, these types of networks began to craft gradients of communities at the urban scale, rather than solely allowing for movement. The developed pedestrian simulation not only provided analysis of an existing network, but could also help locate and alter unused network connections and destinations or areas of little social relevance to mitigate travel and community issues in the future. As such, the plug-in’s use can expand beyond a post-analysis simulation and become a generative tool for designers. Experiment Relevance: This experiment built the foundation for the pedestrian simulation in understanding its use as an analysis and generation tool. With this experiment, the authors could feel confident in using this tool for urban scale experiments during the Design Development phase.

TEST 01

Max. % Social Iterations

Max. Travel Efficiency

Max. Network Usage

TEST 02

Max. % Social Iterations

Max. Travel Efficiency

Max. Network Usage

TEST 03

Max. % Social Iterations

Max. Travel Efficiency

Max. Network Usage

Max. % Social Iterations

TEST 04

9 Pedestrians

Max. Travel Efficiency

Max. Network Usage

0 Pedestrians

Figure 78: Network-Based Pedestrian Simulation Experiment 02

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5.5.3 Socio-Spatial Pedestrian Simulation Functionality The socio-spatial pedestrian simulation is an extension of the network-based pedestrian simulation, but operates on a much smaller scale which utilizes a three-dimensional mesh surface and spatial movements to enable pedestrian behaviors. As such, it is geared towards analyzing spatial sections of networks in relation to program and surrounding context. This pedestrian simulation requires the following inputs: Mesh: Mesh surface, refinement level Context: Building volumes, social level values Destinations: destination type, sociability, sphere of influence, area, count Pedestrians: pedestrian type, sociability, count This information is then initialized by constructing pedestrian, destination, and mesh classes. This initialization process also places program boundaries and pedestrian start locations based on the input destination parameters and pedestrian parameters. At this time, a social value is calculated for each mesh face based on the sociabilities of the surrounding context buildings and placed program. Once all information was compiled, the algorithm runs and pedestrians move from mesh face to mesh face based on three factors. Pedestrians may move towards a neighboring mesh face with the most similar sociability score, towards a nearby mesh face with a similarly social pedestrian inhabiting it, CONSTRUCTORS

INPUTS

INITIALIZATION

or towards a randomly selected neighboring mesh face. One of these operations is chosen through a weighted selection method per pedestrian at every iteration. The probability of each move type can be selected by the user and a global randomness factor is introduced to further influence the selection process. Similarly to the previous pedestrian simulation, socialization behavior can take place if both pedestrians are within a user-specified distance from each other and if their social levels are within a particular range of one another. The chance of socialization is scaled based on the difference of social level, where those with more similar values have a higher chance of interaction. A global randomness factor is also introduced to the algorithm to further mediate social interactions in a way which may more closely represent how individuals interact. Once the simulation is finished, the mesh surface can be analyzed by producing a heat map of pedestrian movements, both collective and individual, and by calculating the time each pedestrian spends socializing or moving. While this pedestrian simulation does not yet enable all types of social behaviors, such as an agent’s ability recognize other agents or influence social factors during the simulation, it does create the groundwork for understanding and analyzing how people might move and socialize within a network. ALGORITHM

person type

PEDESTRIAN PROFILE

social interaction level count for each type

MESH SURFACE PROFILE

pedestrian start locations

interact with other pedestrians

OUTPUT

social interaction

3D mesh faces

refinment level

pedestrian travel times

mesh weighting

building locations

ENVIRONMENT PROFILE

tranverse mesh towards similar face weightings

social level location

program type

heat map of mesh utilization

program social level

PROGRAM PROFILE

sphere of influence

program placement

program area program count

stop at programs

Figure 79: Socio-Spatial Pedestrian Simulation Workflow

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map of individual pedestrian travels

5.5.4 Socio-Spatial Pedestrian Simulation Experiments Similarly to the network-based pedestrian simulation, the authors conducted two smallscale experiments on a simplified mesh to test the simulation’s functionality. The first experiment aimed to understand how the implemented social factors impacted the behaviors of the pedestrians. This experiment was conducted by maintaining a mesh and context environment, parameter set, and pedestrian types, and solely altering the sociability values within the system. Each network was then analyzed based on several fitness criteria relating to movement, program usage, and socialization to understand how the varied social settings impacted the pedestrian movements.

Once the authors understood the base mechanisms of the pedestrian simulation, a second experiment was conducted to leverage this tool to select a high performing mesh from a catalog of possible solutions. Additionally, the authors considered the use of the generated data for new program placement over time. This experiment was conducted by maintaining constant pedestrian types, parameters, and sociability factors, and solely altering the program placement on the mesh. This aimed to study the effect of the program locations and their respective sociabilities on the movements and interactions of pedestrians. Each network was then analyzed based on several fitness criteria relating to movement, program usage, and socialization to understand which system performed better.

WEIGHTED BUILDINGS

sociability factor of building

WEIGHTED PROGRAM

sociability factor of function

INFLUENCE ON MESH WEIGHTING

FO RE

LEI

LEI T OR

SIMILA MESH WE R IGHT SIMILA SOCIAL PE RLY OPLE RANDOM WALKER

PEDESTRIAN MOVEMENT

Figure 80: Socio-Spatial Pedestrian Simulation Setup

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5.5.4.1 Pedestrian Simulation Experiment 01 Experiment Description: This experiment focused on altering the social behavior settings of the pedestrian simulation to understand how these factors affected the algorithm’s functionality. Experiment Set-Up: This experiment was conducted by maintaining a consistent mesh and context environment, parameter set, and pedestrian types, and solely altering the sociability values within the system. The algorithm ran for 100 iterations with a total of 24 pedestrians (6 of each type: young adult, single adult, family, and elderly). Four identical networks were tested, where each were given a unique sociability setting for both the program and individual pedestrian social values, where 0.0 is no social interaction and 1.0 is the highest level of social interaction. Each test studied how the alignment or misalignment of pedestrian and program social factors influenced pedestrian behavior, in terms of the pedestrian movement, socialization, and program usage. Test 01 (Mis-aligned Social): Ped. Factors: 0.0-0.2 Program Factors: 0.7-0.9 Test 02 (Low Alignment Social): Ped. Factors: 0.3-0.4 Program Factors: 0.7-0.9 Test 03 (Med. Alignment Social): Ped. Factors: 0.4-0.7 Program Factors: 0.7-0.9 Test 04 (Aligned Social): Ped. Factors: 0.7-0.9 Program Factors: 0.7-0.9

Each network was analyzed based on three fitness objectives: maximum percentage of iterations socializing (number of iterations socializing / total iterations), maximum percentage of program use (number of visits inside program bounds / total number of mesh face visits), and maximum

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pedestrian usage of each mesh face (average number of visits across all mesh faces). As such, the best performing system would allow for program usage and movement along the mesh, yet provide opportunities for socializing. Experiment Results: The experiment showcased that the pedestrian sociability functionality greatly affected the algorithm’s results. As seen in Figure 81, the systems with more aligned pedestrian and program sociability settings saw more program usage and more socialization, due to the clustering of agents towards similarly social spaces. This may simulate a closely integrated community whose surrounding program meets their social and programmatic needs. On the other hand, when there was a complete misalignment of these values, there was very little program usage or socialization, where most agents evenly wandered throughout the mesh space. In this case, the programmed spaces had very little influence on the pedestrians, but the mesh movement was more efficient. However, a balance is required between these two scenarios. High program usage and socialization means that agents tend to remain in similar places rather than traverse the pathway space. In this case, some variation in the social field is required to facilitate agent movement throughout the space. As such, a compromise is required between social interaction and mesh movement efficiency. Experiment Relevance: This experiment built the foundation for the socio-spatial pedestrian simulation, ensuring that its functionality worked as expected. As such, the authors could confidently use the pedestrian simulation moving forward.

TEST 01 MIS-ALIGNED SOCIABILITY

Max. % Social Iterations

Max. Ave. Mesh Face Use

Max. % Social Iterations

Max. % Program Use Iterations

Max. Ave. Mesh Face Use

Max. % Social Iterations

TEST 03 MED. ALIGNED SOCIABILITY

TEST 02 MILDLY ALIGNED SOCIABILITY

Max. % Program Use Iterations

Max. Ave. Mesh Face Use

Max. % Social Iterations

TEST 04 ALIGNED SOCIABILITY

20 Pedestrians

Max. % Program Use Iterations

Max. Ave. Mesh Face Use

0 Pedestrians

Figure 81: Socio-Spatial Pedestrian Simulation Experiment 01

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5.5.4.2 Pedestrian Simulation Experiment 02 Experiment Description: Once the authors understood the base mechanisms of the pedestrian simulation, a second experiment was conducted to leverage this tool to select a high performing individual from a catalog of possible solutions. Experiment Set-Up: This experiment was conducted by maintaining constant pedestrian types, context, seed parameter values, and sociability factors, and solely altering the program placements on the mesh. The algorithm ran for 100 iterations with a total of 24 pedestrians with varying social levels from 0.3 to 0.8 (6 of each type: young adult, single adult, family, and elderly). Four different networks were tested, where the same number and program area of each destination was maintained, but their placements across the mesh were altered, as seen in Figure 82. Once the algorithm was complete, each mesh surface was analyzed based on three fitness objectives: maximum percentage of iterations socializing (number of iterations socializing / total iterations), maximum percentage of program use (number of visits inside program bounds / total number of mesh face visits), and maximum pedestrian usage of each mesh face (average number of visits across all mesh faces). As such, the best performing system would allow for program usage and movement along the mesh yet provided opportunities for socializing. Experiment Results: The experiment showcased that pedestrian sociability could be used alongside mesh movement efficiency as a suitable analysis tool and selection method. As seen in Figure 82, when solely considering the non-social fitness

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criteria (maximum percentage of program use and maximum average mesh face use), Test 04’s mesh system may be seen as the best selection. However, when considering how pedestrians socialized along the mesh, it was clear that Test 04 failed to be ideal. While agents on this mesh did visit program often and traverse the mesh thoroughly, the placements of programs did not facilitate similarly social people to interact often. However, when considering all criteria, a system such as Test 02 may be more balanced. In this case, the program was placed periodically throughout the mesh, providing a gradient of sociability and allowing pedestrians to wander through the mesh surface more freely than in other tests where program was clustered. This facilitated more interactions across the mesh surface due to this increased mixing of similarly social individuals. As such, these types of programmed spaces provided a balance between socialization, program diversity, and mesh movement. The developed pedestrian simulation not only provided analysis of an existing mesh space, but could highlight programs with mis-aligned sociability or areas which remain largely unused or socially barren. As such, the plug-in’s use could expand beyond a post-analysis simulation and become a generative tool for designers. Experiment Relevance: This experiment built the foundation for the pedestrian simulation in understanding its use as an analysis and generation tool. With this experiment, the authors could feel confident in using this tool for urban scale experiments during the Design Development phase.

TEST 01

Max. % Social Iterations

Max. % Program Use Iterations

Max. Ave. Mesh Face Use

TEST 02

Max. % Social Iterations

Max. % Program Use Iterations

Max. Ave. Mesh Face Use

TEST 03

Max. % Social Iterations

Max. % Program Use Iterations

Max. Ave. Mesh Face Use

Max. % Social Iterations

TEST 04

18 Pedestrians

Max. % Program Use Iterations

Max. Ave. Mesh Face Use

0 Pedestrians

Figure 82: Socio-Spatial Pedestrian Simulation Experiment 02

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Discussion The Research experiments explored a wide range of computational methodologies which were foundational to the Design Development phase and the Case Study, particularly in terms of developing the urban network and analyzing the sociability of these spaces. Through simplified applications, these experiments explored the advantages and disadvantages of these tools to create complex systems that continuously adapt to meet the sociability needs of people over time. While these methodologies proved to be useful, the results of these experiments highlighted potential challenges associated with these tools and provided valuable feedback on how to further improve them, particularly as their application scaled up. The temporal graph experiments highlighted how the consideration of different timescales through the temporal graph afforded the creation of a robust network that performed to the same standard even as it changed over time. Yet, the results of the experiment also brought to attention the limitations of predicting the architectural changes that may occur over time. Further research should consider more specifically context-related architectural changes in order to more accurately align the temporal graph with potential future scenarios. Additionally, the results of the experiment showed the timescale of years had the greatest impact on the initial state, temporal graph, and so, further research should examine how to mitigate this effect and equally consider all three timescales. The weighted shortest path algorithm experiments provided a strong framework for translating the temporal graphs to a context-specific urban environment. The results of the experiment showcased the impact of the five weighting parameters on the shortest path as well as how the bias further altered these paths. While these five parameters related to a range of design goals, further research should consider other contextspecific factors related to the sociability of the spaces and the people in order to better enable these systems to adapt to people’s changing needs over time. The co-evolutionary algorithm experiments showed the parallel evolution of interrelated systems provided a better framework for optimizing complex systems than a sequential approach. Yet,

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the simplified nature of the experiment did not fully explore how the co-evolutionary algorithm would perform for more complex scenarios or larger scales. Therefore, further experiments which employ the co-evolutionary algorithm should carefully analyze its performance both intermittently and after completion. The pedestrian simulation experiments showcased the relevance in analyzing mass social behaviors and subsequently using the resultant data as a generative tool. In doing so, a direct relationship between architectural design and social behaviors could be carefully investigated. However, the two developed simulations could be improved by integrating additional social behaviors. Currently, the simulations solely allowed for social interactions. However, these algorithms could more closely resemble human socialization with the addition of clustering and group-minded behaviors, wandering, dynamic goals, or the ability to recognize others. In doing so, the algorithm’s application could extend into other domains not explored during this research.

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DESIGN PROCESS

06 Design Process

6.1 M.Sc. Revised Experiments 6.2 Micro-Urban Network 6.3 Macro-Urban Network 6.4 Pathway Architectural Design

The initial experiments developed during the Design Research phase facilitated higher level studies which were conducted to more deeply investigate the tower’s urban systems. In this phase, each experiment developed the final workflow for formulating the revised tower scales, as well as the new micro-urban and urban scales of the research. Each workflow was interconnected with the others to create a seamless, holistic system where outputs of one fed directly into the next. Additionally, both urban scales implemented the developed pedestrian simulation tools at two different scales. At the micro-urban scale, the pedestrian simulation was used to analyze and select high performing local pedestrian networks which facilitated sociability on a collective scale. At the urban scale, the simulation was used to analyze portions of architectural bridge designs and to generate potential future adaptations to continuously meet the social needs of the occupants. Such a dynamic, multi-scalar framework offers a new housing solution and urban design strategy which meets the density needs of cities while also facilitating continuous spatial changes to match the sociability demands of people over time. Once developed, this comprehensive workflow was tested in the Case Study phase.

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PRIVATE-PUBLIC URBAN NETWORK

MICRO-URBAN PATHWAYS

TOWER MORPHOLOGY STRUCTURAL

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AL ORGANIZATION ATI SP

YEARS

MATIC TOPO RAM LOG OG R Y P

MONTHS

DISTRIBUTION

SOCIABILITY SCORE

DECADES

FABRICATION SYSTEM SYSTEM

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6.1 M.Sc. Revised Experiments As discussed in Experiment 5.4, it was necessary to revisit the computational workflow developed during the M.Sc. phase and reconsider its sequential nature. Experiment 5.4.1 highlighted the applicability of the cooperative co-evolutionary algorithm as a tool for simultaneously optimizing interconnected parts of a complex system. This experiment built upon the results of Experiment 5.4.1, which looked at the co-

evolution of the structural system and public-private distribution within a single segment of the tower, by applying the same process across the entire tower simultaneously. In doing so, the experiment considered the inherently connected nature of these tower layers and developed a more cohesive system which better related to surrounding urban context.

6.1.1 Co-Evolutionary Algorithm: Tower, Structure, Public-Private Distribution Experiment Description: The experiment utilized a cooperative co-evolutionary algorithm to simultaneously optimize the full structural system and public-private distribution across the entire tower and develop a synergistic relationship between all of the tower layers and systems. Experiment Set-Up: The co-evolutionary algorithm simultaneously evolved two populations. For both populations, the tower morphology was a shared element, where the footprint area (m2), the length:width ratio, the auxiliary tower selection, the segment count, the structural height (m), and the auxiliary tower heights (m) were controlled by seven genes. As a shared element between the two populations, it was evaluated for maximizing its total daylight hours, minimizing its wind angle deflection, and maximizing its floor-to-area ratio. The first population evolved the structural system, which abstracted the multi-layered and directional fiber principles of the bamboo stem, on the exterior of the tower morphology. The structural system was controlled by five genes which determined the shell thickness (cm), the curve division distance (m), the curve connection type, the beam diameter (cm), and the beam thickness (cm) and aimed to optimize for two fitness criteria: minimized embodied carbon and minimized deformation. The second population evolved the public-private distribution, which employed a random walk algorithm to incrementally expand the public and private voxels, on the interior of the tower morphology. The random walk algorithm was

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controlled by nine genes which determined the starting seed, starting count, and the growth rate for the public, private, and transitional space voxels each and aimed to optimize for six fitness criteria: maximized internal public space factors, minimized proximity to public context, maximized internal private space factors, minimized proximity to residential context, maximized transitional space factors, and minimized proximity to buildings and pedestrians. Each of these separate populations optimized independently through a traditional evolutionary algorithm for ten generations with ten individuals in each generation. After the tenth generation, the populations were brought together to be evaluated and ranked collectively based upon the shared fitness criteria of the box. Then, this combined population optimized towards their shared fitness criteria through a traditional evolutionary algorithm for five generations in order to realign the independent optimizations to the results of the other. After these five generations, the shared population separated back into two populations and optimized independently for their own fitness criteria for another ten generations before coming back together again. This back-and-forth between optimizing separately for independent fitness criteria and optimizing collectively for shared fitness criteria continued for five cycles before the co-evolutionary algorithm terminated, and the Pareto Front members were identified for further evaluation and consideration.

TOWER MORPHOLOGY

g1 | Footprint Area (m2) g2 | Length:Width Ratio

g3 | Auxillary Tower Selection

g4 | Segment Count g5 | Structural Height (m)

g6 | Auxillary Tower Heights (m)

g1 | Shell Thickness

g1 | Public Start Seed g2 | Private Start Seed g3 | Transition Start Seed

g7 | Public Growth Rate g8 | Private Growth Rate g9 | Transition Growth Rate

g15-20 | Beam Diameter g21-26 | Beam Shell Thickness

PUBLIC PRIVATE DISTRIBUTION

STRUCTURAL SYSTEM

Figure 83: Co-Evolutionary Algorithm Setup

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Experiment Results: The results of the experiment emphasized the ability for a cooperative coevolutionary algorithm to be a powerful tool for simultaneously optimizing interconnected parts of a complex system. In particular, the experiment showed how the cooperative co-evolutionary algorithm continued to perform well and achieve the desired objectives when scaled up, as compared to Experiment 5.4.1, across the entire tower.

interconnected systems, where none dominate another. This was observed through the parallel coordinate plot and the mean value graph, where each fitness criteria evenly balance alongside one another. Such a convergence emphasized the interconnected nature of the systems and showed how the cooperative co-evolutionary algorithm enabled these discrete systems to inform the optimizations of one another.

Looking at the Pareto Front members of the optimization, a diversity of tower morphologies in combination with different structural systems and public-private distributions showcased the capabilities for the CoEA to explore a broad design space and provide a wide range of potential design options depending on the designer’s goals. These phenotypes, coupled with their fitness criteria highlighted a balance between the three

Experiment Relevance: The cooperative coevolutionary algorithm enhanced the computational workflow developed through this research such that it better considered not only its own context but also the relationship between its own internal systems. The experiment highlighted the algorithms ability to address the challenges of traditional evolutionary algorithms as well as extend throughout various scales.

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Figure 84: Full Tower CoEA Design Space

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Increased Performance

Gen35

Gen0

Shared FC1

Shared FC2

Shared FC3

Population 01 FC1

Population 01 FC2

Population 01 FC3

Population 01 FC4

Figure 85: Full Tower CoEA Parallel Coordinates Plot - Population 01

Shared FC1 Mean Generation Fitness Value

Shared FC2 Shared FC3

Population 01 FC1 Population 01 FC2 Population 01 FC3 0

Generation Figure 86: Full Tower CoEA Mean Value Graph - Population 01

Shared FC1

Shared FC2

Population 01 FC1

Population 01 FC2

Shared FC3

Population 01 FC3

Figure 87: Full Tower CoEA Standard Deviation Graph - Population 01

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Population 01 FC4

Increased Performance

Gen35

Gen0

Shared FC1

Shared FC2

Shared FC3

Population 02 Population 02 Population 02 Population 02 Population 02 Population 02 FC1 FC2 FC3 FC4 FC5 FC6

Figure 88: Full Tower CoEA Parallel Coordinates Plot - Population 02 Shared FC1

Mean Generation Fitness Value

Shared FC2 Shared FC3

Population 02 FC1 Population 02 FC2 Population 02 FC3 Population 02 FC4 Population 02 FC5

Population 02 FC6

Generation

Figure 90: Full Tower CoEA Mean Value Graph - Population 02

Shared FC1

Shared FC2

Shared FC3

Population 02 FC1

Population 02 FC2

Population 02 FC3

Population 02 FC4

Population 02 FC5

Population 02 FC6

Figure 89: Full Tower CoEA Standard Deviation Graph - Population 02

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6.1.2 Co-Evolutionary Algorithm: Tower, Structure, Public-Private Distribution Post-Analysis Experiment Description: The experiment aimed to post-analyze the results of Experiment 6.1.1 by comparing them to a multi-objective optimization of the same scenario using a traditional evolutionary algorithm, where the fitness criteria for both populations as well as the shared ones are optimized simultaneously. Experiment Set-Up: The set-up for the experiment is identical to that of Experiment 6.1.1, where the optimization employed upon the tower morphology, the structural system, and the public-private distribution across the entire tower. The difference between this experiment and the previous one lies in the optimization algorithm employed. While Experiment 6.1.1 utilized a cooperative co-evolutionary algorithm to simultaneously, this experiment employed a traditional evolutionary algorithm to simultaneously evolve the fitness criteria of both the structural system and the publicprivate distribution together. The fitness criteria were minimized primary angle, maximized angle difference between layers, minimized displacement, minimized embodied carbon, maximized public internal needs, minimized proximity to public context, maximized private internal needs, minimized proximity to private context, maximized transition internal needs, minimized proximity to pedestrian zones. The evolutionary algorithm ran for 35 generations with 10 individuals per generation, the same as Experiment 6.1.1, and

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the plugin Wallacei for Grasshopper was used to conduct the optimization. Experiment Results: By looking at the standard deviation graphs from the results of the optimization, it was observed that none of the fitness criteria were able to optimize due to the high number of fitness criteria. Throughout all of the generations, the individuals maintained a wide range of genes and fitness values without any indication of converging. These results, when compared to that of the previous experiment, highlighted the ability for the cooperative co-evolutionary algorithm to carefully dissect a complex problem into more manageable parts and enable all of the fitness criteria to improve. As mentioned in Experiment 5.4.2, it was difficult to directly compared these two experiments due to the technical differences of the genetic algorithm tools utilized, but at a high-level, the results of the experiment emphasized the ways in which a cooperative co-evolutionary algorithm may be better suited to address more complex problem environment than traditional evolutionary algorithms. Experiment Relevance: The post-analysis of the cooperative co-evolutionary algorithm supported it use in the computational workflow as a tool for developing cohesive tower system which is well connected to its surrounding urban context.

-15.72

-6.94

-1.84

10.62

19.41

28.19

36.97

0.0008

FC01 | Min. Primary Angle

-59.79

-32.81

-5.82

21.17

0.0009

-0.59

-0.14

0.29

0.73

1.18

48.16

1.62

FC05 | Max. Public Internal Needs

0.941

2.77

4.61

8.27

10.11

11.94

FC08 | Min. Proximity to Private Context

0.0148

0.0165

0.0182

0.0201

FC02 | Max. Angle Difference Between Layers

75.15

102.14

-555,284

6,373

FC03 | Min. Displacement

-1.03

0.0114

568,031

1,129,689

1,691,347

2,253,005

2,814,663

FC04 | Min. Embodied Carbon

53.82

60.64

67.47

74.30

81.12

87.95

94.78

FC06 | Min. Proximity to Public Context

-0.08

0.01

0.11

0.21

0.31

0.41

0.51

FC09 | Max. Transition Internal Needs

-0.339

-0.349

0.269

0.574

0.878

1.18

1.49

FC07 | Max. Private Internal Needs

35.36

40.38

45.41

50.44

55.46

60.49

65.52

FC10 | Min. Proximity to Pedestrian Zones

Figure 91: Full Tower CoEA Standard Deviation Graph - Post-Analysis

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6.2 Micro-Urban Network Once the tower workflow was redesigned to better facilitate context involvement, the authors continued forward to consider how the tower connected with its urban surroundings. This was achieved through a series of pedestrian networks. On the micro-urban scale, these networks served as bridges between the tower and its local context, facilitating socialization

through network connections. On the larger urban scale, these pathways became programmed spaces and multi-modal transportation networks, creating new urban spaces for socialization along its path. Both scales enabled social interaction at a different scale and time spans, yet were inherently interconnected through the urban environment.

6.2.1 Micro-Urban Pathways Experiment Description: This experiment developed a workflow to generate various micro-urban networks which morphologically responded to its surrounding social fabric and local context. This experiment utilized the results of the Tower, Structure, and Private-Public Distribution CoEA (Experiment 6.1) by selecting a highly performing tower from the CoEA as the a basis to develop the micro-urban pathway workflow, using the newly developed transitional space as the connection between the tower and its context. Since the research developed a workflow and the parameters of its applications potentially might vary drastically, the selected pareto front member was the lowest average of fitness rankings to ensure a balanced performance regardless of the workflow’s application. This experiment also employed a variation of the weighted shortest walk algorithm (Experiment 5.3) to create the urban pathways. Experiment Set-Up: The experiment utilized a multi-objective EA using Wallacei with the default algorithm parameters to generate micro-urban networks. The EA ran for 50 generations with 20 individuals each, with a search space of 9.7 x 1030. The primitive form consisted of the selected P2 Tower surrounded by two blocks of its local context. To generate the networks, several nodes from the P2 Tower’s transitional zone were selected as starting seeds. These nodes were chosen by several genes and their heights were mediated by the average heights of the surrounding buildings. At these node heights, gene-controlled offsets were created from each context building. Their offset intersections were then weighted based on the combined sociabilities of the surrounding context. Next, a shortest weighted path was calculated for each node, where the search radius and segment length were controlled by genes. Finally, connections were created between nearby paths or buildings using a gene-controlled radius. 142

Design Development

The EA optimized towards four fitness criteria: maximum average closeness centrality, maximum path efficiency (total path length/total distance from start to end point), maximum percentage of connected context buildings (total connected / total buildings), and minimum displacement (cm). As such, the goal was to obtain paths which were well connected, efficient in terms of path length and material usage, and structurally stable. Experiment Results: The EA generated 77 pareto front members. All fitness criteria (FCs) continued to improve over the course of the algorithm. However, FC1 and FC3 did not optimize as well as the other criteria, which showed a small conflict between the FC1, 3 and FC2, 4. Looking at the morphologies of the pareto front members, this conflict was further showcased. It was clear that the generated individuals struggled to become both connected to the urban context and efficient or structural. This may signal the need to introduce more weighting criteria in the weighted shortest walk algorithm or may be due to the type and locations of buildings on site. Therefore, further consideration should be given to counter such occurrences. Experiment Relevance: This experiment created a workflow to connect the tower and its local context. In doing so, the micro-urban network provided space to bridge neighborhoods and facilitate sociability within a community setting. This potential for social interaction was explored in the next experiment using the network-scale pedestrian simulation. Within the overarching workflow of the research, this experiment followed the Tower, Structure, and Public-Private Co-EA, integrating its resultant morphologies as a base. The workflow developed from this experiment fed into the urban scale network, which aimed to bridge multiple microurban networks. This workflow will be showcased in the Case Study Section.

TOWER, STRUCTURE PUBLIC-PRIVATE DISTRIBUTION

FC01 | Max. Average Closeness Centrality

EXISTING CONTEXT

g1 | Pathway Start Seed

FC02 | Max. Path Efficiency

g2 | Pathway Num. Start Points

g14-24 | Search Radius g25 | Iterations

g26-36 | Building Connection Radius g37 | Ground Connection Frequency g38-40 | Assign Destinations

FC04 | Min. Displacement

FC03 | Min. Percentage of Connected Buildings

g3-13 | Building Offset Distance

URBAN NETWORK SCALE

Figure 92: Micro-Urban Network EA Set-up

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-0.937

-0.22

0.496

1.21

1.93

2.29

FC01 | Max. Average Closeness Centrality Figure 93: Micro-Urban Network EA Results

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3.00

-0.395

0.865

2.13

3.39

4.65

FC02 | Max. Path Efficiency

5.91

7.17

Last Gen.Last Gen.

First Gen. First Gen.

-3.42 -3.42

-1.87 -1.87

1.24 1.24

3.42 3.42

5.37 5.37

8,24 8,24

10.17 10.17

FC03 FC03 | Max. | Max. %% Connected Connected Context Context Buildings Buildings

-17.385-17.385 -2.494-2.494

12.39712.397 27.28927.289

42.18142.181

57.07357.073

71.96571.965

FC04 FC04 | Min. | Min. Displacement Displacement

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6.2.2 Micro-Urban Scale: Network Pedestrian Simulation Analysis Experiment Description: In order to more closely understand the social impacts of the micro-urban networks, it was necessary to integrate a pedestrian simulation within the workflow to further analyze the significance of the pathways. This experiment integrated the network-based social pedestrian simulation (Experiment 5.2.2) to analyze and select highly performative networks. Since the research developed a workflow for network analysis, this experiment focused on testing the use of the pedestrian simulation, along with a set of developed fitness objectives, to select urban networks which perform well for both the network efficiency and the socialization. To do this, three pareto front members from the Micro-Scale Urban Network experiment (Experiment 6.2.1) were analyzed using the developed pedestrian simulation. More specifically, the lowest relative difference individual, lowest average rank individual, and individual with most repeated values were chosen from the pareto front members to provide a range of performances, while still ensuring that the selected networks were not dominated by any others from the previous experiment. Experiment Set-Up: Each network was analyzed using the network-based social pedestrian simulation. The algorithm ran for 250 iterations using a total of 60 pedestrians with varying social levels from 0.1 to 0.9 based on the type of pedestrian (15 of each type: young adult, single adult, family, and elderly). The destination locations and parameters were selected based on existing program in the local site context. All pedestrian types, destinations, and seed values remained constant throughout all three experiments. Once the simulation was complete, the networks were analyzed based on three fitness criteria: maximum usage of the pedestrian network (average number of visits to each node in the network), maximum percentage social interaction (total social interactions / total actions taken), and maximum travel efficiency (total movements / total actions taken). Using these criteria, the best performing system would allow pedestrians to efficiently travel

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to their destinations and ensure that the network was being fully utilized, while also enabling similarly social individuals to connect regularly throughout the network. Experiment Results: The results showcased the pedestrian simulation and developed fitness objectives were successful in analyzing and subsequently guiding the section process of microurban network systems. As seen in Figure 94, although each individual was non-dominated as a pareto front member during the Micro-Urban Network experiment, it was clear that not every network performed well when considering social characteristics and network usage as well. For example, Test 02 performed well when considering its architectural and structural characteristics in the previous experiment, yet the generated network was shown to be highly inefficient and socially void during this experiment. On the other hand, Test 03 was highly effective in terms of the efficiency and utilization of the network system and provided ample opportunities for individuals to interact. In this case, Test 03 may be selected as the best performing individual with desirable architectural and social characteristics. As such, it is clear that the Micro-Urban Scale Network experiment required the use of a pedestrian simulation and additional fitness criteria to more holistically select appropriate micro-urban networks. Experiment Relevance: The results showcased that using the pedestrian simulation and the created fitness criteria in conjunction with the previous experiment allowed for the development and selection of highly connected, structural, and socially rich micro-urban network systems. In doing so, the micro-urban network can bridge local contexts and facilitate sociability within a community setting. Within the overarching workflow of the research, this experiment worked in conjunction with the Micro-Urban Scale Network EA. The morphologies from these two experiments fed into the urban scale network, which aimed to bridge multiple local networks. This workflow will be showcased in the Case Study Section.

TEST 01 (LOWEST RELATIVE DIFFERENCE)

Max. Use of New Network

Max. Travel Efficiency

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TEST 02 (LOWEST AVERAGE RANK)

Max. Use of New Network

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Max. Use of New Network 20 Pedestrians

Max. Travel Efficiency

Max. Social Interaction

0 Pedestrians

Figure 94: Micro-Urban Network Post-Analysis

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6.3 Macro-Urban Network The experiment employed and built upon the results from Experiment 5.2 and 5.3 in order to develop a macro-urban network which adapted to the shifting sociability of its residents and performed to the same standard over time. A temporal graph was generated to interconnect scattered micro-urban networks

across varying timescales, and a weighted shortest path algorithm translated this temporal graph to a context-specific urban environment in order to create multimodal corridors linking different P2 Towers throughout Hong Kong.

6.3.1 Urban Network Relationships Experiment Description: The experiment conducted a multi-objective optimization to balance the performance an initial state temporal graph with that of the proceeding graphs for different temporal shifts. The optimization process built upon the results of Experiment 5.2.1 and simultaneously considered each timescale as to reconcile their different impacts on the initial system. Experiment Set-Up: After selecting a series of open lots across Hong Kong, an initial state, temporal graph was randomly generated, where the nodes represented these open lots at varying stages of time and the edges represented multimodal corridors physically connecting them, also at varying stages of time. These varying stages of time existed in three architectural states: Constructed, Activated, and Deactivated. If a node or edge did not exist in the temporal graph, then architecturally, it was considered unbuilt. The random generation of the initial state, temporal graph was controlled by five genes: the total node count, the construction percentage, the node activation rate, the edge activation rate, and a random seed. The initial state, temporal graph was evaluated based upon three fitness criteria: minimized edge count, maximized closeness centrality, and maximized mean clustering. After the initial state was generated, three consecutive temporal shifts were applied to this graph, representing architectural changes that may occur at each timescale in the same manner as Experiment 5.2.1. One gene controlled the timescale at which the temporal shifts were applied in order to simultaneously consider multiple timescales throughout the optimization process. After each shift, the graph was re-evaluated for the same three fitness criteria as the initial state graph, and the values were averaged across all three shifts to create three conflicting fitness criteria, challenging the performance of the initial state graph with 148

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that of the shifted state graphs. The evolutionary algorithm for each timescale ran for 50 generations with 50 individuals in each generation. Experiment Results: The evolutionary algorithm evenly considered all three timescales, where 15,912 individuals shifted on the timescale of days, 15,516 individuals shifted on the timescale of months, and 13,572 individuals shifted on the timescale of years, and generated 305 Pareto Front members, which varied widely in terms of node and edge count.

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Figure 95: Urban Network Data Comparison

The standard deviation graphs for the fitness criteria related to the initial state, temporal graph (FC01 to FC03) and the shifted, temporal graph (FC04 to FC 06) showed the impact of considering the timescales simultaneously in the optimization, where the initial state, temporal graph did not optimize well as the static graph in Experiment 5.2.1 that did not consider any timescales.

clustering coefficient by initiating additional nodes and edges in response to temporal shifts across the timescales of days, months, and years. Experiment Relevance: The experiment developed an initial state, temporal graph which considered all three timescales simultaneously and continued to maintain a strong performance, even as conditions changed. As part of the computational workflow developed through this research, one of the Pareto Front members was selected for further consideration to be translated through the weighted shortest path algorithm into the multimodal corridors linking the open lots.

Yet, by comparing the average values across all of the fitness criteria as well as other parameters related to the initial graph, the experiment showed the initial state, temporal graph maintained a strong performance in terms of closeness centrality and

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Figure 96: Urban Network EA Results

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6.3.2 Urban Network Paths Experiment Description: The experiment selected a representative temporal graph from Experiment 6.3.1 to translate to a context-specific urban environment in order to create multimodal corridors linking different P2 Towers throughout Hong Kong. Experiment Set-Up: The experiment utilized the Pareto Front member from Experiment 6.3.1 with the lowest average of fitness ranking to be translated into urban network paths as a way to generalize the workflow and the results of the experiment for varying conditions. After selecting an urban network relationship, the same open-source data as Experiment 5.3.1 was utilized to construct an accurate digital model of the urban context which also stored additional metadata. Then, the existing road network was simplified to a graph network, where the nodes represented road intersections, and the edges represented the roads connecting these intersections. The edges in this digital model were further analyzed for the same five parameters as Experiment 5.3.1, which were then normalized from 0 to 1, biased to

prioritize particular design goals, summed together for each edge, and assigned as the weighting for its associated edge. Lastly, the selected temporal graph identified which open lots needed to be connected physically, so Dijkstra’s Algorithm was applied to the graph network of the urban context to identify a contextspecific path connecting all of the open lots. Experiment Results: Through the shortest path algorithm, the initial state, urban network paths successfully translated the properties of the temporal graph to the context-specific, urban environment of Hong Kong. The generated urban network paths showcased a diverse set of pathways which connect and traverse large swaths of Hong Kong’s urban environment, extending the sociability influence of the research well beyond the confines of the immediate locations for the P2 Towers. Experiment Relevance: The generated initial state, urban network paths provide a framework to begin designing the architectural implications of the multimodal corridors for the entire urban network.

6.3.3 Urban Network Paths - Temporal Shifts Experiment Description: The experiment built upon the results of Experiment 6.3.2 by analyzing how the initial state, urban network paths changed in response to shifts at the three timescales of days, months, and years. Experiment Set-Up: The experiment followed the same set-up as Experiment 6.3.2 in terms of the open-source data utilized, the translation of the road network to a graph network, the analysis of the five parameters, and the weighting of the edges. It utilized the selected urban network relationships from Experiment 6.3.2, but instead of applying the weighted shortest path algorithm to the initial state, temporal graph, it was applied to the shifted temporal graphs for the timescale of days, months, and years. Experiment Results: Comparing the initial state, urban network paths from Experiment 6.3.2 to the 150

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resultant urban network paths from this experiment, the impact of the temporal shifts became evident. In particular, the urban network paths maintained a strong performance and continued to connect a wide swath of Hong Kong’s urban environment after the temporal shifts. Experiment Relevance: The results of the experiment validated the results of Experiment 6.3.1, where the robustness of the initial state, temporal graph was maintained even as it was translated to the urban environment.

Figure 97: Multimodal Corridors - Initial State

Figure 98: Multimodal Corridors - Days Shift

Figure 99: Multimodal Corridors - Years Shift

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6.4 Pathway Architectural Design Once the pedestrian pathways for the M.Arch stage were generated, the paths’ architectural forms were developed. Since the pathways adapted over time, it was important to develop a catalog of possible solutions which catered towards different architectural and social needs. Three unique bridge typologies were generated for pedestrian, light rail, and pedestrian and light rail use. Each category contained four bridge sections, which were optimized for minimum ground disturbance, maximum capacity, maximum structural capacity, or a balanced need. As such, a catalog of twelve

types were crafted for various structural, program, and social needs. Since adaptation was a key factor for the pathway architectural design, all bridge sections were constructed from the same 3m x 3m x 3m module. This module was sized to accommodate the required program heights and to allow for a group of people to transport each cell. Additionally, the module design enabled easy assembly and disassembly. In this way, the catalog and the module design facilitated urban scale adaptation over time.

6.4.1 Pathway Catalog Experiment Experiment Description: This experiment developed a catalog of bridge sections which optimized for three categories of context-based and social need. This experiment utilized information from the Micro- and Macro-Urban Pathway experiments (Experiment 6.2 and 6.3). More specifically, this experiment used the architectural and social contexts which these pathways passed through to develop the types of necessary bridge sections for the catalog. Since the research developed a workflow, this approach enabled a variety of needs to be integrated into the catalog. During the Case Study section, the bridge catalog will then be applied along the pedestrian pathways where required.

and the module’s structural dimensions were controlled by genes. The EA optimized towards four fitness criteria. The first three remained constant among all three algorithms: minimum displacement (cm), minimum ground area (m2), and minimum ground daylighting (hr). The fourth objective was specific to each algorithm. The pedestrian bridge, light rail, and mixed bridge optimized towards maximum connectivity, maximum light rail lines, and maximum bridge connections respectively. As such, the goal was to obtain structurally stable, minimally invasive, and typology specific pathways.

Experiment Set-Up: This experiment conducted three multi-objective EAs using Wallacei with default algorithm parameters to generate bridge sections for the pedestrian only, light rail only, and pedestrian and light rail bridge types. The three EAs ran for 50 generations and 15 individuals in each, with search spaces of 1.9 x 1021.

Experiment Results: All three EAs optimized well, with incremental improvements with each passing generation, as seen in the standard deviation graphs (Fig. 101). Looking at the morphologies of each EA, it was clear that each one generated unique pareto front members which were optimized towards their specific goals, while maintaining a variation within the population. As such, the intention to create context and need-specific morphologies which can be used across a variety of scenarios was successful.

Each EA employed the same primitive and genes, but integrated different objectives related to typology specific goals. The primitive was generated through hierarchical aggregation of the base component using a Grasshopper plugin, Wasp. The first aggregation generated the bridge’s section and the second generated the bridge platform. Each section was spaced 21 meters apart to accommodate appropriate structural spans and module dimensions. The aggregation’s parameters

Experiment Relevance: This experiment developed a catalog of bridge sections which were context- and need-specific. In the following stage, four individuals from each EA’s pareto front will be selected for the catalog which were optimized towards the following four goals: minimum ground disturbance, maximum capacity, maximum structural capacity, and a balanced need. The generated catalog will be applied to the pedestrian pathways in the Case Study section.

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EXISTING CONTEXT

TEMPORAL GRAPH NETWORK

FC01 | Min. Displacement

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g3-6 | Connecting Bridges g7-8 | Secondary Seed and Count

Figure 100: Pathway Architectural Design EA Set-up

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Figure 101: Pathway Architectural Design EA Results

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PEDESTRIAN BRIDGE PEDESTRIAN BRIDGE

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Once all three EAs were conducted in the previous stage, the pareto front members were analyzed for the following criteria: minimum ground disturbance, maximum program capacity, and maximum structural capacity. The best performing individual in each of the three categories, along with the balanced individual,

Figure 102: Pathway Architectural Catalog

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were selected for use in the catalog (See Appendix A.12). In doing so, the resultant morphologies provided the range of use cases, program typologies, and structural characteristics which allowed for application along multiple unique contexts across an urban pedestrian network. The next experiment following this stage will analyze one developed bridge sections using the socio-spatial pedestrian simulation to understand how program sociabilities affect spatial movement and how program adaptations could occur using this tool.

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6.4.2 Pathway Segment: Spatial Pedestrian Simulation Analysis Experiment Description: This experiment utilized the socio-spatial pedestrian simulation developed during the Research Development phase to analyze how program placement and sociability could affect the behavior of pedestrians along the developed bridge sections, as well as how this simulation could drive future adaptations within a space. Experiment Set-Up: This experiment analyzed one bridge section developed during the Pathway Architectural Design experiment (Experiment 6.4) over three states and two major shifts during the timespan of twelve months. The chosen section was a Balanced Need catalog option, in order to explore a representative member among all bridge sections. At each time shift, the socio-spatial pedestrian simulation was conducted to understand how each change altered the social field of the bridge section. Among all three states, the algorithm parameters, seed values, program areas, and pedestrian values remained constant. Only program sociability values and counts were altered. Each simulation ran for 200 iterations with 48 pedestrians with varying social levels from 0.6 to 0.9 (12 of each type: young adult, single adult, family, and elderly). The first shift between state one and two saw a change in the leisure program’s social value towards a value within the range of the pedestrians’ sociabilities. This architecturally represented a change of program typology within the category of leisure spaces. The second shift saw a change in the number of programs, where one new leisure and food type program were introduced along the bridge section. These programs were spread relatively evenly across the mesh surface and the total program areas were maintained. Architecturally, this shift represented the downsizing of some businesses and the introduction of new ones along the mesh. Once the algorithm was complete, each mesh surface was analyzed based on three fitness objectives: maximum percentage of iterations socializing (number of iterations socializing / total iterations), maximum percentage of program use (number of visits inside program bounds / total number of mesh face visits), and maximum pedestrian usage of each mesh face (average number of visits across all mesh faces). As such, the best performing system would

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allow for program usage and movement along the mesh, yet provide opportunities for socializing. Experiment Results: Overall, the three states showcased the importance of program sociability and placement along a mesh surface when considering pedestrian movement. During the first state, pedestrians rarely visited the leisure program despite its central location on the mesh. This was due to the mis-alignment of the leisure program’s sociability (0.3) and the pedestrians’ sociabilities (0.6-0.9). This also influenced the pedestrians’ lack of movement and socialization across the mesh surface. Pedestrians often clustered in one space and were not able to move and interact with the larger population. During the second state, the leisure program’s sociability (0.8) was altered to a value within the pedestrians’ sociabilities (0.6-0.9). As such, pedestrians began to visit this program more often, thereby traversing more of the mesh surface and gaining opportunities to interact with more individuals. However, there was still visible clustering of individuals at this stage. During the final shift, additional programs were introduced on site and their areas were adjusted to maintain a constant total program area. During this state, the pedestrians were able to fully utilize the mesh surface, moving and socializing throughout multiple locations. As such, their clustering tendencies were minimized. While the dispersed program placement reduced the amount of time pedestrians spent within each program, it did increase both the mesh usage and the socialization, which provided a more balanced performance among all three fitness criteria. Experiment Relevance: This experiment showcased how the socio-spatial pedestrian simulation tool could be leveraged to both analyze and generate program placements on a mesh surface. This is highly useful when considering the wide variation of context and needs throughout the developed pedestrian pathway system. As such, this methodology would be employed across multiple pathway locations to understand and generate potential adaptations over time.

TEST 01: MONTH 1

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Figure 103: Pathway Pedestrian Simulation Experiment

Discussion The Design Development phase extended the workflow created during the M.Sc phase to develop a comprehensive workflow for the design and construction of a tower and urban system which met the density needs of Hong Kong while facilitating continuous spatial changes to match the needs of people over time. The workflows and processes developed during this stage deeply investigated innovative methodologies, algorithms, and simulations which facilitated such a temporal, context-specific solution. The use of temporal graph networks introduced social adaptability on an urban network level in accordance to particular events on three major timescales. Additionally, the particular application of this method within an evolutionary algorithm enabled these adaptations to be quantified and evaluated together, ensuring that the holistic system provided appropriate functionalities which meet the social needs of the urban residents at any time. The use of novel pedestrian simulations continued such a careful consideration of evolving sociability. Since the urban scale considered sociability as a collective notion, the developed social pedestrian simulations were essential in analyzing mass behaviors and subsequently using the resultant data as a generative tool. In doing so, a direct relationship between architectural design and social behaviors could be carefully investigated. While this phase was shown to be successful, there were some elements which could be improved. First the results of the micro-scale pathway experiment showcased large conflicts among the fitness criteria. It was clear that the generated individuals struggled to connect with the urban context while maintaining efficient and structural paths. Potentially, this type of conflict was generated due to the limited network weighting factors and restricted algorithm parameters. As such, the methodology should be reconsidered to mitigate such occurrences. Additionally, the predictive nature of the temporal graph and its results were unverified and unverifiable. The multi-objective optimization of the initial state, temporal graph proved how the methodology may begin to consider the added dimension of time, but the temporal shifts were limited in terms of their scope. Further research should look more closely at

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the architectural implications of the temporal shifts applied to the initial state graph. Consideration of knowledge from other field such as economics or sociology or climatology may help provide frameworks for predicting the potential changes which may occur over time. If implemented, these improvements would enable the designed system to gain a more intuitive and functional connection to the urban environment to more easily address the issues of densification and sociability on a larger scale.

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CASE STUDY

07 Case Study

7.1 Design Narratives 7.2 Site Selection 7.3 Tower Morphology 7.4 Structural System 7.5 Public-Private Distribution 7.6 Component Design 7.7 Pedestrian Walkways 7.8 Multimodal Corridors 7.9 The P2 Tower 7.10 Multi-scalar Adaptation

The relevance and use of the comprehensive workflow developed during the thesis was tested through a case study. The case study was driven by four interwoven narratives which guided the design and implementation of the tower and urban system’s social and programmatic needs. These narratives were selected to provide a wide range of perspectives, lifestyles, and requirements in order to more comprehensively show the capabilities of the developed system. In parallel, a site in Hong Kong was selected to drive the context-specific parameters of the design proposal. This site was chosen due to its intense growth and densification over the last ten years. Such a site provided marked shifts in density, and in turn social needs, throughout its lifetime which could further exemplify the use of the P2 Tower’s urban scale workflows. Using the selected narratives and site, the developed workflow was implemented to create a context-specific and socially responsive tower, micro-urban, and urban scale design. The system’s adaptive responses were also showcased at several scales throughout the case study to investigate the abilities of the workflow to continuously meet the sociability requirements of its occupants. In doing so, the workflow could simultaneously cope with the rising densification of the context, yet facilitate growth and adaptation to enable socially rich and programmatically functional lifestyles for the local population in Hong Kong.

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Design Narratives The impact of the proposed design workflow was seen in respect to the lives of the residents. Their local programs and conditions were particularly tailored to their specific needs, where large clusters of each program were placed near the occupants who use them the most and smaller pockets of programs were placed near those with less of a need. As such, the tower and the urban system were tuned to the particular requirements of the residents at this moment in their lives. A representative sample of the implemented resident typologies is seen below.

YOUNG COUPLE (30s)

COUPLE WITH CHILDREN (40-50s)

EMPTY NESTERS (60s)

ELDERLY COUPLE (70-80s)

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Site Selection Buildings: 5138 Area: 2.34545 x 106 m2 Elevation: -6.15 mPD to 58.85 mPD Roadways: 64,423.60m Pedestrian Pathways: 151,984.75m Potential Sites: 42 Lots

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The P2 Tower Re-Neighboring the Vertical City

To thoroughly showcase the functionality and importance of the developed workflow during the case study, the authors selected a site which contained a highly diverse program range and experienced drastic density growth in recent years. In doing so, the selected area most clearly showcased how the workflow can enable critical gradients of sociability across both time and space.

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Tower Morphology Multi-Objective Optimization

Tower Morphology

Once a site was selected, the workflow was used to create a context-specific tower morphology through a co-evolutionary algorithm with the structural system and private-public distribution. From the generated pareto front members, the lowest average rank solution was selected for use on site to ensure a balanced performance across all fitness criteria.

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Maximize Daylighting

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Structural System Finite Element Analysis (FEA)

Structural System

The structural system from the chosen Co-EA individual can be seen here. As mentioned, the individual’s balanced nature ensured minimal deformation from gravity and wind loads while minimizing the embodied carbon of the system. Additionally, the integrated bi-layer system both increased structural performance through the use of bamboo stem principles and facilitated a connection with interior component systems.

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Minimize Embodied Carbon

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Public-Private Distribution Co-Evolutionary Algorithm

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The public-private distribution from the chosen Co-EA individual can be seen here. The balanced nature of the selected member allowed the internal distribution to meet the specific needs of the tower while also facilitating close relationships with the context. This provided a strong basis for the introduction of the urban scale architectural pathways.

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Maximize Public Distribution

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Component Design Robotic Concrete 3D Printing

Component Design

INTERWOVEN BAMBOO ATTACHMENT TO STRUCTURE INTERIOR PANEL

Once the tower’s major systems were developed, the workflow was utilized to create the specific program distribution. The evolutionary algorithm considered the tower’s program topology, program needs, and family types to place all programs throughout the tower. The lowest average rank individual from the EA was selected to ensure a balance performance across all objectives.

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Liesure Space Sports Space Working Space Nature Space Food Space Medical Space Education Space Service Space Gathering Space Private Space

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CONCRETE STRUCTURE FLOOR

Figure 104: Exploded View of Component System

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Adaptation: 1 Year

I finally own a small house in Hong Kong, which is not very big, but it is sufficient for my daily needs. For a high rise public housing unit, the public space is very convenient, and it can evolve as I do.

Single Area: 20m2

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Living Room Bathroom Master Bedroom

As a single person flat, it contained functions that only need to satisfy the basic needs of the individual, and to relieve the pressure of people who have a pressing need for housing and the emergence of a social movement. At the most basic level, people can move into a flat immediately at a relatively cheap price.

Adaptation: 3 Years

Over time, I also found a roommate to share the room with, and together we enlarged the room to better fit two people. The communal space around us also allowed us to meet more people in our daily lives.

Shared Area: 40m2

Living Room Dining Room Bathroom Master Bedroom

The process of building from a studio flat to a shared flat allowed people to change according to their needs. As the size grew, the box can accommodate more personal space features to suit the needs of two people.

Case Study

183

Adaptation: 5 Years

After having a child, the focus of life changed completely. I have to keep an eye on my children’s schooling and life, and the facilities in the building allow me to form closer relationships with my children without the hassle of having to move to a neighbouring primary school.

Family Area: 60m2

184

Case Study

Living Room Study Room Dining Room Bathroom Children’s Room Master Bedroom

With the emergence of children, the center of gravity of space changed, and families needed more gathering centers, the ‘public space’ of the home. As a family home, the rapid growth of children dramatically changed in space, and removable functional modules can be very good to meet the space changes.

Adaptation: 10 Years

Finally, I have brought my parents to live with me, and the tower is very convenient for my elderly parents. With the excellent medical and service facilities, we can rest assured of our parents’ health. It was very convenient to expand the family and it made it possible for me to have my second child.

Extended Area: 120m2

Living Room Study Room Dining Room Elderly Room Children’s Room Master Bedroom Laundry Room

As a large family grew, the relationships between spaces became more complex and the number of functions required increased. But all spaces grew from the basic unit space, which in turn relieved the homeowner of much of the stress of standing in a high-density city.

Case Study

185

Tower Vertical Section

Spring is the right time for morning tea, and people set up their spaces well in advance for the arrival of spring. In the spring breeze, it seems as if the impatient Hong Kong has become gentle. The use of traditional teapots, teacups and bamboo steamers combined with a modern movable space creates a new form of dining. Winter is the time for hot pot. Hot pot brings cold people to gather together. A one sip brings back a feeling one immediately remembers. The transformed space can be made functional in just a few weeks, making it more suitable for the fast-paced city life.

Summer, when parents move in for the summer holidays, the cool ventilation system and well-serviced facilities in a modern public building can make the season more relaxing for the elderly. Autumn, when children come home from school, the space needs to be changed for them, so that their creativity can be better stimulated. In the public space, there are also more people of the same age to play. Case Study

187

Pedestrian Walkways Pedestrian Simulation

Pedestrian Walkways

188

Case Study

189

Pedestrian Walkway Detailed Section

190

Case Study

191

Multimodal Corridors Temporal Graph Network

SINGLE MODULE 3m

Multimodal Corridors

MODULE AGGREGATION

25 modules / span 8 cm dia. beams 8 cm max. deformation under 5kN / m2 live load 14% shaded ground 27,706 kgCO2e/kg

PEDESTRIAN BRIDGE

192

Case Study

LIGHT RAIL BRIDGE

LIGHT RAIL + PEDESTRIAN BRIDGE

Maximize Social Interaction

Maximize Program Use

Maximize Area Movement

Case Study

193

Multimodal Corridor Street Section 0

194

Case Study

195

Tower Rendering

196

Case Study

197

The P2 Tower Re-Neighboring the Vertical City

The P2 Tower

198

Case Study

199

Multiscalar Adaptation Adaptation over Timescales

Multiscalar Adaptation

200

Case Study

201

202

Case Study

203

204

Case Study

205

DISCUSSION

08 Discussion

8.1 M.Sc. Phase to M.Arch. Phase 8.2 Computational Workflow 8.3 Case Study 8.4 Conclusion

The P 2 Tower re-imagined the design process by proposing a material fabrication system and computational workflow which leveraged emerging technologies and techniques. By investigating the gap between the social affordance of the Hong Kong and its people’s sociability needs, the proposed framework created a new design for public housing towers and an urban network which meets the density needs of Hong Kong while also facilitating continuous spatial changes to match the needs of people over time. The research showcased the capabilities for these emerging technologies to step beyond existing as mere tools for architects but instead operate as new design methodologies for the entire profession. In doing so, the P2 Tower addressed modern challenges of densification and facilitated the development of a built environment that continuously transforms with its occupants.

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M.Sc. Phase to M.Arch. Phase The initial development of the material fabrication system and the computational workflow during the M.Sc. Phase provided a strong foundation to which to expand beyond the confines of a single tower and integrate it into a larger urban context. Such a transition required the M.Arch. to revisit some aspects of the M.Sc. Phase, particularly the structural system and the public-private distribution. The tower designed during the M.Sc. Phase was highly introspective and intentionally had little consideration for its context due to a desire for the computational workflow to be applicable to a wide range of different conditions. Therefore, the M.Arch. revised these systems by enabling their context-specific urban conditions to drive their development in addition to their individual performance objectives. Such revisions enabled the P2 Tower to extend its sociability influence to its local context as well as develop an interconnected urban network with other towers. Yet, the research merely understood the extension of the M.Arch. Phase from the M.Sc. Phase as a linear extension and thus, it failed to reconsider the impact of the urban network on an individual tower. Further research should re-examine the M.Sc. Phase experiments through the lens of the urban network and the M.Arch. Phase results. In doing so, the research may more holistically explore the interplay between the various scales of the design and better address their discontinuities. The research during the M.Arch Phase highlighted the emergent nature of complex urban system, but it also brought to light that the inverse is also a powerful concept. By exploring the idea that the rules of an urban system trickle down and directly influence the performance of individual buildings, further research may better understand how this feedback loop between the two scales may enable an urban environment and its buildings to evolve together.

Computational Workflow By approaching the design of the P2 Tower and its urban network from the perspective of a flexible workflow, the research conducted was not merely relegated to a site-specific solution. Instead, it afforded the opportunity for this research and these tools to address modern challenges of densification around the world. Such flexibility and applicability was enabled by employment of emerging computational tools, such as the co-evolutionary algorithm, the small-world network, the artificial neural network, and the pedestrian simulations 208

Discussion

to name a few. The research and the workflow highlight both the applicability and the benefits of integrating these methodologies into the traditional design process of architects and urban planners. Thus, the research exists not only as a potential solution to densification and urban living but also as a catalyst and proof-of-concept for integrating computational tools into the design process. On the flip side, the heavy reliance of these computational tools throughout the entire workflow have the potential to be detrimental to the design process. Architects and urban designers must shift their design process from designing the solution to designing the problem environment in order to properly implement the computational workflow. Failing to do so would hinder the potential of these tools and essentially pigeonhole the design and the designer. Thus, the computational workflow challenges the traditional position of the architect and urban planner and calls for the re-imagining of the design process. Looking closer at the elements of the computational workflow, the extension of the workflow outward from the Tower Morphology stage during the M.Arch. Phase enhanced the workflow to better consider context-specific urban conditions. The development of the micro-urban pathways directly outward from the tower logically influenced the generation of the internal distributions of public, private, and transitional spaces, and likewise, the tower was able to influence its surrounding context. In a similar manner, the development of the macrourban corridors which connected the disjointed micro-urban pathways empowered multiple towers to influence one another’s design. The addition of these two scales to the computational workflow allowed the design of the tower became contextspecific. Yet, the linearity of these two scales in the computational workflow, upon reflection, was antithetical to the concept of an urban system. These two scales, instead, should have evolved in parallel to the generation of a single tower, enabling the multiscalar feedback look discussed previously. The parallel co-evolution of the structural system and the public-private distribution during the M.Arch. Phase proved to be a powerful tool for optimizing interconnected elements of the same system. Therefore, further research should build out from the lessons learned through the co-evolutionary experiments to simultaneously evolve the urban network alongside the development of individual towers in order to generate a cohesive system where each element influences and is influenced by one another.

The material fabrication system developed during the M.Sc. Phase enabled the adaptability and flexibility of the computational workflow at the architectural scale, but upon transitioning to the M.Arch. Phase, their potential was limited. The bamboo weaving system and the robotic concrete 3D printing was employed along the pedestrian pathways and the multimodal corridors as architectural elements for people to engage these spaces locally, but their widespread implication over the entire urban system was not explored properly. Therefore, further research should look at how this material fabrication system may be scaled up to better enable adaptation throughout the urban scale.

Case Study

The case study and research explored the application of the material fabrication system and the computational workflow in the specific urban conditions of Hong Kong. The extension of the workflow to the urban scale enabled the case study to generate a highly context-specific design through its consideration of various urban conditions such as the locations of the roads, the building heights and types, the climate conditions, etc. Yet, the research observed, through the case study, how the increase of scales significantly magnified the potential urban influences, which the computational workflow mostly ignored. While the research considered a wide range of these parameters, further research should examine the impact of additional factors which were not previously explored, such as precipitation, nature, energy flows, etc. Such additional considerations will significantly influence the overall design and better align the computational workflow to the existing demands of architects and urban planners. The generated design, particularly when viewed through a cross-section of the P2 Tower and the along the urban environment, highlights the interwoven nature of public and private spaces, a main goal of the research. Yet, upon further reflection, the workflow optimized the tower for a single point in time, highlighting a paradoxical relationship between the computational tools as optimization tools and an adaptable architectural system. The use of the temporal graph in the development of the urban network mitigated this contradiction on the urban scale, but this methodology was not applied downstream. Instead, the research assumed the material fabrication system would enable the desired adaptability and flexibility, but it still raises the question as to how one might balance the desires

of an optimized the system with the demands of an evolving architecture. The consideration of the added dimension of time through the temporal graphs proved to be a powerful tool. Yet, the future considerations were highly predictive and more research should be aimed at incorporating other fields of knowledge in order to develop more accurate future scenarios for a tower, a city, and its residents. Additionally, further research should explore similar methodologies at the different scales to better develop a truly fluid architecture. While Hong Kong proved to be a well-suited case study, further research should explore the applicability of the computational workflow to other dense cities and in doing so, the bounds of the system, particularly when it begins to fail, may be better understood and fine tuned. Therefore, further research should clarify and outline which elements will adapt and what form these adaptations should take, whether it’s materialistic, computational, or something else entirely when analyzing applying the workflow to other dense cities. The workflow specifically developed an architecture of adaptability driven by the sociability of people, but it would be naïve to assume that the sociability of people from Hong Kong is the same as people living in Beijing, let alone London or Philadelphia. Thus, it would be important for further research to investigate how the cultural and socioeconomic identities of other cities may change the ways in which the workflow considers sociability.

Conclusion Through its research and experimentation, the P2 Tower calls for the idea of an evolving architecture, one where people determine the past, present, and future of the spaces they inhabit. Such a notion transitions the design process from one which generates spaces to one which facilitates the possibilities of spaces by embedding the transiency of life. Thus, the design process becomes a continuous cycle, and a tower, a city, and its residents evolve together over time. An evolving architecture becomes not only a computational tool but a driving design methodology and democratizes architecture and the built environment by empowering people to initiate, implement, and drive the changes that meet their immediate sociability needs. And so, the P2 Tower follows in the lineage and original spirit of Archigram and the Metabolists but also treads its own path by challenging the role of the Architect.

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APPENDIX

09 Appendix

A.01 Public-Private Evaluation Method A.02 Bamboo Node Studies A.03 Tower Morphology A.04 Structural System A.05 Co-Evolutionary Studies A.06 Public-Private Distribution A.07 Programmatic Topology A.08 Programmatic Organization A.09 Variable Control Studies A.10 Material Fabrication System A.11 Artificial Neural Network Data Set A.12 Bridge Selection Matrix A.13 Pedestrian Simulation Sample Code A.14 Co-Evolutionary Algorithm Sample Code

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A.01 Public-Private Evaluation Method Parameter Calculations

DIMENSION

SITE ACCESSIBILITY

S.01

S.02 S.03

S.04

S.05

OWNER.

ENVIRO.

BUILDING AFFORDANCE

B.01

212

Name

Definition

length of ground floor plan not blocked by Visual Site Connection obstructions/length of street (SITE) # entrance points to site / Access Points to Site sqm of lot (SITE) Modes of Transit to Site

# transit stops within 0.5kmR

Remap Metric N/A

Calculation unobstructed length / length

total

1.0 = 1 entrance / 200m2

(# entrance / lot m2) * 200

1.0 = 20 bus, 2 MTR, 1 Ferry (weighting: 0.4 Bus, 0.4 MTR, 0.2 Ferry = 1.0 total)

[(# bus/20) * 0.4] + [(# MTR/2) * 0.4] +[(# Ferry/1) * 0.2]

average distance of all closest amenities to tower 0.0 = 1500m+, 1.0 = 0m remap between 0, 1500 (straight distance, radius) 0.5kmR value of closeness centrality node value remapped between node value Centrality to Context of site 2kmR 0-1 # entrances to building / sqm (# entrance / ground floor m2) Threshold Condition 1.0 = 1 entrance / 100m2 of ground floor * 100 Connectedness to Amenities

B.02

Occupant Density

# occupants / sqm

1.0 = 1 person /100m2

(#ppl / sqm floor area) *100

B.03

Spatial Connectivity

Average of all node values

node value remapped between 0-1

node value

B.04

Spatial Proportions

average height

0.0 = 2.5m, 1.0 = 5.0m+

B.05

Average Area per Space

average sqm / space

0.0 <= 10m2, 1.0 = 500m2+

B.06

Function Density

B.07

Physical Accessibility

B.08

Area of Social Space

B.09

Area of Outdoor Space

E.01

# unique space types / number rooms # accessible spaces / # spaces sqm social spaces inside / sqm of built space (courtyard, balcony, etc)

value remappeed between 2.55.0 value remappeed between 10500

1.0 = 1 unique room / 25 rooms

(# types / # rooms) * 25

N/A

# accessible spaces / spaces

N/A

area social spaces / floor area

sqm outdoor space on lot / sqm of built space

N/A

(outdoor space m2/ floor area m 2)

Daylighting

sDA value on interior floor

N/A

value of sDA

E.02

Thermal Comfort

Thermal Comfort Percent Calculatiom (TCP)

N/A

value of TCP

E.03

Noise Condition

total aborption coefficent for each room (ave.) @ 500 Hz

N/A

sum of (area * material alpha value) / total surface area

OW.01

Ownership

public or private ownership

N/A

0 or 1

OW.02 OW.03

Function Programmtic Use

public or private function public or private use

N/A N/A

0 or 1 0 or 1

Appendix

A.02 Bamboo Node Studies Scaled Equation Results Scaled Equation

12 Segments

11.04cm Deformation

6.97cm Deformation

12 Segments

55.42cm Deformation

10.90cm Deformation

5 Segments

12 Segments

154.74cm Deformation

10.59cm Deformation

100m

150m

5 Segments

Original Equation

12 Segments

17.65cm Deformation

7.77cm Deformation

100m

150m

5 Segments

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A.03 Tower Morphology INPUT INFORMATION URBAN CONTEXT

FC01 | Maximized Daylighting in Winter (hrs)

ENVIRONMENTAL CONDITIONS

g1 | Footprint Area (m2)

FC02 | Maximized SA:V Ratio (m3 / m2)

g2 | Length:Width Ratio

g3 | Auxillary Tower Selection

g4 | Segment Count

FC03 | Minimized Wind Vector Deflection (º)

g5 | Structural Height (m)

FC04 | Maximized Floor-to-Area Ratio (m2/m2)

g6 | Auxillary Tower Heights (m)

g7 | Maelstrom Location (x,y) g8 | Maelstrom Radius (m)

g9 | Edge Fillet Radius (m)

sequential simulation

STRUCTURAL SYSTEM

214

Appendix

Gen50

Gen0

-6167174 -1254142737350735011752208 5970026 4001336 3009061

2411133

2011442 1725420

1510615

1343372 1209470

9.6

1.54

0.836

0.574

FC1 | Max Total Daylighting (kWh)

0.437

0.353

0.296

0.255

0.224

0.199

0.18

0.164

0.15

FC2 | Max SA:V Ratio Gen50

Gen0

0.0414

0.0348

0.03

0.0264

0.0236

0.0213

0.0194

0.0178

0.0165

0.0153

0.0143

FC3 | Min Wind Vector Angle (º)

0.0134

0.0127

-1.22

-1.91

-4.4

14.31

2.72

1.5

1.04

0.794

0.642

0.539

0.465

0.408

0.364

FC4 | Max FAR

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A.04 Structural System INPUT INFORMATION TOWER MORPHOLOGY

FC01 | Minimized Deformation (cm)

sequential simulation

Wind Profile Load

g1 | Utilization Density (%)

PSL Voxelization

steel g2 | Mesh Skeleton Rationalization

g3 | Structural Diameter (cm) g4 | Structural Thickness (cm)

PUBLIC-PRIVATE DISTRIBUTION

216

Appendix

FC02 | Minimized Embodied Carbon (kgCO2)

Principle Stress Lines

Gen50 Gen50

Gen50

Gen0 Gen0

Gen0

-35.36 -35.36

-26.47

-17.58

-8.69

0.202

9.09

17.98

26.87

-26.47 35.76

-17.58

44.65

-8.69

53.54

-26.47

-17.58

-8.69

9.09

17.98

26.87

35.76

44.65

53.54

62.43

71.32

FC1 | Min Deformation (cm) 71.32

-6077751 -4497644 -2917537 -1337430 242676 1822783 3402891 4982998 6563105 8143212 9723319 11303427 12883534

FC2 | Min Embodied Carbon (kgCO2e)

FC1 | Min Deformation (cm) -35.36

0.202

62.43

0.202

9.09

17.98

26.87

35.76

44.65

FC1 | Min Deformation (cm)

53.54

62.43

Gen0

71.32

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A.05 Co-Evolutionary Studies T1 EA Optimization Phenotypes

T2 EA Optimization Phenotypes

T1T2 CoEA w/ Optimized Gene Ranges Phenotypes

218

Appendix

Parasitism Co-Evolutionary Experiment T1 EA Optimization

T2 EA Optimization

FC1 | Maximized Daylighting FC1 Range: 0.010 To 0.333 Δ = 0.323

FC2 | Maximized Tower Height Difference FC2 Range: 2.532e-7 To 2.997e-7 Δ = 4.642e-8

T1T2 CoEA w/ Optimized Gene Ranges

T1T2 CoEA w/o Optimized Gene Ranges

FC1 | Maximized Daylighting

FC1 Range: 0.011 To 1 Δ = 0.988 (+305.99%)

FC1 Range: 0.011 To 1 Δ = 0.988 (+305.91%)

FC2 | Maximized Tower Height Difference

FC2 Range: 2.854e-7 To 6.398e-7

FC2 Range: 3.073e-7 To 1.809e-6

Δ = 3.544e-7 (+763.65%)

FC3 | Minimized Solar Radiation FC3 Range: 83564.656 To 349508.827 Δ = 265944.170

FC4 | Maximized Floor-to-Area Ratio FC4 Range: 0.2283 To 2.285 Δ = 2.057

Δ = 1.502e-6 (+3236.53%)

FC3 | Minimized Solar Radiation

FC3 Range: 56751.533 To 335171.650 Δ = 278420.116 (+104.69%)

FC3 Range: 51691.539 To 370598.854 Δ = 318907.314 (+119.91%)

FC4 | Maximized Floor-to-Area Ratio

FC4 Range: 0.231 To 3.438

Δ = 3.20613 (+155.81%)

FC4 Range: 0.242 To 5.649

Δ = 5.407 (+262.81%)

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Commensalism Co-Evolutionary Experiment

T1 EA Optimization

T2 EA Optimization

FC1 | Minimized Solar Radiation FC1 Range: 29817.880 To 219798.379 Δ = 189989.499

FC2 | Maximized Site Shading FC2 Range: 104079 To 357270

FC1 | Minimized Solar Radiation

FC1 Range: 19871.868 To 73514.449 Δ = 53642.581 (-28.23%)

FC1 Range: 33405.885 To 232178.578 Δ = 198772.692 (104.62%)

FC2 | Maximized Site Shading

Δ = 542676 (+214.33%)

FC3 | Maximized Average Height FC3 Range: 0.02 To 0.046 Δ = 0.026

FC4 | Maximized SA:V Ratio FC4 Range: 0.214 To 0.460 Δ = 0.246

Appendix

T1T2 CoEA w/o Optimized Gene Ranges

FC2 Range: 338244 To 880920

Δ = 253191

220

T1T2 CoEA w/ Optimized Gene Ranges

FC3 | Maximized Average Height FC3 Range: 0.019 To 0.020 Δ = 0.001 (-3.84%)

FC4 | Maximized SA:V Ratio FC4 Range: 0.159648 To 0.241735 Δ = 0.082 (-33.33%)

FC2 Range: 414937 To 1468213

Δ = 1053276 (416.00%)

FC3 | Maximized Average Height FC3 Range: 0.020 To 0.046 Δ = 0.02 (+98.34%)

FC4 | Maximized SA:V Ratio FC4 Range: 0.214 To 0.497

Δ = 0.282 (+114.97%)

Mutualism Co-Evolutionary Experiment

T1 EA Optimization

T2 EA Optimization

FC1 | Minimized Solar Radiation FC1 Range: 29817.880 To 219798.379 Δ = 189989.499

FC2 | Maximized Site Shading

T1T2 CoEA w/ Optimized Gene Ranges

T1T2 CoEA w/o Optimized Gene Ranges

FC1 | Minimized Solar Radiation

FC1 Range: 25664.667 To 86896.257 Δ = 61231.590074 (-32.22%)

FC1 Range: 45672.748 To 241890.065 Δ = 196217.316 (103.27%)

FC2 | Maximized Site Shading

FC2 Range: 306454 To 560282

FC2 Range: 104079 To 357270 Δ = 253191

Δ =253828 (+100.25%)

FC3 | Maximized Open Space

FC2 Range: 155575 To 544443

Δ = 388868 (153.58%)

FC3 | Maximized Open Space

FC3 Range: 0.0237 To 0.0531 Δ = 0.029

FC3 Range: 0.0232 To 0.0335 Δ = 0.0103 (-35.51%)

FC3 Range: 0.0236 To 0.0542 Δ = 0.0306 (+105.51%)

FC4 | Maximized Daylighting

FC4 Range: 7.798e-7 To 2.934e-6

FC4 Range:8.204e-7 To 5.275e-6

FC4 Range: 7.526e-7 To 3.292e-6 Δ = 2.539e-6

Δ = 2.155e-6 (-84.87%)

Δ = 4.4545e-6 (+175.44%)

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A.06 Private-Public Distribution INPUT INFORMATION TOWER MORPHOLOGY

FC01 | Maximized Public Distribution

STRUCTURAL SYSTEM

FC02 | Maximized Public Segment Connections

Base Tower Morphology

FC03 | Maximized Housing Density

Tower Segmentation

g1 | Public Start Point

FC04 | Maximized Private Program Proximity

g2 | Private Start Point

g3 | Public Start Count g4 | Private Start Count g5 | Public Growth Rate g6 | Private Growth Rate PROGRAM TOPOLOGY

SPATIAL ORGANIZATION

222

Appendix

Gen50

Gen0

-672.68

501.91

182.77

111.73

80.45

62.86

51.58

43.73

37.96

33.53

30.03

27.19

-0.775

24.84

-1.19

-2.57

16.33

FC1 | Max Percentage Public

-672.68

501.91

182.77

111.73

80.45

62.86

51.58

43.73

37.96

33.53

1.95

1.04

0.707

0.536

0.432

0.362

0.311

0.273

0.243

FC2 | Max Housing Density

30.03

27.19

-0.775

24.84

-1.19

-2.57

FC1 | Max Percentage Public

16.33

1.95

1.04

0.707

0.536

0.432

Gen0 Gen50

0.362

0.311

0.273

0.243

FC2 | Max Housing Density Gen0

-18.24

-66.76

40.2

15.45

9.56

6.92

5.43

4.46

3.79

3.29

FC3 | Max Private Proximity

2.91

2.61

2.36

-6.01

-7.86

-11.34

-20.38

-100.25

34.34

14.66

9.32

6.83

5.39

4.45

3.79

3.3

FC4 | Max Public Segment Count

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A.07 Programmatic Topology INPUT INFORMATION TOWER MORPHOLOGY

PUBLIC-PRIVATE SEGMENTS

C G B H A I O J N E

C(i) = E(i) / T(i)

g1 | Distance Between Points

FC01 | Maximized Cluster in Network

A J

C G

B H A I E

N K L

B H A

g2 | Proportional Line Reduction

I O J

FC02 | Minimized Path Count

O J

G B

2 E

5 4

N L

J N

g3 | Random Connection with

Other Points

2.22 3.87

SEGMENT A

4.03

vertical connection

2.9

5.5

2 5

4.03

3.88

4 2

1.76

1 2 2.33

4 1 2.01

g4 | Vertical Connection with Other Segments

SPATIAL ORGANIZATION

Appendix

4.55 5

SEGMENT B

224

FC03 | Maximized Path Weight

A I

3 2.05

5.02

3.1

2.85

FC04 | Minimized Difference Between Sociability Scores

Gen50

Gen0

0.0544 8.54e-0034.63e-003 3.18e-003 2.42e-003 1.95e-003 1.64e-003 1.41e-003 1.24e-003 1.10e-003 9.94e-0049.05e-0048.31e-004

0.631

FC1 | Max Cluster Value

0.589

0.553

0.52

0.492

0.466

0.443

0.422

0.403

0.385

0.369

0.355

0.341

FC2 | Min Path Count

Gen50 Gen50

Gen0 Gen0

15.08

13.6715.08 12.5 13.67 11.51 12.5 10.67 11.51 9.95 10.67 9.31 9.95 8.75 9.31 8.26 8.75 7.82 8.26 7.42 7.82 7.06 7.42 6.74 7.06

FC3 | Max FC3Path | MaxWeight Path Weight

6.74

0.0203

0.0203 9.68e-0038.76e-0038.00e-0037.37e-0036.82e-0036.35e-0035.95e-0035.59e-003 0.0166 0.01410.0166 0.01220.0141 0.0108 0.0122 0.0108 9.68e-0038.76e-0038.00e-0037.37e-0036.82e-0036.35e-0035.95e-0035.59e-003

FC4 | Min FC4Sociability | Min Sociability Score Difference Score Difference

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A.08 Programmatic Organization INPUT INFORMATION PUBLIC-PRIVATE DISTRIBUTION

FC01 | Minimized Topological Relationships Difference

PROGRAMMATIC TOPOLOGY

g1 | Program Count

FC02 | Minimized Program Area Difference

g2 | Program Start Point

g3 | Program Placement Iterations g4-12 | Voxel Selection Index g 13-21 | Voxel Selection Direction

FC03 | Minimized Program Count Difference

g22 | Program Maximum Area

Component Placement

COMPONENT DESIGN

FABRICATION SYSTEM

226

Appendix

Gen50

Gen50 Gen0

-32.36

-16.51

-0.662

13.19

31.04

46.89

62.74

78.59

94.44

110.291

141.99

86.41

157.84

218.82

351.22

483.63

748.44

880.84

1013.25

1145.65

1278.06

1410.46

1542.87

1675.22

FC2 | Min Program Area Difference

FC1 | Min Program Relationship Difference Gen0

Gen0

Gen50 748.44 880.84 86.41 218.82 351.22 483.63 1013.25 1145.65 110.291 -32.36 141.99 -16.51157.84 -0.662 -32.3613.19 -16.5131.04 -0.662 46.89 13.1962.74 31.0478.59 46.8994.44 62.74110.291 78.59141.99 94.44157.84 110.291

Difference

1278.06 141.99

1410.46 86.41 1542.87 218.82 1675.22 351.22 86.41483.63 218.82 748.44 351.22 880.84483.63 1013.25748.44 1145.65880.84 1278.061013.25 1410.461145.65 1542.871278.06 1675.221410.46 157.84

FC2 | Relationship Min ProgramDifference Area Difference FC1 | Min Program FC1 | Min Relationship Program Difference

1542.87

Gen50

1675.22

0.109

0.006

Gen0

-16.51

-0.662

13.19

31.04

46.89

62.74

78.59

94.44

110.291

141.99

157.84

0.109

0.006

0.003

0.07

0.127

0.174

86.41

218.82

351.22

483.63

748.44

880.84

0.221

0.268

0.315

0.3621

0.409

0.456

1013.25

0.07

0.127

FC3 | Min R

FC2 | Min Program FC2 | Min AreaProgram Difference Area Difference

Gen0

-32.36

0.003

1145.65

1278.06

1410.46

1542.87

1675.22

FC2 | Min Program Area Difference FC1 | Min Program Relationship Difference FC3 | Min Room Distribution Difference

Bhagat | Wong

227

A.09 Variable Control Studies SYNCLASTIC CURVATURE

Gaussian Curvature

Gaussian Curvature: 0.0067

SYNCLASTIC SYNCLASTIC CURVATURE CURVATURE

SYNCLASTIC CURVATURE

Four Sided Polygon

SYNCLASTIC CU

Four Curvature: Sided Polygon Gaussian 0.00134

Five Sided P

Gaussian Curvature: 0.0067

Gaussian Curvatu

NO CURVATURE

ANTICLASTIC CURVATURE

Five Sided Polygon0.0 Gaussian Curvature:

Six Sided Polygon Gaussian Curvature: -0.00132

SYNCLASTIC Six SidedCURVATURE Polygon

Four Five Sided Sided Polygon Polygon Gaussian Curvature: 0.00134 0.0067 Gaussian Curvature:

Gaussian Curvature: 0.00134

NO CURVATURE ANTICLASTIC CURVATURE

ANTICLASTICCURVATURE CURVATURE ANTICLASTIC

NO CURVATURE Seven Sided Polygon

ANTICLASTIC C

Gaussian Curvature: 0.0

Gaussian Curvatu

ANTICLASTIC CURVATURE

Eight Sided Polygon Seven

Six Sided Seven SidedPolygon Polygon Gaussian Curvature: 0.0 Gaussian Curvature: -0.00132

SYNCLASTIC Five SidedCURVATURE Polygon

GaussianCurvature: Curvature:-0.00132 -0.005 Gaussian

ANTICLASTIC Nine SidedCURVATURE Polygon

ANTICLASTIC C

Eight Curvature: Sided Polygon Gaussian -0.0103

Nine Sided P

Gaussian Curvature: -0.005

Gaussian Curvatu

GAUSSIAN CURVATURE

0.006 0.003 SYNCLASTIC

0.000

ANTICLASTIC

-0.003

ANTICLASTIC ANTICLASTIC CURVATURE CURVATURE

ANTICLASTIC CURVATURE

Eight Nine Sided Sided Polygon Polygon Gaussian Curvature: Curvature: -0.0103 -0.005 Gaussian

Nine Sided Polygon Gaussian Curvature: -0.0103

-0.006 -0.010

NUMBER OF SIDES

228

Appendix

Seven Sided

4mm Width / 0.8mm Thickness

Strip Width/Depth Ratio

0.8mm Thickness

4mm Width // 0.8mm 1.5mm Thickness

Digital Model: 35mm

Deviation from Digital Model: 34mm 35mm

m Width

/ 0.8mm Thickness

epth Ratio: 12.5:1

m Width

m Digital Model: 13mm

+0.001

TARGET CURVATURE 10mm Width / 0.8mm Thickness 7mm Width / 1.5mm Thickness Width/ Depth / DepthRatio: Ratio:4.6:1 12.5:1 Width

+0.002

Deviation from Digital Model: 13mm Deviation from Digital Model: 22mm

2.6 : 1 4.6 : 1 5 : 1 10mm Width

7mm Width

60mm 40mm 20mm Width / Depth Ratio: 12.5:1

Deviation from Digital: 13mm

8.75 : 1

12.5 : 1Target Curvature

Actual Curvature

-0.002

ACCEPTABLE WIDTH +0.001 / DEPTH TARGET CURVATURERATIOS 0.000

+0.002 2.6 : 1

10mm Width -20mm

Deviation from Digital Model: 15mm 60mm

Width Width//Depth DepthRatio: Ratio:12.5:1 6.5:1

4.6 : 1 5 : 1

-40mm 4.6 : 1 5 : 1

6.5 : 1

8.75 : 1

12.5 : 1

WIDTH / DEPTH RATIO

Width / Depth Ratio: 6.5:1

TARGET DEVIATION

2.6 : 1

ACCEPTABLE WIDTH / DEPTH RATIOS

-0.001

10mm Width / 1.5mm Thickness

Deviation from Digital Model: 13mm 15mm

-0.003

0mm

10mm Width / 0.8mm 1.5mm Thickness

7mm Width

6.5 : 1

10mm Width / 1.5mm Thickness 10mm Width / 0.8mm Thickness Width / Depth Ratio: 6.5:1 Width / Depth Ratio: 12.5:1 Deviation from Digital Model: 15mm Deviation from Digital Model: 13mm

WIDTH / DEPTH RATIO

o: 6.5:1 al: 15mm

pth Ratio: 2.6:1 m Digital: 34mm

0.000

Deviation from Digital Model: 22mm 14mm

Width / Depth Ratio: 8.75:1 Deviation from Digital: 14mm

Devia

ACCEPTABLE WIDTH / DEPTH RATIOS

-0.001

Width Width//Depth DepthRatio: Ratio:8.75:1 4.6:1

DEVIATION FROM DIGITAL MODEL (mm)

epth Ratio: 5:1 m Digital: 35mm

Deviation from Digital Model: 14mm

-0.002

7mm 7mm Width Width // 0.8mm 1.5mm Thickness

dth

Devia

-0.003

DEVIATION FROM TARGET GAUSSIAN CURVATURE

o:pth 12.5:1 Ratio: 8.75:1 al: Digital13mm Model: 14mm 0.8mm Thickness

7mmCurvature Width / 1.5mm Thickness Target7mm Width / 0.8mm Thickness Width / Depth Ratio: 4.6:1 Width / Depth Ratio: 8.75:1 Actual Curvature Deviation from Digital Model: 22mm

7mm Width / 0.8mm Thickness 4mm Width / 1.5mm Thickness Width / Depth Ratio: 8.75:1 Width / Depth Ratio: 2.6:1 Deviation from Digital Model: 14mm Deviation from Digital Model: 34mm

Width Width//Depth DepthRatio: Ratio:2.6:1 5:1

DEVIATION FROM TARGET GAUSSIAN CURVATURE

epth Ratio: 5:1

Deviation from Digital Model: 35mm

DEVIATION FROM DIGITAL MODEL (mm)

dth

4mm Width / 1.5mm Thickness 4mm Width / 0.8mm Thickness Width / Depth Ratio: 2.6:1 Width / Depth Ratio: 5:1 Deviation from Digital Model: 34mm Deviation from Digital Model: 35mm

Width / Depth Ratio: 5:1

40mm

ACCEPTABLE WIDTH / DEPTH RATIOS

20mm 0mm

6.5 : 1

-20mm

8.75 : 1

12.5 : 1

TARGET DEVIATION

WIDTH / DEPTH -40mm RATIO Width / Depth Ratio: 4.6:1 Deviation from Digital: 22mm

Width / Depth Ratio: 6.5:1 Deviation from Digital: 15mm

2.6 : 1

4.6 : 1 5 : 1

6.5 : 1

8.75 : 1

12.5 : 1

WIDTH / DEPTH RATIO

Bhagat | Wong

229

Weave Density for 3D Printing: Sagging and Material Deformation 2cm 2cmWeave WeaveOpening Opening

3cm 3cmWeave WeaveOpening Opening

2cm Openings / 0.8mm Thickness

4cm 4cmWeave WeaveOpening Opening

4cm Openings / 2mm Thickness

3cm Openings / 1.5mm Thickness

DEVIATION FROM DEVIATION FROM DIGITAL MODEL (mm) DIGITAL MODEL (mm)

end end

middle middle

end end

middle middle

end end

middle middle

30mm 30mm

end end

PRINT PRINTPATH PATHDEVIATION DEVIATION

25mm 25mm 20mm 20mm 15mm 15mm 10mm 10mm 5mm 5mm 0mm 0mm

2cm 2cmOpening Opening

3cm 3cmOpening Opening WEAVE OPENING WEAVE OPENINGSIZE SIZE

4cm 4cmOpening Opening

DEFORMATION OF DEFORMATION OF PHYSICAL MODEL (mm) PHYSICAL MODEL (mm)

Appendix

end end

middle middle

end end

middle middle

end end

50mm 50mm 40mm 40mm 30mm 30mm 20mm 20mm 10mm 10mm 0mm 0mm

230

middle middle

60mm 60mm

end end

DEFORMATION DEFORMATIONOF OFWOVEN WOVENMODEL MODEL

2cm 2cmOpening Opening

3cm 3cmOpening Opening WEAVE OPENING WEAVE OPENINGSIZE SIZE

4cm 4cmOpening Opening

Digital to Physical Translation DIGITAL SAMPLES

PHYSICAL SAMPLES

DEVIATION FROM TARGET GAUSSIAN CURVATURE

GAUSSIAN CURVATURE

0.006

GAUSSIAN CURVATURE

0.003

STRIP WIDTH / DEPTH RATIO SYNCLASTIC

-0.003 0.000

-0.002

ANTICLASTIC

-0.003

ACCEPTABLE WIDTH / DEPTH RATIOS

-0.001

-0.006

0.000

-0.010

+0.001 4

TARGET CURVATURE 5

NUMBER OF SIDES

+0.002 2.6 : 1

4.6 : 1

5:1

6.5 : 1 WIDTH / DEPTH RATIO

PHYSICAL SAMPLES 12.5 : 1 DIGITAL SAMPLES

8.75 : 1

PHYSICAL SAMPLES DIGITAL SAMPLES

Bhagat | Wong

231

A.10 Material Fabrication System MODULE

3D PRINTED CONCRETE

SECTION DETAIL

6cm

WOVEN BAMBOO FORMWORK 4cm 3.5m

SECTION

COMPONENT

3D PRINTED CONCRETE shell

6cm

WOVEN BAMBOO formwork

ORK

3D PRINTED CONCRETE

4cm

studs

WOVEN BAMBOO joinery

SECTION THROUGH SHELL

232

Appendix

DIGITAL TO PHYSICAL

3D PRINTING WEAVE DENSITY

JOINT SYSTEM

STRIP WIDTH / DEPTH

GAUSSIAN CURVATURE

Component Weaving Pattern

DEVIATION OF WOVEN MODEL

DEVIATION OF PHYSICAL MODEL (mm)

100mm 80mm 60mm 40mm 20mm 0mm Left Edge

Center

Right Edge

LOCATION OF TEST POINT

Bhagat | Wong

233

234

Appendix

Component Structural Analysis 12cm Concrete Shell 8cm Shell + 4cm Studs

Max. Deformation = 0.109 cm

0.112cm

Wind Load 0.5kN/m2

Gravity Load

3.5m

0cm

-0.112cm

10cm Concrete Shell + Bamboo Weaving 6cm Shell + 4cm Studs

Max. Deformation = 0.112 cm

0.112cm

Wind Load 0.5kN/m2

Gravity Load

3.5m

0cm

-0.112cm

Bhagat | Wong

235

A.11 Artificial Neural Network Data Set Data ID

236

500 of 95,000 Samples

X-Coordinate

Y-Coordinate

Z-Coordinate

Wind Speed (m/s)

Inputs Node Proximity

Normal Vector X-Unit

Normal Vector Y-Unit

Normal Vector Z-Unit

Output Pressure (kPa)

-8.258355

31.304214

8.284926

-0.007444

-8.258355

31.304214

60.58545

-0.013546

-8.258355

31.304214

58.573892

-0.01415

-8.258355

31.304214

10.296484

-0.008035

-8.258355

31.304214

56.562333

-0.014857

-8.258355

31.304214

12.308043

-0.008514

-8.258355

31.304214

14.319601

-0.009238

-8.258355

31.304214

54.550775

-0.015382

-8.258355

31.304214

52.539216

-0.015682

-8.258355

31.304214

16.33116

-0.009914

-8.258355

31.304214

50.527658

-0.015795

-8.258355

31.304214

18.342718

-0.010667

-8.258355

31.304214

20.354277

-0.011408

-8.258355

31.304214

48.516098

-0.015768

-8.258355

31.304214

22.365836

-0.012144

-8.258355

31.304214

46.504541

-0.015711

-8.258355

31.304214

44.492981

-0.015651

-8.258355

31.304214

24.377394

-0.012733

-8.258355

31.304214

42.481422

-0.015545

-8.258355

31.304214

26.388954

-0.013416

-8.258355

31.304214

28.400512

-0.013911

-8.258355

31.304214

40.469864

-0.015422

-8.258355

31.304214

30.412071

-0.01428

-8.258355

31.304214

38.458305

-0.01529

-8.258355

31.304214

36.446746

-0.015129

-8.258355

31.304214

34.435188

-0.014894

-8.258355

31.304214

32.423629

-0.014661

-8.177571

31.304214

5.808657

-0.006841

-8.177571

31.304214

63.061718

-0.013641

-6.979643

31.304214

22.084393

-0.013494

-6.979643

31.304214

12.737844

-0.008811

-6.979643

31.304214

36.771824

-0.016725

-6.979643

31.304214

56.132531

-0.016296

-6.979643

31.304214

28.760498

-0.015602

-6.979643

31.304214

52.126869

-0.016537

-6.979643

31.304214

44.783152

-0.016681

-6.979643

31.304214

24.087224

-0.014321

-6.979643

31.304214

16.743507

-0.010803

-6.979643

31.304214

40.777489

-0.016748

-6.979643

31.304214

42.780319

-0.016729

-6.979643

31.304214

34.768993

-0.01661

-6.979643

31.304214

38.107045

-0.016766

-6.272966

31.304214

36.104214

-0.017734

-6.272966

31.304214

44.115541

-0.017596

-6.979643

31.304214

20.749172

-0.012864

-6.979643

31.304214

26.757667

-0.015169

-6.979643

31.304214

10.735013

-0.007982

-6.979643

31.304214

18.078728

-0.01166

-6.272966

31.304214

16.075897

-0.011234

-6.979643

31.304214

46.118374

-0.016639

-6.272966

31.304214

28.092888

-0.016615

-6.979643

31.304214

58.802975

-0.016341

-6.979643

31.304214

32.766162

-0.016411

-6.979643

31.304214

30.095719

-0.015979

-6.272966

31.304214

56.800143

-0.017427

-6.272966

31.304214

18.746339

-0.012968

-6.272966

31.304214

22.752003

-0.01488

-6.979643

31.304214

8.06457

-0.007172

-6.272966

31.304214

46.785984

-0.01748

-6.272966

31.304214

58.135365

-0.017636

-6.272966

31.304214

26.090056

-0.016034

-6.272966

31.304214

8.732181

-0.007546

-6.272966

31.304214

42.112709

-0.017687

-6.272966

31.304214

12.070234

-0.008896

-6.272966

31.304214

20.081561

-0.013704

-6.272966

31.304214

40.109879

-0.01775

-6.272966

31.304214

24.754834

-0.015541

-6.272966

31.304214

52.794479

-0.017313

-6.979643

31.304214

54.1297

-0.016433

-6.979643

31.304214

14.073065

-0.009486

-6.272966

31.304214

38.774657

-0.01776

-6.272966

31.304214

10.067402

-0.007976

-6.979643

31.304214

60.138195

-0.016065

Appendix

12386

2.781329

20.911909

87.436455

-0.02376

12387

2.781329

20.911909

82.801094

-0.023636

12388

2.781329

20.911909

67.570633

-0.021787

12389

2.781329

20.911909

101.342529

-0.021543

12390

2.11882

20.911909

91.40962

-0.022985

12391

2.781329

20.911909

85.449872

-0.023722

12392

2.11882

20.911909

99.355947

-0.021646

12393

2.781329

20.911909

92.734009

-0.023559

12394

2.781329

20.911909

35.123121

-0.013322

12395

2.781329

20.911909

61.610884

-0.020769

12396

2.781329

20.911909

56.975526

-0.019668

12397

2.11882

20.911909

75.51696

-0.022349

12398

2.781329

20.911909

74.854767

-0.02287

12399

2.11882

20.911909

41.745063

-0.015212

12400

2.781329

20.911909

21.879239

-0.009192

12401

2.11882

20.911909

23.203628

-0.009324

12402

2.781329

20.911909

80.814514

-0.023449

12403

2.781329

20.911909

27.176793

-0.010675

12404

2.11882

20.911909

55.651137

-0.018849

12405

2.781329

20.911909

54.988942

-0.019197

12406

2.781329

20.911909

98.693751

-0.022409

12407

2.11882

20.911909

19.892658

-0.008629

12408

2.781329

20.911909

9.297553

-0.007304

12409

2.11882

20.911909

49.029198

-0.017216

12410

2.781329

20.911909

11.946329

-0.007529

12411

2.781329

20.911909

69.557213

-0.022084

12412

2.11882

20.911909

109.288857

-0.031185

12413

2.781329

20.911909

62.935272

-0.02086

12414

2.781329

20.911909

7.310971

-0.007257

12415

2.11882

20.911909

58.962109

-0.019704

12416

2.781329

20.911909

25.852405

-0.010194

12417

2.11882

20.911909

15.919494

-0.007975

12418

2.781329

20.911909

19.230464

-0.008581

12419

2.11882

20.911909

97.369362

-0.022033

12420

2.11882

20.911909

37.109704

-0.013639

12421

2.11882

20.911909

104.653498

-0.021297

12422

2.781329

20.911909

106.640083

-0.022057

12423

2.11882

20.911909

73.530378

-0.022111

12424

2.11882

20.911909

47.70481

-0.016932

12425

2.781329

20.911909

102.666916

-0.021514

12426

2.781329

20.911909

53.664555

-0.018887

12427

2.781329

20.911909

76.841347

-0.023076

12428

2.781329

20.911909

96.707169

-0.023102

12429

2.781329

20.911909

105.315694

-0.021588

12430

2.781329

20.911909

41.082868

-0.015435

12431

2.781329

20.911909

39.75848

-0.014944

12432

2.781329

20.911909

47.042615

-0.017257

12433

2.781329

20.911909

23.865822

-0.009654

12434

2.781329

20.911909

59.624302

-0.020324

12435

2.781329

20.911909

17.906076

-0.008333

12436

2.781329

20.911909

90.747424

-0.02364

12437

2.781329

20.911909

72.868182

-0.022529

12438

2.781329

20.911909

29.163375

-0.011325

12439

2.781329

20.911909

49.691391

-0.017887

12440

2.781329

20.911909

43.731644

-0.01626

12441

2.11882

20.911909

45.056032

-0.016188

12442

2.781329

20.911909

37.771899

-0.014287

12443

2.781329

20.911909

108.626663

-0.024691

12444

2.781329

20.911909

45.718226

-0.016742

12445

2.11882

20.911909

78.827929

-0.02269

12446

2.781329

20.911909

79.490125

-0.0234

12447

2.781329

20.911909

15.257299

-0.007932

12448

2.629368

20.911909

113.452441

-0.060727

12449

2.729368

20.911909

5.765851

-0.007271

12450

4.106348

20.911909

76.841347

-0.024603 -0.023912

12451

4.106348

20.911909

98.693751

12452

4.106348

20.911909

7.310971

-0.007271

12453

4.106348

20.911909

96.707169

-0.024685

12454

4.106348

20.911909

88.760841

-0.025332

12455

4.106348

20.911909

57.637721

-0.021112

12456

4.106348

20.911909

66.90844

-0.023049

12457

4.106348

20.911909

109.288857

-0.030602

12458

4.106348

20.911909

83.463287

-0.025226

12459

4.106348

20.911909

31.812152

-0.012966

12460

4.768858

20.911909

89.423035

-0.026414

12461

4.106348

20.911909

37.109704

-0.014926

Bhagat | Wong

237

24622

4.996605

9.071654

10.50902

-1

0.04878

24623

4.996605

9.071654

51.837371

-1

0.066702

24624

4.996605

9.071654

25.840504

-1

0.045058

24625

4.996605

9.071654

63.835925

-1

0.073675

24626

4.996605

9.071654

62.502752

-1

0.072804

24627

4.996605

9.071654

27.840263

-1

0.046275

24628

4.394247

9.071654

6.117392

-1

0.055127

24629

4.394247

9.071654

84.225622

-1

0.095125

24630

5.137565

9.071654

85.28432

-1

0.095129

24631

5.137565

9.071654

5.058696

-1

0.055667

24632

6.389268

9.071654

31.839781

-1

0.04889

24633

6.389268

9.071654

61.836165

-1

0.071706

24634

6.389268

9.071654

17.841469

-1

0.042416

24635

6.389268

9.071654

46.504679

-1

0.061445

24636

7.0856

9.071654

32.506368

-1

0.048933 0.049465

24637

6.389268

9.071654

9.842433

-1

24638

6.389268

9.071654

37.839057

-1

0.05428

24639

6.389268

9.071654

55.836889

-1

0.068743

24640

6.389268

9.071654

51.837371

-1

0.066034

24641

6.389268

9.071654

64.502511

-1

0.072957

24642

7.0856

9.071654

38.505643

-1

0.054364

24643

6.389268

9.071654

15.84171

-1

0.043354

24644

6.389268

9.071654

78.500824

-1

0.081693

24645

6.389268

9.071654

71.834958

-1

0.076023

24646

6.389268

9.071654

12.508778

-1

0.046304

24647

6.389268

9.071654

7.842674

-1

0.051932

24648

6.389268

9.071654

35.8393

-1

0.052395

24649

6.389268

9.071654

25.840504

-1

0.044164

24650

7.0856

9.071654

16.508296

-1

0.043014

24651

6.389268

9.071654

82.500338

-1

0.085599

24652

7.0856

9.071654

52.503957

-1

0.066323

24653

7.0856

9.071654

72.501544

-1

0.07603

24654

6.389268

9.071654

58.503232

-1

0.070325

24655

6.389268

9.071654

39.838816

-1

0.056217

24656

6.389268

9.071654

42.505163

-1

0.058606

24657

6.389268

9.071654

47.837851

-1

0.063097

24658

7.0856

9.071654

48.504438

-1

0.063241

24659

6.389268

9.071654

49.837611

-1

0.06453

24660

6.389268

9.071654

69.835203

-1

0.075471

24661

7.0856

9.071654

57.836646

-1

0.069803

24662

7.0856

9.071654

77.834236

-1

0.079713

24663

6.389268

9.071654

67.835442

-1

0.074213

24664

7.0856

9.071654

68.502029

-1

0.07379

24665

7.0856

9.071654

8.509261

-1

0.050678

24666

6.389268

9.071654

74.501305

-1

0.078119

24667

7.0856

9.071654

63.835925

-1

0.072318

24668

6.389268

9.071654

59.836405

-1

0.071072

24669

6.389268

9.071654

54.503717

-1

0.067906

24670

6.389268

9.071654

30.506608

-1

0.04766

24671

6.389268

9.071654

13.841951

-1

0.045122

24672

7.0856

9.071654

11.842192

-1

0.047091

24673

7.0856

9.071654

73.834717

-1

0.07688

24674

7.0856

9.071654

36.505885

-1

0.052462

24675

7.0856

9.071654

40.505403

-1

0.056325

24676

7.0856

9.071654

29.840022

-1

0.046562

24677

7.0856

9.071654

45.838094

-1

0.060878

24678

6.389268

9.071654

44.504922

-1

0.060166

24679

7.0856

9.071654

18.508055

-1

0.042208

24680

7.0856

9.071654

10.50902

-1

0.048482

24681

7.0856

9.071654

43.838336

-1

0.059195

24682

6.389268

9.071654

27.840263

-1

0.045281

24683

6.389268

9.071654

22.507573

-1

0.042469

24684

6.389268

9.071654

20.507814

-1

0.042114

24685

7.0856

9.071654

81.833753

-1

0.083313

24686

7.0856

9.071654

70.501788

-1

0.075037

24687

7.0856

9.071654

60.502992

-1

0.071174

24688

7.0856

9.071654

50.504197

-1

0.064909

24689

7.0856

9.071654

21.840987

-1

0.042139

24690

7.0856

9.071654

14.508537

-1

0.044676

24691

7.0856

9.071654

56.503474

-1

0.068887

24692

7.0856

9.071654

41.838576

-1

0.057189

24693

7.0856

9.071654

26.507091

-1

0.044126

24694

6.389268

9.071654

75.834478

-1

0.080004

24695

6.389268

9.071654

66.502268

-1

0.073862

24696

7.0856

9.071654

19.841227

-1

0.042012

24697

7.0856

9.071654

62.502752

-1

0.071621

238

Appendix

33590

11.688945

15.104332

13.534166

0.009849

33591

11.688945

15.104332

16.185796

0.010757

33592

11.688945

15.104332

53.971511

0.02583

33593

11.688945

15.104332

91.09432

0.032952

33594

11.688945

15.827182

57.286046

0.026124

33595

11.688945

15.104332

46.016623

0.02363

33596

11.688945

15.104332

71.870005

0.029798

33597

11.688945

15.104332

97.723391

0.033595

33598

11.688945

15.827182

93.083041

0.033005

33599

11.688945

15.104332

83.80234

0.031897

33600

11.688945

15.104332

85.791059

0.032145

33601

11.688945

15.104332

25.466498

0.015031

33602

11.688945

15.104332

38.061736

0.020775

33603

11.688945

15.827182

59.937675

0.026768

33604

11.688945

15.104332

89.105596

0.032661

33605

11.688945

15.827182

35.410107

0.019312

33606

11.688945

15.104332

107.004092

0.034203

33607

11.688945

15.104332

18.174518

0.011555

33608

11.688945

15.104332

21.489054

0.012993

33609

11.688945

15.104332

49.331159

0.02467

33610

11.688945

15.827182

19.500333

0.011755

33611

11.688945

15.104332

43.364994

0.022694

33612

11.688945

15.827182

40.050457

0.021061

33613

11.688945

15.827182

73.858729

0.029735

33614

11.688945

15.104332

55.960232

0.026334

33615

11.688945

15.104332

79.824893

0.031142

33616

11.688945

15.104332

77.173266

0.030743

33617

11.688945

15.827182

53.308603

0.025159

33618

11.688945

15.827182

49.994067

0.02429

33619

11.688945

15.827182

95.734667

0.033257

33620

11.688945

15.104332

61.26349

0.027612

33621

11.688945

15.104332

63.915119

0.028056

33622

11.688945

15.827182

22.151962

0.01293

33623

11.688945

15.827182

79.161985

0.030826

33624

11.688945

15.827182

85.128153

0.031777

33625

11.688945

15.104332

65.240934

0.028388

33626

11.688945

15.104332

99.712115

0.03389

33627

11.688945

15.827182

89.768504

0.032467

33628

11.688945

15.827182

34.084292

0.018681

33629

11.688945

15.827182

15.522888

0.010151

33630

11.688945

15.104332

32.09557

0.018322 0.014986

33631

11.688945

15.827182

26.129405

33632

11.688945

15.104332

8.230908

0.00893

33633

11.688945

15.827182

9.556722

0.008591

33634

11.688945

15.827182

37.398828

0.020112

33635

11.688945

15.827182

107.666997

0.03608

33636

11.688945

15.827182

69.881284

0.02885

33637

11.688945

15.827182

83.139432

0.031447

33638

11.688945

15.104332

75.184545

0.030415

33639

11.688945

15.827182

87.77978

0.032218

33640

11.688945

15.827182

45.353715

0.022902 0.017063

33641

11.688945

15.104332

29.443942

33642

11.688945

15.827182

17.511611

0.010874

33643

11.688945

15.827182

67.892565

0.028549

33644

11.688945

15.827182

61.926398

0.027245

33645

11.688945

15.104332

103.689555

0.034132

33646

11.688945

15.104332

24.140683

0.014459

33647

11.688945

15.827182

103.026647

0.033971

33648

11.688945

15.827182

31.432663

0.017437

33649

11.688945

15.827182

75.847453

0.030178

33650

11.688945

15.827182

71.207097

0.029214

33651

11.688945

15.104332

51.982788

0.025344

33652

11.688945

15.827182

44.027901

0.022394

33653

11.688945

15.104332

101.037928

0.034052

33654

11.688945

15.827182

65.903842

0.028058

33655

11.688945

15.104332

42.039179

0.022323

33656

11.688945

15.827182

7.568001

0.008568

33657

11.688945

15.827182

91.757228

0.03277

33658

11.688945

15.827182

99.049207

0.033737

33659

11.688945

15.104332

105.678279

0.034072

33660

11.688945

15.104332

47.342438

0.023978

33661

11.688945

15.827182

97.060483

0.033439

33662

11.688945

15.827182

101.700834

0.033913

33663

11.688945

15.827182

30.106849

0.016846

33664

11.688945

15.104332

81.150709

0.031463

33665

11.688945

15.827182

14.197073

0.009679

Bhagat | Wong

239

A.12 Bridge Selection Matrix

240

ID {0;1} {0;3} {0;6} {0;13} {1;7} {1;9} {1;10} {2;2} {2;7} {2;10} {2;14} {3;2} {3;4} {3;9} {3;14} {4;14} {6;13} {7;3} {8;2} {8;12} {9;2} {9;13} {10;1} {10;3} {10;14} {11;7} {12;2} {12;3} {12;12} {13;3} {14;1} {14;2} {15;4} {15;6} {16;3} {17;10} {17;11} {17;12} {17;13} {19;10} {19;13} {20;14} {21;13} {22;7} {23;9} {23;10} {24;9} {24;10} {24;14} {27;11} {28;2} {28;5} {28;8} {29;11} {31;0} {31;5} {31;13} {32;2} {32;10} {32;14} {33;7} {33;14} {34;0} {34;10} {35;7} {35;13} {35;14} {36;13} {36;14} {37;2} {37;6} {38;13} Appendix {39;4} {39;13} {39;14} {40;0}

01: Min. Deformation 50.592 24.401 12.247 4.760 53.949 65.178 17.204 3.806 13.593 41.793 27.815 65.178 33.671 14.216 4.760 4.346 33.446 114.882 119.189 528.663 10.707 9.788 119.189 75.706 31.562 834.440 1736.041 27.572 38.927 2815.931 1736.041 119.189 3.365 872.439 1366.189 130.610 6061.531 19.038 36.018 2219.040 39.062 39.062 2254.070 2254.070 4624.057 112.902 54.620 6.411 4619.485 5138.663 5466.575 8.097 3096.742 53.394 35.955 8.663 306.177 22.858 4331.549 46.103 9618.414 34.247 8.183 2385.594 3.020 26.135 8.142 37.901 37.350 7.949 37.901 39.247 5466.575 3.042 23.663 3.020

ORIGINAL 02: Min. 03: Max. Anchors Daylight 8.000 8.000 12.000 8.000 12.000 4.000 16.000 12.000 20.000 8.000 8.000 4.000 16.000 8.000 8.000 12.000 8.000 8.000 8.000 4.000 4.000 8.000 8.000 4.000 20.000 4.000 4.000 16.000 20.000 4.000 4.000 8.000 12.000 4.000 4.000 4.000 4.000 12.000 8.000 4.000 8.000 8.000 4.000 4.000 4.000 4.000 12.000 4.000 4.000 4.000 4.000 8.000 4.000 12.000 4.000 16.000 4.000 28.000 4.000 24.000 4.000 24.000 8.000 4.000 12.000 20.000 8.000 4.000 24.000 8.000 4.000 12.000 4.000 12.000 16.000 12.000

18.473 24.544 22.928 14.830 18.280 18.085 17.781 16.987 21.136 14.612 20.644 18.085 12.601 12.703 14.830 18.568 14.130 12.200 10.943 14.339 12.562 14.501 10.943 17.731 13.610 17.741 16.013 20.297 15.752 17.020 16.013 10.943 17.380 15.867 18.616 17.150 20.396 12.726 13.908 15.065 18.799 18.799 14.256 14.256 16.366 24.050 12.086 18.634 16.366 13.805 15.927 27.280 15.373 12.113 18.413 20.309 14.783 17.254 14.828 17.433 14.139 16.697 10.836 15.531 15.111 19.757 27.235 23.265 15.393 27.362 23.265 13.187 15.927 13.658 20.309 15.111

04: Min. Area 0.292 0.264 0.250 0.317 0.263 0.745 0.278 0.375 0.298 0.296 0.301 0.745 0.543 0.452 0.317 0.325 0.388 0.571 0.475 0.625 0.583 0.475 0.475 0.745 0.409 0.580 0.510 0.192 0.299 0.366 0.510 0.475 0.350 0.520 0.427 0.706 0.240 0.419 0.438 0.475 0.262 0.262 0.475 0.475 0.313 0.409 0.571 0.347 0.319 0.571 0.272 0.263 0.366 0.619 0.667 0.186 0.588 0.289 0.425 0.247 0.425 0.294 0.414 0.472 0.396 0.207 0.246 0.580 0.290 0.263 0.580 0.359 0.272 0.667 0.186 0.396

NORMALIZED (1:1:1:1) 01: Min. 02: Min. 03: Max. Deformation Anchors Daylight 0.997 0.999 0.999 1.000 0.997 0.996 0.999 1.000 0.999 0.998 0.999 0.996 0.998 0.999 1.000 1.000 0.998 0.993 0.993 0.969 0.946 1.000 0.993 0.996 0.998 0.951 0.899 0.999 0.998 0.836 0.899 0.993 1.000 0.949 0.920 0.993 0.646 0.999 0.998 0.871 0.998 0.998 0.869 0.869 0.730 0.994 0.997 0.992 0.731 0.700 0.681 1.000 0.819 0.997 0.998 0.999 0.982 0.999 0.747 0.997 0.439 0.998 0.997 0.861 1.000 0.999 1.000 0.998 0.998 1.000 0.998 0.998 0.681 1.000 0.999 1.000

0.833 0.833 0.667 0.833 0.667 1.000 0.500 0.667 0.333 0.833 0.833 1.000 0.500 0.833 0.833 0.667 0.833 0.833 0.833 1.000 1.000 0.833 0.833 1.000 0.333 1.000 1.000 0.500 0.333 1.000 1.000 0.833 0.667 1.000 1.000 1.000 1.000 0.667 0.833 1.000 0.833 0.833 1.000 1.000 1.000 1.000 0.667 1.000 1.000 1.000 1.000 0.833 1.000 0.667 1.000 0.500 1.000 0.000 1.000 0.167 1.000 0.167 0.833 1.000 0.667 0.333 0.833 1.000 0.167 0.833 1.000 0.667 1.000 0.667 0.500 0.667

0.521 0.165 0.260 0.735 0.533 0.544 0.562 0.609 0.365 0.748 0.394 0.544 0.866 0.860 0.735 0.516 0.776 0.889 0.963 0.764 0.868 0.754 0.963 0.565 0.807 0.564 0.666 0.414 0.681 0.607 0.666 0.963 0.586 0.674 0.513 0.599 0.409 0.859 0.789 0.721 0.502 0.502 0.769 0.769 0.645 0.194 0.896 0.512 0.645 0.795 0.671 0.005 0.703 0.894 0.525 0.414 0.738 0.593 0.735 0.582 0.776 0.626 0.969 0.694 0.719 0.446 0.007 0.240 0.702 0.000 0.240 0.832 0.671 0.804 0.414 0.719

04: Min. Area 0.782 0.829 0.853 0.737 0.830 0.000 0.805 0.638 0.770 0.774 0.766 0.000 0.348 0.506 0.737 0.724 0.616 0.299 0.466 0.207 0.279 0.466 0.466 0.000 0.580 0.285 0.405 0.953 0.768 0.654 0.405 0.466 0.681 0.388 0.548 0.068 0.871 0.561 0.530 0.466 0.832 0.832 0.466 0.466 0.746 0.580 0.299 0.686 0.734 0.299 0.815 0.831 0.654 0.217 0.135 0.964 0.270 0.786 0.552 0.858 0.552 0.778 0.570 0.470 0.602 0.927 0.861 0.285 0.785 0.831 0.285 0.666 0.815 0.135 0.964 0.602

01: Min. Deformation

LEAST IMPACT (1:10:10:1) 02: Min. 03: Max. Anchors Daylight

0.997 0.999 0.999 1.000 0.997 0.996 0.999 1.000 0.999 0.998 0.999 0.996 0.998 0.999 1.000 1.000 0.998 0.993 0.993 0.969 0.996 1.000 0.993 0.996 0.998 0.951 0.899 0.999 0.998 0.836 0.899 0.993 1.000 0.949 0.920 0.993 0.646 0.999 0.998 0.871 0.998 0.998 0.869 0.869 0.730 0.994 0.997 0.992 0.731 0.700 0.681 1.000 0.819 0.997 0.998 0.999 0.982 0.999 0.747 0.997 0.439 0.998 0.992 0.861 1.000 0.999 1.000 0.998 0.998 1.000 0.998 0.998 0.681 1.000 0.999 1.000

8.333 8.333 6.667 8.333 6.667 10.000 5.000 6.667 3.333 8.333 8.333 10.000 5.000 8.333 8.333 6.667 8.333 8.333 8.333 10.000 10.000 8.333 8.333 10.000 3.333 10.000 10.000 5.000 3.333 10.000 10.000 8.333 6.667 10.000 10.000 10.000 10.000 6.667 8.333 10.000 8.333 8.333 10.000 10.000 10.000 10.000 6.667 10.000 10.000 10.000 10.000 8.333 10.000 6.667 10.000 5.000 10.000 0.000 10.000 1.667 10.000 1.667 8.333 10.000 6.667 3.333 8.333 10.000 1.667 8.333 10.000 6.667 10.000 6.667 5.000 6.667

5.214 1.653 2.601 7.351 5.327 5.442 5.620 6.086 3.652 7.479 3.941 5.442 8.659 8.599 7.351 5.159 7.762 8.894 9.631 7.639 8.682 7.544 9.631 5.649 8.067 5.644 6.657 4.144 6.810 6.066 6.657 9.631 5.855 6.743 5.130 5.990 4.086 8.585 7.892 7.213 5.023 5.023 7.688 7.688 6.450 1.942 8.961 5.120 6.450 7.953 6.708 0.048 7.032 8.945 5.249 4.137 7.379 5.929 7.353 5.824 7.756 6.256 9.694 6.940 7.186 4.461 0.074 2.403 7.021 0.000 2.403 8.315 6.708 8.039 4.137 7.186

04 Ar

Pedestrian Network Selection Method Data

(1:1:1:1) 03: Max. Daylight 0.521 0.165 0.260 0.735 0.533 0.544 0.562 0.609 0.365 0.748 0.394 0.544 0.866 0.860 0.735 0.516 0.776 0.889 0.963 0.764 0.868 0.754 0.963 0.565 0.807 0.564 0.666 0.414 0.681 0.607 0.666 0.963 0.586 0.674 0.513 0.599 0.409 0.859 0.789 0.721 0.502 0.502 0.769 0.769 0.645 0.194 0.896 0.512 0.645 0.795 0.671 0.005 0.703 0.894 0.525 0.414 0.738 0.593 0.735 0.582 0.776 0.626 0.969 0.694 0.719 0.446 0.007 0.240 0.702 0.000 0.240 0.832 0.671 0.804 0.414 0.719

01: Min. Deformation

LEAST IMPACT (1:10:10:1) 02: Min. 03: Max. Anchors Daylight

MOST PROGRAM AREA (1:1:10:10) 01: Min. 02: Min. 03: Max. 04: Min. Area Deformation Anchors Daylight 0.997 0.999 0.999 1.000 0.997 0.996 0.999 1.000 0.999 0.998 0.999 0.996 0.998 0.999 1.000 1.000 0.998 0.993 0.993 0.969 0.946 1.000 0.993 0.996 0.998 0.951 0.899 0.999 0.998 0.836 0.899 0.993 1.000 0.949 0.920 0.993 0.646 0.999 0.998 0.871 0.998 0.998 0.869 0.869 0.730 0.994 0.997 0.992 0.731 0.700 0.681 1.000 0.819 0.997 0.998 0.997 0.982 0.999 0.747 0.997 0.439 0.998 0.992 0.861 1.000 0.999 1.000 0.998 0.998 1.000 0.998 0.998 0.681 1.000 0.999 1.000

7.815 8.288 8.533 7.371 8.302 0.000 8.055 6.379 7.702 7.735 7.656 0.000 3.480 5.058 7.371 7.237 6.162 2.993 4.660 2.070 2.788 4.660 4.660 0.000 5.800 2.851 4.049 9.530 7.683 6.537 4.049 4.660 6.810 3.880 5.484 0.676 8.713 5.614 5.302 4.660 8.322 8.322 4.660 4.660 7.456 5.800 2.993 6.863 7.342 2.993 8.152 8.307 6.537 2.173 1.352 9.636 2.704 7.856 5.517 8.577 5.517 7.779 5.704 4.703 6.020 9.269 8.609 2.851 7.847 8.307 2.851 6.655 8.152 1.352 9.636 6.020

MOST STRUCTURAL/HIGH LOADS (10:10:1:1) 01: Min. 02: Min. 03: Max. 04: Min. Deformation Anchors Daylight Area 9.972 9.988 9.995 9.999 9.970 9.964 9.992 10.000 9.994 9.977 9.986 9.964 9.982 9.993 9.999 9.999 9.982 9.935 9.932 9.693 9.458 9.996 9.932 9.958 9.983 9.515 8.989 9.986 9.979 8.358 8.989 9.932 10.000 9.493 9.204 9.926 6.464 9.991 9.981 8.707 9.979 9.979 8.686 8.686 7.303 9.936 9.970 9.998 7.306 7.003 6.811 9.997 8.194 9.971 9.981 9.988 9.823 9.988 7.474 9.975 4.388 9.982 9.923 8.610 10.000 9.987 9.997 9.980 9.980 9.997 9.980 9.979 6.811 10.000 9.988 10.000

8.333 0.521 8.333 0.165 6.667 0.260 8.333 0.735 6.667 0.533 10.000 0.544 5.000 0.562 6.667 0.609 3.333 0.365 8.333 0.748 8.333 0.394 10.000 0.544 5.000 0.866 8.333 0.860 8.333 0.735 6.667 0.516 8.333 0.776 8.333 0.889 8.333 0.963 10.000 0.764 10.000 0.868 8.333 0.754 8.333 0.963 10.000 0.565 3.333 0.807 10.000 0.564 10.000 0.666 5.000 0.414 3.333 0.681 10.000 0.607 10.000 0.666 8.333 0.963 6.667 0.586 10.000 0.674 10.000 0.513 10.000 0.599 10.000 0.409 6.667 0.859 8.333 0.789 10.000 0.721 8.333 0.502 8.333 0.502 10.000 0.769 10.000 0.769 10.000 0.645 10.000 0.194 6.667 0.896 10.000 0.512 10.000 0.645 10.000 0.795 10.000 0.671 8.333 0.005 10.000 0.703 6.667 0.894 10.000 0.525 5.000 0.414 10.000 0.738 0.000 0.593 10.000 0.735 1.667 0.582 10.000 0.776 1.667 0.626 8.333 0.969 10.000 0.694 6.667 0.719 3.333 0.446 8.333 0.007 10.000 0.240 1.667 0.702 8.333 0.000 10.000 0.240 6.667 0.832 Bhagat 10.000 | Wong 0.671 6.667 0.804 5.000 0.414 6.667 0.719

0.782 0.829 0.853 0.737 0.830 0.000 0.805 0.638 0.770 0.774 0.766 0.000 0.348 0.506 0.737 0.724 0.616 0.299 0.466 0.207 0.279 0.466 0.466 0.000 0.580 0.285 0.405 0.953 0.768 0.654 0.405 0.466 0.681 0.388 0.548 0.068 0.871 0.561 0.530 0.466 0.832 0.832 0.466 0.466 0.746 0.580 0.299 0.686 0.734 0.299 0.815 0.831 0.654 0.217 0.135 0.964 0.270 0.786 0.552 0.858 0.552 0.778 0.570 0.470 0.602 0.927 0.861 0.285 0.785 0.831 0.285 0.666 241 0.815 0.135 0.964 0.602

A.13 Pedestrian Simulation Sample Code namespace PedSim.Run_Script DO NOT COPY { public class Simulator : GH_Component { int counterSim = 0; List<Pedestrian> newPedList = new List<Pedestrian>(); /// Initializes a new instance of the Simulator class. public Simulator() : base(“Simulator”, “Sim”, “Engine which Simulates Pedestrian Behavior”, “PedSim”, “Simulator”) { } /// Registers all the input parameters for this component. protected override void RegisterInputParams(GH_Component.GH_InputParamManager pManager) { pManager.AddGenericParameter(“Pedestrians”, “P”, “Pedestrians as a List”, GH_ParamAccess.list); pManager.AddNumberParameter(“Societal Sociability”, “SS”, “Value Which Determines how Social Pedestrians Will Be Globally (1.0 = barely social, 0.5 = fairly social, 0.1 highly social”, GH_ParamAccess.item, 0.3); pManager.AddIntegerParameter(“Seed”, “S”, “Seed to Add Randomness to Social Interaction Probability”, GH_ParamAccess.item); pManager.AddIntegerParameter(“Iterations”, “I”, “Number of Iterations to Run Simulation”, GH_ParamAccess.item); pManager.AddBooleanParameter(“Solver Mode”, “SM”, “0 = Zombie Solver (No Trigger), 1 = Step Solver (Requires Trigger Attached)”, GH_ParamAccess.item); pManager.AddBooleanParameter(“Run”, “R”, “Set to True to Run Simulation”, GH_ParamAccess.item, false); } /// Registers all the output parameters for this component. protected override void RegisterOutputParams(GH_Component.GH_OutputParamManager pManager) { pManager.AddBooleanParameter(“move”, “”, “”, GH_ParamAccess.list); pManager.AddIntegerParameter(“index”, “”, “”, GH_ParamAccess.list); pManager.AddTextParameter(“State”, “S”, “State of Pedestrians”, GH_ParamAccess.list); pManager.AddIntegerParameter(“counter”, “C”, “”, GH_ParamAccess.item); pManager.AddTextParameter(“History Log”, “H”, “”, GH_ParamAccess.tree); pManager.AddNumberParameter(“State as Index”, “SI”, “State of Pedestrians”, GH_ParamAccess.list); } /// This is the method that actually does the work. protected override void SolveInstance(IGH_DataAccess DA) { List<Pedestrian> pedList = new List<Pedestrian>(); double socialFactor = 0.4; int seed = 100; int iterations = 10; bool modeBool = false; bool runBool = false; if (!DA.GetDataList(0, pedList)) return; if (!DA.GetData(1, ref socialFactor)) return; if (!DA.GetData(2, ref seed)) return; if (!DA.GetData(3, ref iterations)) return; if (!DA.GetData(4, ref modeBool)) return; if (!DA.GetData(5, ref runBool)) return;

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//if false, return if (!runBool) {{ counterSim = 0; newPedList.Clear(); return; } //run algorithm if (runBool) { Random rand = new Random(seed + counterSim); //Set up pedestrians at onset of new algorithm simulation if (counterSim == 0) { newPedList.Clear();

}

foreach (Pedestrian ped in pedList) { Pedestrian clonedPed = ped.Duplicate() as Pedestrian; newPedList.Add(clonedPed); }

// true = step solver if (modeBool) { ConvergenceCheck(newPedList, iterations); if (iterations >= counterSim) { CreateHistoryLog(newPedList); RunPedestrianSimulator(seed, newPedList, counterSim, socialFactor, rand, DA);

}

counterSim += 1; }} else { GH_Structure<GH_String> historyLog = ExportHistoryLog(newPedList); DA.SetDataTree(5, historyLog); }

// false = zombie solver if (!modeBool) { for (int i = 0; i < iterations; i++) { CreateHistoryLog(newPedList); RunPedestrianSimulator(seed, newPedList, i, socialFactor, rand, DA); }

}

GH_Structure<GH_String> historyLog = ExportHistoryLog(newPedList); DA.SetDataTree(5, historyLog);

DA.SetData(4, counterSim);

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public void RunPedestrianSimulator(int seed, List<Pedestrian> newPedList, int i, double socialFactor, Random rand, IGH_DataAccess DA) { List<Point3d> currentGlobalLocationList = new List<Point3d>(); List<string> globalStateList = new List<string>(); List<bool> globalMoveList = new List<bool>(); List<int> indexList = new List<int>(); List<int> globalStateIndexList = new List<int>();

for (int j = 0; j < newPedList.Count; j++) { //if it is time to move again (or past time), set bool to true if (newPedList[j].iterMove <= i) { newPedList[j].move = true; } // if no more destinations to move towards, just continue if (!newPedList[j].movePointDict.ContainsKey(newPedList[j].dictionaryKey)) { continue; } //if points are left else { if (newPedList[j].move == true) { //CHECK 01 //if within radius of another person, stop to chat for (int k = 0; k < newPedList.Count; k++) { //if it is not the same pedestrian, already checked at this iteration (j<K) or if already talked to that ped if (j < k && !newPedList[j].talkedToList.Contains(newPedList[k])) { //only chat if both are on the move and not chatting if (newPedList[j].move == true && newPedList[k].move == true && newPedList[j].state != “Chatting” && newPedList[k].state != “Chatting”) { if (newPedList[j].currentLocation.DistanceTo(newPedList[k].currentLocation) < 5) { newPedList[j].ChatWithPedestrian(newPedList[j], newPedList[k], socialFactor, rand, i);

}

244

}

//CHECK 02 //if reached a destination, stop moving if (newPedList[j].movePointDict[newPedList[j].dictionaryKey].Count == newPedList[j].indexPath) { newPedList[j].AtDestination(newPedList[j], i); DO NOT COPY }

//if move is true, set new move point if (newPedList[j].move == true) { DO NOT COPY newPedList[j].MovePedestrian(newPedList[j]); }

Appendix

currentGlobalLocationList.Add(newPedList[j].currentLocation); globalStateList.Add(newPedList[j].state); globalMoveList.Add(newPedList[j].move); indexList.Add(newPedList[j].indexPath); int tempStateIndex = 3; if (newPedList[j].state == “At Destination”) { DO NOT COPY tempStateIndex = 0; } if (newPedList[j].state == “On the Move”) { tempStateIndex = 1; } if (newPedList[j].state == “Chatting”) { tempStateIndex = 2; } globalStateIndexList.Add(tempStateIndex); }

DA.SetDataList(0, currentGlobalLocationList); DA.SetDataList(3, globalStateList); DA.SetDataList(1, globalMoveList); DA.SetDataList(2, indexList); DA.SetDataList(6, globalStateIndexList); }

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A.14 Co-Evolutionary Algorithm Sample Code namespace CoEA DO NOT COPY { public class CoEAComponent : GH_Component { //Persistant Data int delay = 500; int cyclesCounter = 1; int sGeneCount = 0; int p1GeneCount = 0; int p2GeneCount = 0; int sFCCount = 0; int p1FCCount = 0; int p2FCCount = 0; int individualCounter = 0; int p1IndividualCounter = 0; int p2IndividualCounter = 0; int generationCounter = 0; PopulationClass populationOne = new PopulationClass(); PopulationClass populationTwo = new PopulationClass(); PopulationClass sharedPopulation = new PopulationClass(); bool CoEA = true; bool generation = false; bool population = false; bool initialized = false; bool standardized = false; Tuple<List<GH_NumberSlider>, List<GH_NumberSlider>, List<GH_NumberSlider>> sliderCollection = new Tuple<List<GH_NumberSlider>, List<GH_NumberSlider>, List<GH_NumberSlider>> (new List<GH_NumberSlider>(), new List<GH_NumberSlider>(), new List<GH_NumberSlider>()); bool rank = true; /// Each implementation of GH_Component must provide a public constructor without any arguments. public CoEAComponent() : base(“CoEAComponent”, “CoEA”, “Run a co-evolutionary alogorithm”, “Params”, “CoEA”) { }} /// Registers all the input parameters for this component. protected override void RegisterInputParams(GH_Component.GH_InputParamManager pManager) { pManager.AddNumberParameter(“Shared Genes”, “G”, “”, GH_ParamAccess.list); pManager.AddNumberParameter(“Population 01 Genes”, “G1”, “”, GH_ParamAccess.list); pManager.AddNumberParameter(“Population 02 Genes”, “G2”, “”, GH_ParamAccess.list); pManager.AddNumberParameter(“Shared Fitness Criteria”, “FC”, “”, GH_ParamAccess.list); pManager.AddNumberParameter(“Population 01 Fitness Criteria”, “FC1”, “”, GH_ParamAccess.list); pManager.AddNumberParameter(“Population 02 Fitness Criteria”, “FC2”, “”, GH_ParamAccess.list); pManager.AddIntegerParameter(“Individual Count”, “I”, “”, GH_ParamAccess.item); pManager.AddIntegerParameter(“Generation Count”, “G”, “”, GH_ParamAccess.item); pManager.AddIntegerParameter(“Cycles Count”, “C”, “”, GH_ParamAccess.item); pManager.AddNumberParameter(“Mutation Rate”, “M”, “”, GH_ParamAccess.item); pManager.AddIntegerParameter(“Seed”, “S”, “”, GH_ParamAccess.item);

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pManager.AddBooleanParameter(“Initialize”, “I”, “”, GH_ParamAccess.item); pManager.AddBooleanParameter(“Run”, “R”, “”, GH_ParamAccess.item); pManager.AddBooleanParameter(“Reset”, “R”, “”, GH_ParamAccess.item);

}

pManager[0].Optional = true; pManager[1].Optional = true; pManager[2].Optional = true; pManager[3].Optional = true; pManager[4].Optional = true; pManager[5].Optional = true;

/// Registers all the output parameters for this component. protected override void RegisterOutputParams(GH_Component.GH_OutputParamManager pManager) { pManager.AddGenericParameter(“Population 01”, “P1”, “”, GH_ParamAccess.list); pManager.AddGenericParameter(“Data”, “D”, “”, GH_ParamAccess.list); } /// This is the method that actually does the work. protected override void SolveInstance(IGH_DataAccess DA) { RhinoApp.WriteLine(“Running...”); List<double> sGeneList = new List<double>(); List<double> p1GeneList = new List<double>(); List<double> p2GeneList = new List<double>(); List<double> sFCList = new List<double>(); List<double> p1FCList = new List<double>(); List<double> p2FCList = new List<double>(); int individualCount = 0; int generationCount = 0; int cyclesCount = 0; double mutationRate = 0.0; int seed = 0; bool initialize = false; bool run = false; bool reset = false; if (!DA.GetData(6, ref individualCount)) return; if (!DA.GetData(7, ref generationCount)) return; if (!DA.GetData(8, ref cyclesCount)) return; if (!DA.GetData(9, ref mutationRate)) return; if (!DA.GetData(10, ref seed)) return; if (!DA.GetData(11, ref initialize)) return; if (!DA.GetData(12, ref run)) return; if (!DA.GetData(13, ref reset)) return; //Data Checks if (individualCount <= 1) { AddRuntimeMessage(GH_RuntimeMessageLevel.Error, “Individual count must be larger than 1.”); return; } else if (generationCount < 1) { AddRuntimeMessage(GH_RuntimeMessageLevel.Error, “Generation count must be at least 1.”); return; } else if (mutationRate < 0.0 || mutationRate > 1.0) { AddRuntimeMessage(GH_RuntimeMessageLevel.Error, “The mutation rate must be between 0.0 and 1.0”); return; }

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// Get the active Grasshopper document GH_Document ghDoc = Instances.ActiveCanvas.Document; //Get the component that owns this script IGH_Component component = this; //Reset Component if (reset) { Reset(); } //Gather all number sliders in the document nicknamed “Gene” and all of the number containers nicknamed “FV” if (initialize && initialized == false) { populationOne._IndividualDict.Add(0, new List<IndividualClass>()); populationTwo._IndividualDict.Add(0, new List<IndividualClass>()); sharedPopulation._IndividualDict.Add(0, new List<IndividualClass>()); ghDoc.ScheduleSolution(100, doc => { //Get all genes Tuple<List<GH_NumberSlider>, List<GH_NumberSlider>, List<GH_NumberSlider>> slidersTuple = GetNumberSliders(ghDoc); sliderCollection = slidersTuple; foreach (GH_NumberSlider slider in sliderCollection.Item1) { component.Params.Input[0].AddSource(slider); } foreach (GH_NumberSlider slider in sliderCollection.Item2) { component.Params.Input[1].AddSource(slider); } foreach (GH_NumberSlider slider in sliderCollection.Item3) { component.Params.Input[2].AddSource(slider); } //Get all fitness values Tuple<List<GH_DocumentObject>, List<GH_DocumentObject>, List<GH_DocumentObject>> numContainerTuple = GetNumberContainers(ghDoc); foreach (GH_DocumentObject numContainer in numContainerTuple.Item1) { component.Params.Input[3].AddSource(numContainer as GH_Param<GH_Number>); } foreach (GH_DocumentObject numContainer in numContainerTuple.Item2) { component.Params.Input[4].AddSource(numContainer as GH_Param<GH_Number>); } foreach (GH_DocumentObject numContainer in numContainerTuple.Item3) { component.Params.Input[5].AddSource(numContainer as GH_Param<GH_Number>); } }); }

initialized = true;

//Run the CoEA if (run && initialize) { //Get all inputs and cast them to variables if (!DA.GetDataList(0, sGeneList)) return; if (!DA.GetDataList(1, p1GeneList)) return; if (!DA.GetDataList(2, p2GeneList)) return; if (!DA.GetDataList(3, sFCList)) return; if (!DA.GetDataList(4, p1FCList)) return; if (!DA.GetDataList(5, p2FCList)) return;

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sGeneCount = sGeneList.Count; p1GeneCount = p1GeneList.Count + sGeneCount; p2GeneCount = p2GeneList.Count + sGeneCount; sFCCount = sFCList.Count; p1FCCount = p1FCList.Count; p2FCCount = p2FCList.Count; //Generate an initial population if (generationCounter == 0) { //Generate P1 individuals if (populationOne._IndividualDict[0].Count < individualCount) { population = true; GenerateInitialPopulation(sliderCollection.Item2, sliderCollection.Item1, ghDoc, seed, p1GeneList, sGeneList, p1FCList, sFCList); } //Generate P2 individuals else if (populationTwo._IndividualDict[0].Count < individualCount) { population = false; GenerateInitialPopulation(sliderCollection.Item3, sliderCollection.Item1, ghDoc, seed, p2GeneList, sGeneList, p2FCList, sFCList); } //Move on to the next generations else { population = true; p1IndividualCounter = 0; p2IndividualCounter = 0; generationCounter++;

}

populationOne._IndividualDict.Add(generationCounter, new List<IndividualClass>()); populationTwo._IndividualDict.Add(generationCounter, new List<IndividualClass>());

//Run the parallel evolution stage of the CoEA if (generationCounter > 0) { if (CoEA) { //Evolve Population 01 for population = true if (population && !generation) { if (rank && population) { //Gather all of the individuals of the current generation into a single list List<IndividualClass> currentGenIndividuals = populationOne._IndividualDict[generationCounter - 1]; //Rank Individuals based upon each fitness criteria Dictionary<int, List<IndividualClass>> rankedIndividualDict = RankIndividuals(currentGenIndividuals, p1FCCount); //Select Parents based upon their rankings List<Tuple<IndividualClass, IndividualClass>> parentPairList = SelectParents(rankedIndividualDict, individualCount, p1FCCount); //Breed parents to create children for the next generation BreedParents(parentPairList, populationOne, individualCount, p1IndividualCounter); //Expire solution and schedule a new solution ghDoc.ScheduleSolution(delay, doc => { ExpireSolution(false); });

}

p1IndividualCounter = 0; rank = false;

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//Assign the slider genes to create the new children for Population 01 and evaluate their fitness values else if (!rank && population) { if (p1IndividualCounter < individualCount) { SetGenesP1(ghDoc, p1FCList, sFCList, sliderCollection.Item2, sliderCollection.Item1, individualCount, mutationRate, seed); } else { rank = true; population = false; ghDoc.ScheduleSolution(delay, doc => { ExpireSolution(false); }); } }

}

//Evolve Population 02 for population = false else if (!population && !generation) { if (rank) { //Gather all of the individuals of the current generation into a single list List<IndividualClass> currentGenIndividuals = populationTwo._IndividualDict[generationCounter - 1]; //Rank Individuals based upon each fitness criteria Dictionary<int, List<IndividualClass>> rankedIndividualDict = RankIndividuals(currentGenIndividuals, p2FCCount); //Select Parents based upon their rankings List<Tuple<IndividualClass, IndividualClass>> parentPairList = SelectParents(rankedIndividualDict, individualCount, p2FCCount); //Breed parents to create children for the next generation BreedParents(parentPairList, populationTwo, individualCount, p2IndividualCounter); //Expire solution and schedule a new solution ghDoc.ScheduleSolution(delay, doc => { ExpireSolution(false); });

}

p2IndividualCounter = 0; rank = false;

//Assign the slider genes to create the new children for Population 02 and evaluate their fitness values else if (!rank) { if (p2IndividualCounter < individualCount) { SetGenesP2(ghDoc, p2FCList, sFCList, sliderCollection.Item3, sliderCollection.Item1, individualCount, mutationRate, seed); } else { generation = true; ghDoc.ScheduleSolution(delay, doc => { ExpireSolution(false); }); } } } //Move onto the next generation else { //Check whether to continue looping the parallel optimization for the next generation or move onto the collective optimization if (generationCounter < (cyclesCounter * generationCount - 1)) { generationCounter++; p1IndividualCounter = 0; p2IndividualCounter = 0; rank = true; population = true; generation = false; populationOne._IndividualDict.Add(generationCounter, new List<IndividualClass>());

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populationTwo._IndividualDict.Add(generationCounter, new List<IndividualClass>()); sharedPopulation._IndividualDict.Add(generationCounter, new List<IndividualClass>()); RhinoApp.WriteLine(“Generation: “ + generationCounter.ToString()); }

ghDoc.ScheduleSolution(delay, doc => { ExpireSolution(false); });

//Otherwise, move on to the collective evolution of the shared genes and fitness values else { cyclesCounter++; //Check whether or not to terminate the algorithm based upon the number of specified cycles if (cyclesCounter >= ((cyclesCount * 2) + 1)) { RhinoApp.WriteLine(“Finished!”); OutputIndividuals(cyclesCount, DA); } //Otherwise, continue executing the algorithm else { generationCounter++; p1IndividualCounter = 0; p2IndividualCounter = 0;

}

rank = true; population = true; generation = false; CoEA = false;

//Run the collective evolution stage of the CoEA if (!CoEA) { //Evaluate shared fitness criteria between the two populations and standardize the shared fitness criteria from the CoEA of the two populations if (!standardized && !generation) { RhinoApp.WriteLine(“Starting Collective Analysis”); //Gather all of the individuals of the current generation into a single list List<IndividualClass> p1CurrentGenIndividuals = populationOne._IndividualDict[generationCounter - 1]; List<IndividualClass> p2CurrentGenIndividuals = populationTwo._IndividualDict[generationCounter - 1]; List<IndividualClass> allIndividuals = new List<IndividualClass>(); allIndividuals.AddRange(p1CurrentGenIndividuals); allIndividuals.AddRange(p2CurrentGenIndividuals); //Rank Individuals based upon the shared fitness criteria Dictionary<int, List<IndividualClass>> rankedIndividualDict = RankIndividuals(allIndividuals, sFCCount); Dictionary<IndividualClass, double> averageRankedIndividualDict = new Dictionary<IndividualClass, double>(); foreach (IndividualClass individual in allIndividuals) { int fc1Ranking = rankedIndividualDict[0].IndexOf(individual); int fc2Ranking = rankedIndividualDict[1].IndexOf(individual); int fc3Ranking = rankedIndividualDict[2].IndexOf(individual); double averageRanking = ((double)fc1Ranking + (double)fc2Ranking + (double)fc3Ranking) / 3; averageRankedIndividualDict.Add(individual, averageRanking); } averageRankedIndividualDict.OrderBy(i => i.Value);

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//Select the 10 best performing individuals on average List<IndividualClass> currentIndividuals = new List<IndividualClass>(); for (int i = 0; i < individualCount; i++) {{ if (!sharedPopulation._IndividualDict.ContainsKey(generationCounter - 1)) { sharedPopulation._IndividualDict.Add(generationCounter - 1, new List<IndividualClass>()); sharedPopulation._IndividualDict[generationCounter - 1].Add(averageRankedIndividualDict.Keys.ElementAt(i)); } else { sharedPopulation._IndividualDict[generationCounter - 1].Add(averageRankedIndividualDict.Keys.ElementAt(i)); } } RhinoApp.WriteLine(“Standardization Complete.”); standardized = true; ghDoc.ScheduleSolution(delay, doc => { ExpireSolution(false); }); } //If the populations are already standardized, begin evolving the shared genes and fitness criteria else if (standardized && !generation) { if (rank) { //Gather all of the individuals of the current generation into a single list List<IndividualClass> currentGenIndividuals = sharedPopulation._IndividualDict[generationCounter - 1]; //Rank Individuals based upon each fitness criteria Dictionary<int, List<IndividualClass>> rankedIndividualDict = RankIndividuals(currentGenIndividuals, sFCCount); //SelectParents based upon their rankings List<Tuple<IndividualClass, IndividualClass>> parentPairList = SelectParents(rankedIndividualDict, individualCount, sFCCount); //Breed parents to create children for the next generation BreedSharedParents(parentPairList, sharedPopulation, individualCount, individualCounter); individualCounter = 0; rank = false;

}

//Expire solution and schedule a new solution if (ghDoc != null) ghDoc.ScheduleSolution(delay, doc => { ExpireSolution(false); });

//Assign the slider genes to create the new children for the Shared Population and evaluate their fitness values else if (!rank) { if (individualCounter < individualCount) { SetGenesS(ghDoc, sFCList, sliderCollection.Item1, individualCount, mutationRate, seed); } else { generation = true; ghDoc.ScheduleSolution(delay, doc => { ExpireSolution(false); }); } }

//Move onto the next generation else { //Check whether to continue looping the parallel optimization for the next generation or move onto the collective optimization if (generationCounter < ((cyclesCounter * generationCount) - 1)) { generationCounter++; individualCounter = 0; rank = true; population = true;

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generation = false; sharedPopulation._IndividualDict.Add(generationCounter, new List<IndividualClass>()); RhinoApp.WriteLine(“Generation: “ + generationCounter.ToString()); }

ghDoc.ScheduleSolution(delay, doc => { ExpireSolution(false); });

//Otherwise, split the population and return to the parallel evolution of the two populations, using the independent genes from the last generation of the parallel evolution stage along with the newly optimized shared genes else { SplitSharedPopulation(generationCounter, cyclesCounter);

cyclesCounter++; generationCounter++; individualCounter = 0; rank = true; population = true; generation = false; standardized = false; CoEA = true;

}

}}

}

ghDoc.ScheduleSolution(delay, doc => { ExpireSolution(false); });

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Re-Neighboring the Vertical City