ABSTRACT MACHINES
DATA TRAWL
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A graphical analysis of
THE NEW MATHEMATICS OF ARCHITECTURE
CONTENTS
Chapter 1 - Surface and Seriality 6 - Surface and Seriality 7 - Thinness 8 - Plane 9 - Curvature 10 - Minimal surface 11 - Self Intersection 12 - Main Station - Stuttgart Chapter 2 - Complexity 13 - Complexity 14 - Materiality 15 - Responsiveness 16 - Recursion 17 - Chaos theory 19 - The Lourve - Abu Dhabi Chapter 3 - Nesting and Packing 22 - Nesting 23 - Symmetry 24 - Mathematical Principle 25 - Tiling 26 - The Water Cube
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Chapter 4 - Optimisation 28 - Optimise 29 - Material Optimisation 30 - Multiple Optimisation 32 - Qatar Education Centre Chapter 5 - Topology 34 - Topology Infinite Space 35 - Infinite Space 36 - Dimension in Space 37 - Datascapes 38 - Dynamic Interaction 39 - Human Interaction 40 - The Mobius Bridge Chapter 6 - Nature and Civilisation 44 - Cohabitation 45 - Natural Landforms 46 - City Forms 47 - Embodied Energy 48 - Networks and Systems 49 - Emergent restructure
Chapter 7 - Climate and Atmosphere 50 - Energy Process 51 - Energy Systems 52 - Negative Feedback 53 - Positive Feedback 54 - Planet Recycling 55 - Planet Formation Chapter 8 - Surface Landforms 56 - Live Processes 57 - Glacial Landforms 58 - Hydrology Landforms 59 - Glacial Systems Chapter 9 - Living forms 60 - Mutation 61 - Organism Efficiency 62 - Speciation 63 - Meiosis and Mitosis Chapter 10 - The forms of metabolism 64 - Food Webs 65 - Metabolic Rate 66 - Tree Shading 67 - Leaf Arrays 68 - Endothermic and Ectothermic
Chapter 11 - Humans (Cultural form) 69 - Heat Retention 70 - Heat Regulation 71 - Rift Theory 72 - Over Specification 73 - Generalisation 74 - Preferential Prey 75 - Extinction Thresholds Chapter 12 - City forms 76 - Civilisation Development 77 - Critical Extinction 78 - Higher Complexity 79 - Public/Private zones Chapters 13 - The forms of information 80 - Fragmentation 81 - Intelligent Networks 82 - Energy and Ecology Chapter 14 - Emergence 83 - Collapse and Reorganisation 84 - Emergence
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SURFACE AND SERIALITY
Surface
Series
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Surface
THINNESS
Void
Divided space using an infinitesimal surface
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PLANE
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CURVATURE
Material limitations, example torsion on wooden element
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MINIMAL SURFACE
Equal net curvature values based upon surfaces equally transformed in universal direction
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SELF INTERSECTION
Kleine surface, acting in a mobius fashion whilst self intersects
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MAIN STATION STUTTGART - IN MAIN STATION STUTTGART - INGENHOVEN ARCHITECTS The new main station in Stuttgart incorporates new construction techniques to explore the ideas of thinness, creating a shell with a disappearing dimension that uses a minimal surface to provide both vertical and roof structure as well as providing openings allowing light and air into the central chamber
COMPLEXITY THEORY
Variable outcomes from a parametrised system
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MATERIALITY
Material development derived from naturally occurring systems at a micro scale
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RESPONSIVENESS
Design with a confined set of parameters such as height and volume, allowing for multiple generative forms
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RECURSION
A system in which outputs are reintroduced as inputs
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CHAOS THEORY
Micro-scale changes that extrapolate exponential
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THE LOUVRE ABU DHABI – A THE LOUVRE ABU DHABI – ATELIERS JEAN NOUVEL
This proposal for the new Louvre in Abu Dhabi utilises a recurring fractal pattern to create a canopy that spans the site, modelled on traditional eastern screening techniques, explored through varying iterations studying the light qualities created within the “other world” beneath
NESTING
Advanced digital fabrication method to optimise space
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SYMMETRY
Sierpinski’s mathematical formula demonstrating formation within multiple iterations of triangles
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MATHEMATICAL PRINCIPLE
2D and 3D spatial optimisation of simple and optimal geometries
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TILING
Macro, meso and micro scale of structural weight analysis
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THE WATER CUBE – P THE WATER CUBE – PTW ARCHITECTS This water sports facility in Beijing has an optimised bubble like facade capable of displaying and outputting various information through the flexible usage of its smart facade. The facade suggests the boundaries between specific geometries have evolved and self optimised based on a special paradigm.
OPTIMISATION
Geometrical reaction to external forces
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MATERIAL OPTIMISATION
Optimisation to minimise material waste
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MULTI OPTIMISATION
Evolving systems may have a detrimental effect upon surrounding systems
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QATAR EDUCATIONAL CENTRE– A AR EDUCATIONAL CENTRE– ARATA ISOZAKI The design was based upon a cultural icon in the region, the Bonsai tree. The imagery and geometry produced was difficult to construct and a clever amalgamation of digital principles previously mentioned were put into practice when designing the internal structure of the tree.
TOPOLOGY
A mathematical problem being solved to optimise a route
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INFINITE SPACE
By intersecting an infinite plane with a boundary you can create a boundaryless plane
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DIMENSIONS IN SPACE
0 Dimensions
1 Dimension
2 Dimensions
Intrinsic and extrinsic perception of dimension in space
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3 Dimensions
DATASCAPES
Manipulation of a modular system for intelligent display
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DYNAMIC INTERACTION
Place and experience varying over time for example lighting within a smart facade
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HUMAN INTERACTION
Responsive systems based on human interactions
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THE MOBIUS BRIDGE – H THE MOBIUS BRIDGE – HAKES ASSOCIATES This competition winning design for a footbridge across the River Avon was structurally independent of the river banks and unthreatening to the surroundings. This was achieved through the best known non-orientable surface, the Mobius strip. The bridge encompasses a minimal crossing point and compressional arches to optimise the structure.
A graphical analysis of
THE ARCHITECTURE OF EMERGENCE
COHABITATION
The symbiosis of Anthropogenic and biological systems
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NATURAL LANDFORMS
Hydraulic action is a live process to form a natural landscape
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CITY FORMS
Hierarchy and social orders within a conurbation
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EMBODIED ENERGY
States of energy, solar, chemical and thermal
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NETWORK AND SYSTEM
Interconnectivity between nodal systems
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EMERGENT RESTRUCTURE
A system breakdown can lead to a reorganisation of a network
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ENERGY PROCESS
Constant terrestrial energy cycles with solar input
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ENERGY SYSTEMS
Lapse rate and magnetic orientation. Lapse rate is a microscheme that retains radiation levels within the atmosphere
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NEGATIVE FEEDBACK
A system that’s outputs rein-forms its input further reinforcing an outcome
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POSITIVE FEEDBACK
Positive feedback is an unregulated system
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PLANET RECYCLING
Tectonic recycling allowing the Earth’s crust to renew
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PLANET FORMATION
Pangea
Archipelago
Triassic
Modern
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LIVE PROCESSES
Interlocking glacial systems that restrict tectonic movements
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GLACIAL LANDFORMS
Glacial land formation
Aoelion land formation
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HYDROLOGY LANDFORMS
Water defining a landscape dependent upon its weight speed and volume
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GLACIAL SYSTEMS
Varied sea-level rise from differing glacial formations
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MUTATION
Hopeful monsters, mutation most commonly resulting in detrimental affects upon the organism
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ORGANISM EFFICIENCY
Direct energy transfer to organisms capable of photosynthesis increase efficiency
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SPECIATION
Expansion beyond a sustainable boundary and retraction
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MEIOSIS AND MITOSIS
Self replication or hybridisation within cells
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FOOD WEB
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METABOLIC RATE
Lower metabolic rate increases lifespan, requires less energy to sustain
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TREE SHADING
Adaptation to optimise light to lower branches
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LEAF ARRAYS
Natural attractors between zonal demarcations
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ENDOTHERMIC AND ECTOTHERMIC
Heat transfer from environment to organism
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HEAT RETENTION
Increased surface areas means greater heat loss
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HEAT REGULATION
35⁰C
35⁰C
Regulation of micro climate to increase metabolic rate
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35⁰C
RIFT THEORY
Early separation of developing species can lead to varied environment development
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OVER SPECIFICATION
Over specification for particular climates can leave you vulnerable to programmatic change
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GENERALISATION
Generalisation to multiple climates allows for increased adaptability
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PREFERENTIAL PREY
Species with larger metabolic values are preferential to those with a lower metabolic rate
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EXTINCTION THRESHOLDS
10% 25% 40%
The larger the species the lower its critical threshold with regards to extinction
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CIVILISATION DEVELOPMENT
Self regulated systems optimise, reorganise and subdivide within an emergent order
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CRITICAL THRESHOLD
Expanding beyond the boundaries of a system causing restructuring
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HIGHER COMPLEXITY
Self sufficient components interacting within a regulated construct
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PUBLIC PRIVATE ZONES
Hierarchical development of space
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FRAGMENTATION
Increased yield from resource via spatial distribution of settlement
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INTELLIGENT NETWORKS
Connectivity and resource transfer within nodal settlements
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INFORMATION ENERGY AND ECOLOGY
Genetic modification to increase crop yields
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COLLAPSE AND REORGANISATION
Resource depletion via deforestation and desertification
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EMERGENCE
Emergent systems occurring on a multitude of scales within the same parameters
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NICK HART-WOODS, SAM HAYES, DOMINIC KENNEDY