Cellular Automata : Developing a Rule Based System for Spatial Organization by Jinal Shah

C E L LU L A R A U T O M ATA

Developing Rule Based System for Spatial Organization

Faculty of Design | CEPT University International Masters of Interior Architectural Design Jinal Shah | PI00617 Guided by : Ar. Radhika Amin

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ACKNOWLEDGMENT Without the contribution of certain people, i would not have been able to realize this work. First, I would like to express my gratitude to Ar. Radhika Amin, with her guidance and support i was able to explore new dimension for my thesis. Her constant efforts, weekly discussions and motivation helped me finish my thesis on time. I am also very grateful to my professors Ar. Jwalant Mahadevwala and Ar. Arpi Maheshwari for giving me advice, inspiration and encouragement during the entire course of computational design. Additionally, i would like to thank my family and friends for supporting and inspiring me thoughout this time.

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CONTENTS ABSTRACT 1. INTRODUCTION 1.1 Overview

.....09

1.2

Cellular Automata

.....10

1.3

Research Question

.....13

2. DOMAIN 2.1 Overview

.....16

2.2

Low Cost Housing in Cities

.....17

2.3

Cellular Automata in Architecture

.....18

2.4 Ambition

.....19

3. METHODS 3.1 Overview

.....23

3.2

Generative Method

.....24

3.2

Evaluation Methods

.....30

4. CA RULE DEVELOPMENT 4.1 Overview

.....38

4.2

.....42

CA Rule Exploration

4.3 Conclusion

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.....81

5. LOW COST HOUSING TYPOLOGIES 5.1 Overview

.....85

5.2

.....86

Case Studies

5.3 Conclusion

.....100

6. CA RULE IMPLEMENTATION 6.1 Overview

.....107

6.2

.....110

CA Rule Implementation for Housing

6.3 Conclusion

.....168

7. CONCLUSION 7.1 Overview

.....175

7.2

.....176

A Way Forward

8. APPENDIX 9. REFERENCE & BIBLIOGRAPHY

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ABSTRACT The metropolitan cities across the world are facing an insurgent growth resulting in constant inflow of people in urban areas. The ever increasing urban population and the booming land rates have led to an increase in housing deficit within the metropolitan areas. New strategies for developing affordable housing are implemented to bridge the gap. The current design models for affordable housing, in the city of Mumbai are based on development control rules, which aims at achieving maximum density within minimum area. This model of planning neglects the spatial quality and relation between the built, open and semi open spaces. This thesis aims at developing new strategies of spatial planning for affordable housing for a metropolitan city like Mumbai, by exploring the concept of rule based system of 2 dimension Cellular Automata. A sequence of experiments are developed to explore the different rules of cellular automata. The generated volume by iterative design process is tested for environmental and spatial performances. The thesis concludes with the potential of this rule based model as an alternate growth strategy for housing.

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01 INTRODUCTION

1.1

OVERVIEW

1.2

CELLULAR AUTOMATA

1.3

RESEARCH QUESTION

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1.1 Overview In todayâ&#x20AC;&#x2122;s time, designing urban environments is a complex process where many constraints are to be considered (Negroponte, 1970 ). Currently, such designs are an outcome of the decisions taken by architects and urban planners. A more holistic and a context based understanding, which incorporates various parameters is required, as a result generative design approaches have emerged as a tool to search for strategies to design (Negroponte, 1970 ). Computer Aided Designs are used as variance - producing engines to navigate large solution spaces and come up with unexpected solution (Negroponte, 1970 ). The strength of the computer as a tool stems from its capability to perform tasks that rely on numerical formalized dimensional or relational constraints. In this context, Cellular Automata, is used as a generative design tool by architects as it is characterized by the simplicity of the input and complexity of the output. CA is driven by local communication between cells which are arranged on a larger grid. The individual state of the cell is determined by the state of its neighboring cells. The design process is a bottom up approach where the input is in form of rules which govern the state of each cell, however the results are complex and as a result various spatial organization systems can be explored and evaluated.

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fig 1 : Rule 250 - Diagram showing the rules of neighborhood for 1D CA

1.2 Cellular Automata The concept of Cellular automata was first introduced by John von Neumann ( von Neumann, 1963 ) in 1940’s and developed along with Sanislaw Ulam. The concept of 2D CA became more popular by John Conway’s ‘ Game of Life’ and later approximated in three dimension ( Bays, 1987). Cellular Automata (CA) is a rule based system, where application of simple rules can result into complex patterns. CA is model is formed by a infinite regular grid of cells, where each cell has a definite state. The state of the cell at particular time ( t ) is determined by the state of its neighboring cells in the previous time, t= (t-1). The universe of CA has evolved over all the three dimensions. The CA patterns can be explored for all the 3 dimensions by defining the neighborhood rules (Krawcyk, 2002). The diagram above shows the pattern developed by defining the neighborhood rules for 1D CA. The universe of 1D CA consists of a line of cells, each colored black or white. At every step there is a definite rule that determines th color of a given cell from the color of that cell and its neighbors on the step before ( fig 1.1). (Wolfram, 2002).

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fig 2 : Recreated frame from Conway’s ‘Game of Life ‘

1.2.1 Game of Life The ‘Game of Life’, is a 2D Cellular Automaton developed by John Horton Conway in 1970. It is an infinite, two- dimensional orthogonal grid of square cells, with each cell having either of the two states or value - dead or alive ( 0 or 1). The state of black cell is considered - alive (value = 1) and white cell dead (value = 0). Rule 23 | 3

< 2 neighbors | loneliness

Each cell under consideration has eight neighbors the adjacent horizontal, vertical and diagonal cells. The state of the cell in next generation are governed by a set of rules which are defined as follows.

• Loneliness - an alive cell with less than 2 neighbors dies due to underpopulation.

• Birth - a dead cell with exactly 3 live neighbors comes to life

= 3 neighbors | newborn

• Overpopulation - an alive cell with more than 3 neighbors die due to overpopulation.

• Stasis - any alive cell with exactly 2 or 3 live fig 3 : Diagram showing rules of Game of Life

neighbors stays alive.

> 3 neighbors | Overpopulation

This rule of Game of Life is stated as - Rule 23|3

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fig 4: Patterns achieved by varying rule-set of GOL for the same initial state

1.2.2 Game of Life - Variation For a cell under consideration in 2D CA, the minimum number of neighboring cells = 1 and the maximum number of neighboring cells = 8 Thus the different patterns can be achieved and analyzed by varying the rules of birth and death. The figure above shows the research done by AA Design Research Lab Workshop on Cellular Automata. In each experiment the initial state is constant and the patterns generated by varying the rules of birth and death are observed and analyzed.

1.2.3 Game of Life -2D Spatial Layering The generative process is considered as a set of layers instead of a change of a single system. The two dimensional grid of the cellular automata is given the third dimension and thus it has a spatial context. The rectangular cells are converted into a cubic block and the change in the state of cell in every generation is reproduced on the level above, resulting in a volume which can be analyzed spatially and volumetrically. The figure 5 shows the representation of the rules of Game of life in 2D Spatial Layering.

14 | Cellular Automata

< 2 neighbors | loneliness

= 3 neighbors | newborn

= 2 neighbors | stasis

> 3 neighbors | Overpopulation

fig 5 : Diagram showing the rules of Game of Life - 2D Spatial Layering

1.3 Research Question How can the concept of rule based System of Cellular Automata be explored to generate organized spatial forms of different scales ? How can a system of layering 2D Cellular Automata be explored to generate spatial form at different scales with varying volumetric density, connectivity and relation between the spaces ?

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02 DOMAIN

2.1

OVERVIEW

2.2

LOW COST HOUSING

2.3

CELLULAR AUTOMATA IN ARCHITECTURE

2.4 AMBITION

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fig 6 : Map showing the increase and projected growth in the World City Population.

1950

2.1 Overview The world is facing an insurgent growth in population. Over decades urbanization have become an inevitable part of these emerging economies. More then 50% of worldâ&#x20AC;&#x2122;s population ( approximately 4.5 billion) lives in developing countries of Asia, with China and India having the maximum population of 1.4 billion and 1.2 billion respectively. India is on the path of constant and rapid development and economic growth. This rapid development has resulted into rapid urbanization. The urban India constitutes 32% of countryâ&#x20AC;&#x2122;s population, housing 377million people as per 2011 census (JLL, 2018). According to the World Population report by UN, 40% of countries population is expected to dwell in Urban area, by 2030. As a result our cities face the consequences of exponential urbanization and development - increase in the number of informal settlements, decrease in the availability of land, increase in real estate-prices, lack of infrastructure and lack of housing. Housing the urban poor and providing a quality of life is one of the challenging tasks faced by the cities (JLL, 2018)..

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1990

2015

2035

fig 7 : Low cost, SRA building in Mumbai

2.2 Low Cost Housing The cities of India, especially the metropolitans of Mumbai and Delhi are under constant pressure and are struggling to accommodate the ever increasing population. The increasing land prices and the constant pressure of accommodating densities have resulted in the development of regulation which provide higher FSI for plots and decreasing the open spaces between adjacent buildings. In Mumbai, various schemes have been developed and implemented to house the economically weaker sections. Such housing projects aim at achieving maximum density within a limited plot area. In such high rise, high dense buildings, there is no relation between the built, open and the semi open spaces Even the basic necessities of light and ventilation are not addressed. Over time a few low cost housing projects have been designed and constructed which exhibit the spatial, cultural and community relations. One such project is the Aranya Housing designed by Ar. B. V. Doshi in Indore. The unit typology designed for the project was user defined and provided the possibility of future increment for each dwelling.

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fig 8b :

fig 8a : Aranya Housing , Indore, India

the design intended at creating community space and establishing relation between the built, open an semi-open spaces but not accommodating high densities. it is important to find a design approach which strikes a balance between accommodating density and providing a good quality of life. Thus It is important to explore a new design concept which is not governed by the rules of development but by defining the relation between the adjacencies. The top down approach for designing needs to be altered and a bottom - up approach needs to be implemented.

2.3 Cellular Automata in Architecture Cellular Automata has received attention as a generative strategy to design volumes due to the simplicity of the rules and the complexity of the outcomes. It is a bottom up approach where the state of each cell is based on the state of its neighbors.. Thus by the adopting the concept of Cellular Automata as a design tool, various organization patterns with inherent spatial relations can be achieved. There patterns can be further evaluated and various strategies can be defined for the application of CA within a domain.

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Incremental growth of units

2.4 Ambition Cellular Automata dwells on the concept of establishing and defining the rules of adjacencies, which is a self organizing system to achieve a spatial form. Each state of cell can correspond to a spatial function and thus organization of patterns achieved by defining the rules of adjacencies can be evaluated for spatial performance. The research aims at exploring the concept of spatial layering of 2D Cellular Automata as a design tool to develop a rule based spatial organization system for low cost housing.

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03 METHODS

3.1

OVERVIEW

3.2

GENERATIVE METHODS

3.3

EVALUATION METHODS

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3.1 Overview The aim of thesis is to explore the concept of 2D Cellular Automata as a tool to develop spatial organization system for low cost housing. For this purpose, the research is conducted in three main stages which are as follows : Stage 01 : Cellular Automata Rule Development Stage 02 : Case Studies - Low Cost Housing Stage 03 : Cellular Automata Rule Implementation In this chapter, the general process adopted and the tools used for evaluation and analysis are explained.

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3.2 Generative Method Stage 01 - CA Rule Development The first set of experiments were conducted to explore the different rules of 2D Cellular Automata for Spatial Layering. Varying rules of birth, death, transformation and stasis were explored and the cell densities, ratio of densities, continuity of void and the similarity of cell organization achieved were observed at regional ( individual level ) and global ( entire volume ) level. A comparative analysis of the different rules enable us to further explore the potential of rules within spatial context. The flow diagram on the adjacent page shows the general method adopted and analyzing the CA rules. Further, the different state of cell, rules of adjacencies are explained in detail in Chapter 04 CA Rule Development. The various rules of adjacencies were defined using Java - Processing as a cosing language. The patterns achieved by running the rule for â&#x20AC;&#x2DC; n â&#x20AC;&#x2DC; number of time were further analzyed based on defined parameters.

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CA Rule 2D Spatial Layering

Evaluation of Level ( t )

Evaluation of Volume

Density

Void

Ratio of the Black , Grey and white Cells

Continuity of Void

Evaluation and Implementation

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Stage 02 - Case Studies - Low Cost Housing A set of 6 Low Cost Housing projects in Mumbai with varying unit typology and layout, built over time are selected for the purpose of this research. The Housing Typology considered are as follows :

• • • •

Chawl Typology Incremental Housing Project Slum Rehabilitation Authority (SRA) Project Redevelopment Project - Rehab Building

Each project was analyzed for spatial and environmental performance. The flow diagram on the adjacent page shows the general process adopted for the analysis. A comparative analysis was conducted to evaluate the values obtained from each case and the optimum values for environmental and spatial performance were extracted.

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Housing Typology Climatic Habitability

6 Low Cost Housing Projects

Environmental Analysis

Volumetric Analysis

Sunlight Hours Solar Radiation Visibility

Linkage Circulation Access

Existing Climatic Conditions

Optimum Values for human comfort

Circulation & Semi Open Area

Built Area

Optimum density ratio

Extracting Parameters for implementation and evaluation of CA rules

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Stage 03 - CA Rule Implementation Based on the extracted parameters from the case studies, the rules applicable for the spatial organization are further explored and analyzed. The rules were evaluated and analyzed for spatial and environmental performance at global, regional and local levels. The flow diagram on the adjacent page shows the general process adopted for the analysis. Environmental analysis were conducted on the circulation and semi- open areas at each level to determine the areas with optimum solar radiation visibility, sunlight hours and wind speed. Furthermore, strategies for incremental growth were developed for these areas. Neighborhood analysis were conducted to develop strategies for linkage, access, circulation and further determine the density of people, unit typologies, circulation area and semi open area at local, regional and global levels.

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Implementation of CA Rule Spatial organization for Low Cost Housing

Neighborhood Analysis

Environmental Analysis

Global

Regional

Local

Evaluation for entire Volume

Evaluation for Individual Level ( t )

Evaluation of relation between cells

Climatic

Spatial

Density

Linkage + Circulation

Access

Sunlight hours Solar Radiation CFD

Visibility Continuity of Void

% of Black & Grey cells

Clustering of Black cell Continuity of grey cell

Relation between adjacent black & grey cell

Strategies for Incremental growth

Unit Typology

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3.3 Evaluation Methods Environmental Analysis

Sunlight Hours Analysis

Adequete amount of sunlight is essential to keep the interior spaces lit. It reduces the need of artificial lighting. For exterior spaces it helps to understand the areas which are under shade due to self shading. Based on the analysis different functions can be defined for the exterior spaces. The sunlight hour analysis was conducted for the summer and winter solstice i.e 21st June and 22nd December respectively. The circulation and semi open areas at each level were analyzed to determine the area receiving 2 hours of sunlight. The analysis was conducted using ladybug.

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Visibility Analysis

Visibility analysis provides a quantification of the exterior area which has a range of optimum visibilty. The analysis was conducted for the circulation and semi open area at each level to determine the area receiving 0 - 100 % visibility of the surroundings. It quatifies the area which will receive optimum visibilty after increment. The visibility analysis considers the 360o Horizontal 60 degree cone of vision. The analysis was conducted using ladybug.

Solar Radiation Analysis

Computational Fluid Dynamics ( CFD ) Analysis

Appropriate solar radiation is important for building to function. It improves the quality of the occupied areas and reduces energy consumption for artificial lighting and, paired with material albedo, determines the heat gain of the building, which is desirable during summers and winters.

Computational Flud Dynamics ( CFD ) is a virtual simulation environment that provides qualitative and sometimes quantitative predictions about behaviour of fluids within closed or open spaces. The CFD analysis was conducted to determine the average wind speed and wind movement within the open and semi-open spaces of the volume.

The solar radiation analysis was conducted for the summer and winter solstice i.e 21st June and 22nd December respectively. The circulation and semi open area at each level were analyzed to determine the area receiving solar radiation within the range of human comfort. This was measured to determine the possibility of future increment. The analysis was conducted using ladybug for grasshopper.

In order to conduct the wind flow tests, Autodesk Simulation CFD was tested. The CFD analysis was conducted for the entire volume and the average wind speed was calculated by analysing the wind rose diagram for the months of July - September for Mumbai. Wind Speed = 4 m/ s Wind Direction = West

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Environmental Analysis _ Optimum Surface Area

Level

Sunlight Hour Analysis 21st June

Visibility Analysis

22nd Dec

Surface Area receiving more than 2 hrs of direct Sunlight / day

Surface Area with more than 30% of Visibility

> 2hrs of sunlight / day

> 30% Visibility

< 2hrs of sunlight / day

< 30% Visibility

Surface Area with optimum sunlight hours

Surface Area with optimum visibility

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Solar Radiation Analysis 21st June

CFD Analysis

22nd Dec

Surface Area receiving more than 1kwh of Solar Radiation / day

Wind Movement

> 1kwh / m2 of Solar Radiation / day < 1kwh / m2 of Solar Radiation / day

Surface Area with optimum solar radiation

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Neighborhood Analysis ( Von Neumann Neighborhood )

Linkage

Circulation

Black cell adjacent to black cell

Grey cell adjacent to grey cell

Linkage + Circulation + Access

Possibilities of Clustering of black cells

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Access Grey cell adjacent to black cell

Strategy 01 Grey Cell =

50 % Semi Open Area + 50 % Circulation Area

Possibilities of position of Semi Open Area

Strategy 02 Grey Cell =

100 % Semi Open Area ( Internal Courtyard )

Possibilities of position of Courtyard

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04 CA RULE DEVELOPMENT

4.1

OVERVIEW

4.2

CA RULE EXPLORATION

4.3 CONCLUSION

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4.1 OVERVIEW 4.1.1 State of Cell John Conway’s ‘ Game of Life’, explores various CA patterns achieved by defining 2 states of a cell black and white ( alive and dead respectively) where the value of black cell = 1 & white cell = 0 The experiments aim at exploring and analyzing the patterns achieved by defining more then 2 states of cell and modifying the basic rules of 2D CA. For the purpose of this research 3 states of a cell and their corresponding values are defined. fig ( ) shows the state of cell and its corresponding values. As the state of cell in next generation depends on the sum of its neighboring cells, by defining 3 states for a cell increase the total of the neighboring cells and thus increasing the possibilities of variation in the rules for loneliness, overpopulation and birth.

White = 0

Black = 1

Grey = 2

For any cell under consideration the minimum total of neighboring cells = 1 the maximum total of neighboring cells = 16 For the purpose of this research, two different rule - sets are defined which explore various rules of 2D CA. Rule Set 1 - The state of cell in next level is defined by total of its neighboring cells as range of values Rule Set 2 - The state of cell in next level is defined by total of its neighboring cells as absolute values. The fig. ( ) demonstrates the rules of adjacencies for Rule 1 from Rule-set 1. Keeping the number of levels, each ruleset explores 3 rules and each of the 3 rules are explored for 3 different grid sizes which are as follows : • 12 x 12 • 9 x 9 • 9 x 18 The flow diagram 4.1.3 shows the experimental setup for the exploration of the 2D CA rules.

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Total of neighboring cells

fig 9 : State of Cell

= 16

BIrth / Death / Transformation

Birth

Stasis

White

Grey

White

Black

Grey

Black

White

Grey

Black

Grey

White

Death

Transformation

White

Black

Death

Transformation

Black

Grey

fig 10 : Possible state of cell in next level

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4.1.2 Rule Demonstration Current state of Cell

Loneliness - Death

State of Cell in Next Level

Sum of Neighbors

< 2 Black

White

< 2

Overpopulation - Transformation

Grey

>=3 & <=6 Black

Grey

Overpopulation - Death

White

Black

Grey

>=3 & <=6

> 6 & < = 16

Black

White

Birth

>=3 & <=5 White

White

The state of other cells remain constant

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Black

>=6 & <=9

Grey fig 11 : Demonstration of Rule 1 _ Rule set 1

4.1.3 Experimental Setup

CA Rule 2D Spatial Layering

Rule Set 1

Rule Set 2

sum of the values of Neighboring cells as range of values

sum of the values of Neighboring cells as absolute values

Rule 1

Rule 2

Rule 3

Rule 5

Rule 4

Rule 6

Grid Size 12 x 12

9x9

9 x 18

Initial State = Random No. of levels = 9

Evaluation Criteria Density of Black, Grey & White cells

= Individual Level & Volumetric

Location of Void

= Individual Level

Continuity of Void

= Volumetric

Ratio of Black : Grey cell

= Volumetric

Similarity of cell organization

= Volumetric

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4.2 CA Rule Exploration Rule -Set 1 Rule 1 - 3 The state of cell in next level is defined by sum of its the neighboring cells as a range of values. Different rules of adjacencies can be explored for different states such as loneliness, overpopulation and birth.

Current state of Cell

Sum of Neighbors

Overpopulation = Transformation

State of Cell in Next Level

Black

>=3 & <=6

Grey

Black

> 6 & < = 16

White

Overpopulation = Death

fig 12 : Rule of Adjacencies from rule 1

The figure 12 demonstrates a set of rules of adjacencies from Rule 1. The rules stated are as follows : â&#x20AC;˘ a black cell transforms into a grey cell due to overpopulation when the total of the neighboring cells range between > = 3 & < = 6 â&#x20AC;˘ a black cell transforms into a grey cell due to overpopulation when the total of the neighboring cells range between > 3 & < = 16 Likewise, figure 11 on the previous page demonstrates the entire Rule 1 from Rule set 1 where varying rules for overpopulation and birth are defined.

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Rule - Set 2 Rules 4 - 6 The state of cell in next level is defined by, exploring the rules of transformation, birth and death by defining the sum of the neighboring cells as an absolute value

Current state of Cell

State of Cell in Next Level

Sum of Neighbors

White

Black

White

Grey

fig 13 : Rule of adjacencies from rule 5

The figure 13 demonstrates a set of rules of adjacencies from Rule 5. The rules stated are as follows: â&#x20AC;˘ a white cell is born as a grey cell, when the total of neighboring cells = 3 & â&#x20AC;˘ a white cell is born as a black cell when the total of neighboring cells = 4 Thus it can be observed that different rules of birth can be defined for same state of cell depending on the sum of the neighbors defined. Furthermore, varying rules for death and overpopulation can be defined.

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Rule 1 Current state of Cell

Black Loneliness - Death

State of Cell in Next Level

Sum of Neighbors

White < 2

Grey

White

Overpopulation - Transformation

< 2

Black

Grey >=3 & <=6

Grey

Black

Overpopulation - Death

>=3 & <=6

Black

White > 6 & < = 16

Grey

White > 6 & < = 16

White

Black

Birth

>=3 & <=5 White

Grey >=6 & <=9

The state of other cells remain constant

fig 14a : Diagram explaining 2D CA Rule 1

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Experiment 1a Grid size Initial State No. of Levels

= 12 x 12 = Random =9

t1a = 00

t1a = 01

t1a = 02

t1a = 03

t1a = 04

t1a = 05

t1a = 06

t1a = 07

t1a = 08

Inference The range of volumetric density achieved for each cell are as follows : Black = 19% - 39% Grey = 24% - 33% White = 30% - 57 %

Volumetric Packing

fig 14b : Rule 1_ 12 x 12 Plans for each levels and volumetric packing

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Experiment 1b Grid size Initial State No. of Levels

=9x9 = Random =9

t1b = 00

t1b = 01

t1b = 02

t1b = 03

t1b = 04

t1b = 05

t1b = 06

t1b = 07

t1b = 08

Inference The range of volumetric density achieved for each cell are as follows: Black = 20% - 36% Grey = 22% - 40% White = 32% - 52%

Volumetric Packing

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fig 14c : Rule 1_ 9 x 9 Plans for each levels and volumetric packing

Experiment 1c Grid size Initial State No. of Levels

= 9 x 18 = Random =9

t1c = 00

t1c = 01

t1c = 02

t1c = 03

t1c = 04

t1c = 05

t1c = 06

t1c = 07

t1c = 08

Inference The range of volumetric density achieved for each cell are as follows : Black = 19% - 38% Grey = 19% - 35% White = 41% - 62 %

Volumetric Packing

fig 14d : Rule 1_ 9 x 18 Plans for each levels and volumetric packing

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Rule 1

Experiment 1a

Levels

Experiment 1c

Experiment 1b

t1 = 00

t1 = 01

t1 = 02

t1 = 03

t1 = 04

t1 = 05

t1 = 06

t1 = 07

t1 = 08

table 1a : Rule 1 - Cell densities at Individual Level

Inference It is observed from the above set of experiments 1a, 1b and 1c that the minimum and maximum cell density that can be achieved at a particular level by the application of Rule 1 are as follows : Min Max Black = 19% 39 % Grey = 19% 40 % White = 30% 62 %

All values are in %

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Range of cell density observed at maximum levels are as follows : Black = Grey = White =

24% 24% 37% -

35 % 32 % 49 %

Volume

Experiment 1a

Experiment 1b

Experiment 1c

Black

28.54 %

28.80 %

27.09 %

Grey

26.46 %

28.25 %

25.51 %

White

45 %

42.95 %

52.60 %

Continuity of Volumetric Void

0 %

Volumetric Ratio (B:G)

1:1 (Approximately)

1:1

1:1 (Approximately)

Similarity of cell organization

Volumetric Density

table 1b : Rule 1 - Volumetric evaluation

Conclusion It is observed from the above set of experiments - 1a, 1b and 1c that the volume achieved by the application of Rule 3 has different cell organization at every level. • The variation in the density of cell at every level ranges between 10% - 12%. • There is a difference of 1% between the ratio of overall volumetric density of black : grey cells. • The void achieved at maximum number of level range between 37% - 49% but the overall continuity of void across the entire volume is 0%

All values are in %

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Rule 2

Loneliness - Death

Current state of Cell

Black

State of Cell in Next Level

Sum of Neighbors

White

< 2

White

Grey

Overpopulation - Transformation

< 2

Grey

Black >=3 & <=9

Black

Grey

Overpopulation - Death

>=3 & <=9

White

Black > 9 & < = 16

White

Grey > 9 & < = 16

Black

White Birth

>=3 & <=5

Grey

White >=6 & <=9 The state of other cells remain constant

fig 15a : Diagram explaining 2D CA Rule 1

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Experiment 2a Grid size Initial State No. of Levels

= 12 x 12 = Random =9

t2a = 00

t2a = 01

t2a = 02

t2a = 03

t2a = 04

t2a = 05

t2a = 06

t2a = 07

t2a = 08

Inference The range of volumetric density achieved for each cell are as follows : Black = 19% - 38% Grey = 23% - 53% White = 08% - 58 %

Volumetric Packing

fig 15b : Rule 2_ 12 x 12 Plans for each levels and volumetric packing

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Experiment 2b Grid size Initial State No. of Levels

=9x9 = Random =9

t2b = 00

t2b = 01

t2b = 02

t2b = 03

t2b = 04

t2b = 05

t2b = 06

t2b = 07

t2b = 08

Inference The range of volumetric density achieved for each cell are as follows: Black = 25% - 44% Grey = 17% - 62% White = 10% - 53%

Volumetric Packing

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fig 15c : Rule 2_ 9 x 9 Plans for each levels and volumetric packing

Experiment 2c Grid size Initial State No. of Levels

= 9 x 18 = Random =9

t2c = 00

t2c = 01

t2c = 02

t2c = 03

t2c = 04

t2c = 05

t2c = 06

t2c = 07

t2c = 08

Inference The range of volumetric density achieved for each cell are as follows : Black = 21% - 43% Grey = 27% - 41% White = 12% - 49 %

Volumetric Packing

fig 15d : Rule 2_ 9 x 18 Plans for each levels and volumetric packing

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Rule 2

Experiment 2a

Levels

Experiment 2c

Experiment 2b

t = 00

t2 = 01

t2 = 02

t2 = 03

t2 = 04

t2 = 05

t2 = 06

t2 = 07

t2 = 08

table 2a : Rule 2 - Cell densities at Individual Level

Inference It is observed from the above set of experiments 2a, 2b and 2c that the minimum and maximum cell density that can be achieved at a particular level by the application of Rule 6 are as follows : Min Max Black = 19% 44 % Grey = 17% 62 % White = 08% 58 %

All values are in %

60 | Cellular Automata

Range of cell density observed at maximum levels are as follows : Black = Grey = White =

28% 26% 20% -

40 % 46 % 38 %

Volume

Experiment 2a

Experiment 2b

Experiment 2c

Black

32.25 %

34.43 %

34.29 %

Grey

35.33 %

37.72 %

35.87 %

White

32.42 %

27.85 %

29.84 %

Continuity of Volumetric Void

0 %

Volumetric Ratio (B:G)

1:1 (Approximately)

1:1

1:1 (Approximately)

Similarity of cell organization

Volumetric Density

table 2b : Rule 2 - Volumetric evaluation

Conclusion It is observed from the above set of experiments - 2a, 2b and 2c that the volume achieved by the application of Rule 2 has different cell organization at every level. • The variation in the density of cell at maximum number of levels range between 10% - 20%. • There is a difference of 2% - 3% between the ratio of overall volumetric density of black : grey cells. • The void achieved at maximum number of levels range between 20% - 38% but the overall continuity of void across the entire volume is 0%.

All values are in %

IMIAD | CEPT University | 61

Rule 3 Current state of Cell

Loneliness - Death

State of Cell in Next Level

Sum of Neighbors

White

Black < 2

White

Grey

Overpopulation - Transformation

Black

Overpopulation - Death

< 2

Black

Grey >=3 & <=6

Black

Grey >=3 & <=6

White > = 12 & < = 16

White

Grey > = 12 & < = 16

Black

White Birth

>=3 & <=5

Grey

White >=6 & <=9 The state of other cells remain constant

fig 16a : Diagram explaining 2D CA Rule 1

62 | Cellular Automata

Experiment 3a = 12 x 12 = Random =9

Grid size Initial State No. of Levels

t3a = 00

t3a = 01

t3a = 02

t3a = 03

t3a = 04

t3a = 05

t3a = 06

t3a = 07

t3a = 08

Inference The range of volumetric density achieved for each cell are as follows : Black = 28% - 45% Grey = 39% - 47% White = 12% - 25%

Volumetric Packing

fig 16b : Rule 3_ 12 x 12 Plans for each levels and volumetric packing

IMIAD | CEPT University | 63

Experiment 3b Grid size Initial State No. of Levels

=9x9 = Random =9

t3b = 00

t3b = 01

t3b = 02

t3b = 03

t3b = 04

t3b = 05

t3b = 06

t3b = 07

t3b = 08

Inference The range of volumetric density achieved for each cell are as follows: Black = 33% - 44% Grey = 35% - 53% White = 10% - 27%

Volumetric Packing 64 | Cellular Automata

fig 16c : Rule 3_ 9 x 9 Plans for each levels and volumetric packing

Experiment 3c Grid size Initial State No. of Levels

= 9 x 18 = Random =9

t3c = 00

t3c = 01

t3c = 02

t3c = 03

t3c = 04

t3c = 05

t3c = 06

t3c = 07

t3c = 08

Inference The range of volumetric density achieved for each cell are as follows : Black = 33% - 43% Grey = 37% - 47% White = 12% - 30%

Volumetric Packing

fig 16d : Rule 3_ 9 x 18 Plans for each levels and volumetric packing

IMIAD | CEPT University | 65

Rule 3

Experiment 3a

Levels

Experiment 3c

Experiment 3b

t3 = 00

t3 = 01

t3 = 02

t3 = 03

t3 = 04

t3 = 05

t3 = 06

t3 = 07

t3 = 08

table 3a : Rule 3 - Cell densities at Individual Level

Inference It is observed from the above set of experiments 3a, 3b and 3c that the minimum and maximum cell density that can be achieved at a particular level by the application of Rule 6 are as follows : Min Max Black = 28% 45 % Grey = 35% 53 % White = 10% 30 %

All values are in %

66 | Cellular Automata

Range of cell density observed at maximum levels are as follows : Black = Grey = White =

35% 39% 12% -

43 % 47 % 25 %

Volume

Experiment 3a

Experiment 3b

Black

36.72 %

38.82 %

38.80 %

Grey

43.67 %

42.66 %

41.58 %

White

19.61 %

18.52 %

19.62 %

Continuity of Volumetric Void

4.86 %

2.40 %

Volumetric Ratio (B:G)

18 : 22

19 : 21

19 : 22

Experiment 3c

Volumetric Density

Similarity of cell organization

table 1b : Rule 3 - Volumetric evaluation

Conclusion It is observed from the above set of experiments - 3a, 3b and 3c that the volume achieved by the application of Rule 3 has different cell organization at every level. • The variation in the density of cell at maximum number of levels range between 10% - 20%. • There is a variation of 6% - 8% between the ratio of overall volumetric density of black : grey cells. • The void achieved at maximum number of levels range between 12% - 25% but the overall continuity of void is only 2% - 4%

IMIAD | CEPT University | 67

Rule 4 Current state of Cell

White

Black Loneliness - Death

State of Cell in Next Level

Sum of Neighbors

<=3 White

Grey

Overpopulation - Transformation

<=3

Black

Grey >4

Grey

Black >4

White

Black

Birth

=3 White

Grey =4

The state of other cells remain constant

fig 17a : Diagram explaining 2D CA Rule 1

68 | Cellular Automata

Experiment 4a Grid size Initial State No. of Levels

= 12 x 12 = Random =9

t4a = 00

t4a = 01

t4a = 02

t4a = 03

t4a = 04

t4a = 05

t4a = 06

t4a = 07

t4a = 08

Inference The range of volumetric density achieved for each cell are as follows : Black = 35% - 40% Grey = 31% - 36% White = 25% - 33%

Volumetric Packing

fig 17b : Rule 4_ 12 x 12 Plans for each levels and volumetric packing

IMIAD | CEPT University | 69

Experiment 4b Grid size Initial State No. of Levels

=9x9 = Random =9

t4b = 00

t4b = 01

t4b = 02

t4b = 03

t4b = 04

t4b = 05

t4b = 06

t4b = 07

t4b = 08

Inference The range of volumetric density achieved for each cell are as follows: Black = 31% - 40% Grey = 25% - 38% White = 31% - 40%

Volumetric Packing

70 | Cellular Automata

fig 17c : Rule 4_ 9 x 9 Plans for each levels and volumetric packing

Experiment 4c Grid size Initial State No. of Levels

= 9 x 18 = Random =9

t4c = 00

t4c = 01

t4c = 02

t4c = 03

t4c = 04

t4c = 05

t4c = 06

t4c = 07

t4c = 08

Inference The range of volumetric density achieved for each cell are as follows : Black = 35% - 40% Grey = 31% - 38% White = 25% - 31%

Volumetric Packing

fig 17d : Rule 4_ 9 x 18 Plans for each levels and volumetric packing

IMIAD | CEPT University | 71

Rule 4

Experiment 4a

Levels

Experiment 4c

Experiment 4b

t4 = 00

t4 = 01

t4 = 02

t4 = 03

t4 = 04

t4 = 05

t4 = 06

t4 = 07

t4 = 08

table 4a : Rule 4 - Cell densities at Individual Level

Inference It is observed from the above set of experiments 4a, 4b and 4c that the minimum and maximum cell density that can be achieved at a particular level by the application of Rule 6 are as follows : Min Max Black = 31% 40 % Grey = 25% 38 % White = 25% 40 %

All values are in %

72 | Cellular Automata

Range of cell density observed at maximum levels are as follows : Black = Grey = White =

33% 32% 28% -

38 % 36 % 36 %

Volume

Experiment 4a

Experiment 4b

Black

36.12 %

33.47 %

36.28 %

Grey

35.09 %

32.64 %

35.66 %

White

28.79 %

33.89 %

28.06 %

Continuity of Volumetric Void

21.52 %

20.98 %

20.37 %

Volumetric Ratio (B:G)

18 : 22

19 : 21

19 : 22

87 - 92% ( Alternate levels )

85 - 95 % ( Alternate levels )

84 - 90 % ( Alternate levels )

Experiment 4c

Volumetric Density

Similarity of cell organization

table 4b : Rule 4 - Volumetric evaluation

Conclusion It is observed from the above set of experiments - 4a, 4b and 4c that the volume achieved by the application of Rule 4 has a 85% - 90% of similarity of cell organization at alternate levels. • The variation in the density of cell at maximum number of levels range between 5% - 8%. • The overall volumetric ratio of Black : Grey cells is approximately 1 : 1. • The void achieved at maximum number of levels ranges between 28% - 36% and the overall continuity of void is 21%.

IMIAD | CEPT University | 73

Rule 5 Current state of Cell

White

Black Loneliness - Death

State of Cell in Next Level

Sum of Neighbors

< 2 Black

Grey

Overpopulation - Transformation

< 2

Black

Grey > 3

Grey

Black > 3

Death

Black

White =3

Grey

White =3

White

Grey

Birth

=3 White

Black =4

The state of other cells remain constant

74 | Cellular Automata

fig 18a : Diagram explaining 2D CA Rule 1

Experiment 5a Grid size Initial State No. of Levels

= 12 x 12 = Random =9

t5a = 00

t5a = 01

t5a = 02

t5a = 03

t5a = 04

t5a = 05

t5a = 06

t5a = 07

t5a = 08

Inference The range of volumetric density achieved for each cell are as follows : Black = 36% - 42% Grey = 36% - 41% White = 20% - 25%

Volumetric Packing

fig 18b : Rule 5_ 12 x 12 Plans for each levels and volumetric packing

IMIAD | CEPT University | 75

Experiment 5b Grid size Initial State No. of Levels

=9x9 = Random =9

t5b = 00

t5b = 01

t5b = 02

t5b = 03

t5b = 04

t5b = 05

t5b = 06

t5b = 07

t5b = 08

Inference The range of volumetric density achieved for each cell are as follows: Black = 32% - 37% Grey = 35% - 40% White = 25% - 30%

Volumetric Packing

76 | Cellular Automata

fig 18c : Rule 5_ 9 x 9 Plans for each levels and volumetric packing

Experiment 5c Grid size Initial State No. of Levels

= 9 x 18 = Random =9

t5c = 00

t5c = 01

t5c = 02

t5c = 03

t5c = 04

t5c = 05

t5c = 06

t5c = 07

t5c = 08

Inference The range of volumetric density achieved for each cell are as follows : Black = 30% - 41% Grey = 31% - 39% White = 25% - 31%

Volumetric Packing

fig 18d : Rule 5_ 9 x 18 Plans for each levels and volumetric packing

IMIAD | CEPT University | 77

Rule 5

Experiment 5a

Levels

Experiment 5c

Experiment 5b

t5 = 00

t5 = 01

t5 = 02

t5 = 03

t5 = 04

t5 = 05

t5 = 06

t5 = 07

t5 = 08

table 5a : Rule 5 - Cell densities at Individual Level

Inference It is observed from the above set of experiments 5a, 5b and 5c that the minimum and maximum cell density that can be achieved at a particular level by the application of Rule 6 are as follows : Min Max Black = 30% 42 % Grey = 31% 41 % White = 20% 30 %

All values are in %

78 | Cellular Automata

Range of cell density observed at maximum levels are as follows : Black = Grey = White =

36% 35% 20% -

40 % 41 % 30 %

Volume

Experiment 5a

Experiment 5b

Black

38.76 %

35.25 %

36.48 %

Grey

39.35 %

36.35 %

35.73 %

White

23.89 %

28.40 %

27.79 %

Continuity of Volumetric Void

19.44 %

24.69 %

Volumetric Ratio (B:G)

1:1

85 - 90% ( Alternate levels )

82 - 92 % ( Alternate levels )

87 - 90 % ( Alternate levels )

Experiment 5c

Volumetric Density

Similarity of cell organization

table 5b : Rule 5 - Volumetric evaluation

Conclusion It is observed from the above set of experiments - 5a, 5b and 5c that the volume achieved by the application of Rule 5 has a 85% - 90% of similarity of cell organization at alternate levels. • The variation in the density of cell at maximum number of levels range between 5% - 10%. • The overall volumetric ratio of Black : Grey cells is approximately 1 : 1. • The void achieved maximum number of levels range between 20% - 30% but the overall continuity of void is between 20% - 25%.

IMIAD | CEPT University | 79

Rule 6 Current state of Cell

Loneliness - Death Loneliness - Transformation

Grey

Overpopulation - Transformation

Grey

Transformation

Grey

Birth

Black

White

State of Cell in Next Level

Sum of Neighbors

White < 2

Black < 2

White > 3

Black = 3

The state of other cells remain constant

80 | Cellular Automata

Grey = 3

fig 19a : Diagram explaining 2D CA Rule 6

Experiment 6a Grid size Initial State No. of Levels

= 12 x 12 = Random =9

t6a = 00

t6a = 01

t6a = 02

t6a = 03

t6a = 04

t6a = 05

t6a = 06

t6a = 07

t6a = 08

Inference The range of volumetric density achieved for each cell are as follows : Black = 27% - 36% Grey = 07% - 16% White = 54% - 62 %

Volumetric Packing

fig 19b : Rule 6_ 12 x 12 Plans for each levels and volumetric packing

IMIAD | CEPT University | 81

Experiment 6b Grid size Initial State No. of Levels

=9x9 = Random =9

t6b = 00

t6b = 01

t6b = 02

t6b = 03

t6b = 04

t6b = 05

t6b = 06

t6b = 07

t6b = 08

Inference The range of volumetric density achieved for each cell are as follows: Black = 25% - 37% Grey = 06% - 17% White = 43% - 68%

Volumetric Packing

82 | Cellular Automata

fig 19c : Rule 6_ 9 x 9 Plans for each levels and volumetric packing

Experiment 6c Grid size Initial State No. of Levels

= 9 x 18 = Random =9

t6c = 00

t6c = 01

t6c = 02

t6c = 03

t6c = 04

t6c = 05

t6c = 06

t6c = 07

t6c = 08

Inference The range of volumetric density achieved for each cell are as follows : Black = 24% - 36% Grey = 02% - 21% White = 46% - 65 %

Volumetric Packing

fig 19d : Rule 6_ 9 x 18 Plans for each levels and volumetric packing

IMIAD | CEPT University | 83

Rule 6

Experiment 6a

Levels

Experiment 6c

Experiment 6b

t6 = 00

t6 = 01

t6 = 02

t6 = 03

t6 = 04

t6 = 05

t6 = 06

t6 = 07

t6 = 08

table 6a : Rule 6 - Cell densities at Individual Level

Inference It is observed from the above set of experiments 6a, 6b and 6c that the minimum and maximum cell density that can be achieved at a particular level by the application of Rule 6 are as follows : Min Max Black = 24% 36 % Grey = 06% 21 % White = 43% 68 %

All values are in %

84 | Cellular Automata

Range of cell density observed at maximum levels are as follows : Black = Grey = White =

27% 11% 53% -

33 % 17 % 62 %

Volume

Experiment 6a

Experiment 6b

Black

31.01 %

30.31 %

31.00%

Grey

11.34 %

12.20 %

12.31 %

White

57.65 %

57.49 %

56.69 %

Continuity of Volumetric Void

24.30 %

18.51 %

21.60 %

Volumetric Ratio (B:G)

3:1

5:2 ( 2.5 : 1 )

15 - 25% ( Alternate levels )

18 - 27 % ( Alternate levels )

15 - 25 % ( Alternate levels )

Experiment 6c

Volumetric Density

Similarity of cell organization

table 6b : Rule 6 - Volumetric evaluation

Conclusion It is observed from the above set of experiments - 6a, 6b and 6c that the volume achieved by the application of Rule 6 has 85% - 90% of similarity of Black cell organization at every level, whereas the organization of grey cell varies. • The variation in the density of cell at maximum number of levels range between 6% - 9%. • The overall volumetric ratio of Black : Grey cells is approximately 2.5 :1 - 3 : 1. • The void achieved at maximum number of level s range between 53% - 62% and the overall continuity of void range between 18% - 21%.

IMIAD | CEPT University | 85

86 | Cellular Automata

4.3 Conclusion From the above exploration, it can be observed that By exploring different rules for 2D Cellular Layering, we observe that different range of volumetric densities can be achieved Simple rules can lead to complex relations between the neighboring cells at different levels and across the volume. These relations can be analyzed and different spatial organization systems can be developed by defining the rules of adjacencies. The rules can be implemented to explore spatial organization for various environment as follows :

• • • •

Interior / Office layout Housing Project Pavilion design Exhibition spaces

Furthermore, various parameters and fitness criteria can be extracted from the context and the Rules of CA can be further evaluated and implemented within a domain. For the purpose of this research the rules of 2D CA are evaluated and implemented to achieve spatial organization system for low cost housing.

IMIAD | CEPT University | 87

88 | Cellular Automata

05 LOW COST HOUSING TYPOLOGIES

5.1

OVERVIEW

5.2

CASE STUDIES

5.3 CONCLUSION

IMIAD | CEPT University | 89

90 | Cellular Automata

5.1 OVERVIEW The quality of a dwelling area can be qualitatively and quantitatively evaluated by understanding the relations between the built and open spaces, circulations and access etc. It can also be analyzed based on the various environmental factors like, sunlight hours, solar radiation, wind flow, visibility. that are required for human comfort. To understand the spatial quality of the existing low cost housing in Mumbai, 6 different housing projects with varying housing typologies were selected for the purpose of this research. Each typology was evaluated based on its spatial and environmental performance. Built and Open space relation. Access and Circulation area relation Density - BUA , BUA / person, CA / person To establish the relation between built, open and semi open spaces, the typical floor plan was divided into a square grid and each cell corresponds to a spatial function, defined as follows : Built Area = Black Semi Open / Circulation Area = Grey Void = White The environmental analysis were conducted on the semi open and circulation areas of the built form and the optimum values were extracted for further analysis. Thus various spatial and environmental paramaters were extracted and CA rules were further analyzed based on these parameters.

IMIAD | CEPT University | 91

5.2 CASE STUDIES 5.2.1 Sample 01- Atmaram Chawl The Atmaram chawl was built in 1866. The built form consists of 2 corridors running along the structure. The internal corridor acts as a semi private space, which separates the kitchen area from the living and the bedroom space which are clubbed together. The internal courtyard is lit and ventilated by the open to sky courtyards. The external corridor is the main circulation spine and gives access to the living spaces. The provision of circulation area on both sides of the living area, create a sense of continuity along the entire unit.

fig. 20a : Typical Floor Plan

Total no. of Units / floor Total no. floors BUA BUA / person CA / person Increment in the floor space

fig. 20b : Unit Plan

=8 =G+2 = 51.4 m2 = 9.01 m2 = 3.64 m2 = Addition of loft area

Environmental Analysis Average Sunlight Hours

Average Solar Radiation

21st June

22nd Dec

21st June

0.82

4.01

0.60

92 | Cellular Automata

22nd Dec 1.28

Average Visibility

20.32 %

Volumetric Analysis Size of each unit = 2x X 6.5x. Each unit comprises of 8 black cells, 4 grey cells and 1 white cell arranged in a rectangular pattern. The 8 black cells are clustered in 2 parts - 6 cells and 2 cells separated by grey and white cells. The 6 black cells, clustered together have grey cells adjacent on both sides, function as a circulation and semi open space which provides access. The white cell adjacent to the black cell, functions as a void which provides light and ventilation to the adjacent grey and black cells.

fig. 20c : Volumetric Floor Plan

Volumetric Density

Extracted Parameter

Black Grey White

= 64 % = 24 % = 12 %

Volumetric Ratio ( Black : Grey )

= 8:3

Volumetric Continuity of Void

= 12 %

Maximum Linkage of Black Cell / unit

= 6

Access

fig. 20d : Volumetric Unit Plan

= Grey cell adjacent to black cells on both sides

The clustering of black, grey and white cells create a spatial relation between the built and semi open spaces. The grey cells function as a circulation as well as social ( semi open ) spaces. Volumetric Density Grey > = 24 % White > = 12 % Circulation = Linear arrangement of grey cells with access to units Optimum CA / person = 3.64 m2

IMIAD | CEPT University | 93

5.2.2 Sample 02 - BDD Chawl The BDD chawl was built in 1925. The built form is a rectangular volume with a central corridor, running along the entire length of the buiding. As a result it lacks proper light and ventilation. The corridor is the main circulation spine with access to the units on either sides. The floor space of the units have been increased over time by addition of concrete slabs

fig. 21a : Typical Floor Plan

Total no. of Units / floor Total no. floors BUA BUA / person CA / person Increment in the floor space Floor Area after Increment

fig. 21b : Unit Plan

= 20 =G+3 = 16.6 m2 = 2.76 m2 = 1.12 m2 = Cantilevered Extensions = 1 1/2 time the original area

Environmental Analysis Average Sunlight Hours

Average Solar Radiation

21st June

22nd Dec

21st June

0.41

0.55

0.32

94 | Cellular Automata

22nd Dec 0.51

Average Visibility

12.20 %

fig. 21c : Incremental Plan

Volumetric Analysis Size of each unit = 1x X 3x. Each unit comprises of 2 black cells and 1 grey cells arranged in a linear pattern. The grey cell adjacent to the black cell functions as a circulation space and provides access to the unit.

fig. 21e : Volumetric Unit Plan

fig.21d : Volumetric Plan

Extracted Parameter

Volumetric Density

The unit typology i.e linear clustering of 2 black cells serves as an optimum unit size for a low cost housing with high density.

Black Grey White

= 78 % = 22 % =0%

Volumetric Ratio ( Black : Grey )

= 3.5 : 1

Volumetric Continuity of Void

= 0%

Circulation

= 2

= Linear arrangement of grey cells with access to units

Maximum Linkage of Black Cell / unit Access

Linakge to form a Unit Linear arrangement of 2 black cells

Optimum BUA & BUA / person = Grey cell adjacent to black cells on both sides

= 16.6 m2 & 2.76 m2

IMIAD | CEPT University | 95

5.2.3 Sample 03 - Site and Services The Site and Services scheme was built in 1986. The entire layout is a cluster of dwelling units with a common internal Courtyard. The internal courtyard functions as a social area The access to the units is through the semi open space which divides the living spaces from the central courtyard.

fig. 22a : Layout Pan

Unit a Plan

Unit b Plan

Ground floor plan

fig. 22b : Unit Plan

Total no. of Units BUA Increment in the floor space Floor Area after Increment area

96 | Cellular Automata

First floor plan

First floor plan fig. 22c : Incremental Plan

= Unit a = 6 Unit b = 29 = Unit a = 25 m2 Unit b = 40 m2 = Additional Floor = twice the original

BUA / person CA / person

= Unit a = 4.16 m2 Unit b = 6.66 m2 = 0 m2

Volumetric Analysis Size of Unit a = 1x X 2.5x | Size of Unit b = 1x X 4.5x Unit a comprises of 2 black and 1 grey cell and Unit b comprises of 3 black cell and 2 grey cells arranged in a linear pattern. The grey cell adjacent to black cell functions as a semi open space and provides access to the unit.

Unit a fig. 22d : Volumetric Pan

Unit b

fig. 22e : Volumetric Unit Pan

Environmental Analysis Average Sunlight Hours

Average Solar Radiation

21st June

22nd Dec

4.13

4.21

2.8

22nd Dec 1.81

Volumetric Density = 50 % = 15 % = 35 %

Volumetric Ratio ( Black : Grey )

= 10 : 3

Volumetric Continuity of Void

= 35 %

Access

29.50 %

Extracted Parameter

Black Grey White

Maximum Linkage of Black Cell / unit

Average Visibility

Creating social spaces Volumetric Density Black < = 50% Linakge to form Unit Linear arrangement of 2 - 3 black cells Access = Grey cell adjacent to black cell

= 3 = Grey cell adjacent to black cells ( Semi open Space )

Optimum BUA & BUA / person = 25 m2 - 40 m2 & 4.16 m2 - 6.66 m2 Average Visibility > = 30 %

IMIAD | CEPT University | 97

5.2.4 Sample 04 - Belapur Housing The Belapur Housing was built in 1960â&#x20AC;&#x2122;s. The entire layout is a cluster of dwelling units with a common internal Courtyard. Each unit has an internal courtyard which connects the living areas to the services. The units were deigned with a possibility of future increment

Unit a

Unit b fig. 23a : Layout Plan

Total no. of Units Total no. Floors BUA BUA / person CA / person Increment in the floor space Floor Area after Increment

Unit c fig. 23b : Unit Plan

=7 = G / G +1 = 40 m2 - 75 m2 = 7.5 m2 - 11.6 m2 = 0 m2 = Additional Floor space = 1 1/2 time the original area

Environmental Analysis Average Sunlight Hours

Average Solar Radiation

21st June

4.23

22nd Dec 4.75

98 | Cellular Automata

3.81

22nd Dec 4.67

Average Visibility

50.20 %

Volumetric Analysis Size of each unit = 3x X 4x. Each unit comprises of 6 black cells, 4 grey cells and 5 white cell. The grey cell adjacent to black cell functions as a semi open space and provides access to the unit. Internal courtyard spaces are created by clustering on units.

fig. 23c : Volumetric Layout Plan

Volumetric Density

fig. 23d : Volumetric Unit Plan

Extracted Parameter

Black Grey White

= 46 % = 24 % = 30 %

Creating internal courtyard and social spaces

Volumetric Ratio ( Black : Grey )

= 11.5 : 6

Black < = 45% Grey > = 24%

Volumetric Continuity of Void

= 30 %

Volumetric Ratio = 2 : 1

Maximum Linkage of Black Cell / unit Access

Volumetric Density

Linkage to form Unit = 5 = Grey cell adjacent to black cells (Semi open space )

â&#x20AC;&#x2DC;Lâ&#x20AC;&#x2122; shaped arrangement of black cells Access = Grey cell adjacent to black cell which functions as a semi open space Average Visibility > = 30 % IMIAD | CEPT University | 99

5.2.5 Sample 05 - Ambedkar Nagar SRA The Amdedkar Nagar SRA was built in 2011 The built form is a rectangular volume with a central corridor, running along the entire length of the building. The corridor is the main circulation spine with access to the units on either sides. The ventilation for the entire circulation spine is provided at both the end, as a result it lacks proper light and ventilation.

fig. 24a : Typical Floor Plan

Total no. of Units /floor Total no. of floors BUA BUA / person CA / person Increment in the floor space Distance between adjacent buildings

fig. 24b : Unit Plan

= 16 = G + 1C + 14 = 31.4 m2 = 5.23 m2 = 1.72 m2 = Not permissible = 6m

Environmental Analysis Average Sunlight Hours

Average Solar Radiation

21st June

22nd Dec

21st June

0.42

0.64

0.21

100 | Cellular Automata

22nd Dec 0.31

2/3 x

Average Visibility

10.20 %

Volumetric Analysis Size of each unit = 2x X 2.6x. Each unit comprises of 4 black cells and 2 grey cells arranged in a square pattern. The grey cell adjacent to the black cell functions as a circulation area and provides access to the unit.

fig. 24c : Volumetric Floor Plan

Volumetric Density

fig. 24d : Volumetric Unit Plan

Extracted Parameter

Black Grey White

= 70 % = 30 % = 0%

The unit size is optimum to achieve high density built form.

Volumetric Ratio ( Black : Grey )

= 7:3

Arrangement of 4 black cells in square grid

Volumetric Continuity of Void

= 0%

Maximum Linkage of Black Cell / unit

= 4

Access

Linkage to form Unit

Optimum BUA & BUA / person = 31.4 m2 & 5.23 m2

= Grey cell adjacent to black cells (Circulation Space)

IMIAD | CEPT University | 101

5.2.6 Sample 06 - Sanaswadi (Rehab) The Sanaswadi rehab building was built in 2016 The built form is rectangular volume with a service core and a corridor which serves as the access to the unit. The corridor is not properly ventilated as the window opens onto an internal chowk. There no relation between the built and open spaces.

1.5x

2x 1.4 x

2x 12 x

0.5 x

fig. 25a : Typical Floor Plan

Total no. of Units /floor Total no. of floors BUA BUA / person CA / person Increment in the floor space

fig. 25b : Unit Plan

=8 = G + 2C + 15 = 52.7 m2 = 8.78 m2 = 1.68 m2 = Not permissible

Environmental Analysis Average Sunlight Hours

Average Solar Radiation

21st June

0.37

22nd Dec 0.51

102 | Cellular Automata

0.27

22nd Dec 0.34

Average Visibility

13.10 %

Volumetric Analysis Size of each unit = 2x X 3x Each unit comprises of 6 black cells linked together and an adjacent grey cell arranged in a rectangular grid. The grey cell functions as circulation area and provides access to the unit.

fig.25c : Volumetric Floor Plan

Volumetric Density

fig. 25d : Volumetric Unit Plan

Extracted Parameter

Black Grey White

= 66.66% = 12.25 % = 21.09 %

There is a continuity of void and this enables a relation between built and open spaces only at ground level.

Volumetric Ratio ( Black : Grey )

= 11 : 2

Volumetric Density

Volumetric Continuity of Void

= 21.09 %

Maximum Linkage of Black Cell / unit

= 6

Access

White > = 21% Continuity of Void > = 21 %

= Grey cell adjacent to black cells ( Circulation Area )

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Unit Type

Unit Typology

Atmaram Chawl

BDD Chawl

Site & Services

BUA ( sq. m )

54.1

16.6

Unit a = 25 Unit b = 40

No. of people / unit

BUA / person (sq. m)

9.01

2.76

Unit a = 4.16 Unit b = 6.66

CA / person (sq. m)

3.65

1.12

-----

Location of Semi Open spaces

% of Increment per unit

50 %

50 % - 125 %

Volumetric Ratio / unit (B:G)

2:1

Linkage ( No. of Black Cells)

6 & 2

Unit a = 2 Unit b = 3

Linkage ( Clustering Pattern )

Rectangular

Linear

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Belapur Housing

Ambedkar Nagar SRA

Sanaswadi ( Rehab )

Unit a = 45 ; Unit b = 60 ; Unit c = 70

31.4

52.7

Unit a = 7.5 ; Unit b = 8.3 ; Unit c = 11.6

5.23

8.78

1.72

1.68

-----

2:1

4:1

6 :1

Rectangular

Linear

Rectangular table 7 : Unit Type

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5.3 Conclusion From the above set of case studies and its analysis, it can be observed that the typologies which perform well spatially and environmentally do not accommodate high densities and the typologies which achieve high density lack optimum light and ventilation. A set of spatial, environmental and density parameters with optimum values were extracted at the end of every case study and a larger set of parameters was defined.

106 | Cellular Automata

x x

Spatial Parameters Size of Each Cell

x x

= 2.5 m - 3 m

Maximum no. of black linked cells =4

Maximum size of Floor Layout 4x

x 8x

8x x

8x - 9x

5x - 6x

x 2x

= ( 8x - 9x ) X ( 5x - 6x) = Excluding the service core

Unit Typology = Clustering of 1 - 4 cells

Access = Semi Open space = Grey Cell adjacent to black cell

Similarity of Cell Organization at different levels = 80 % - 90 %

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Environmental Parameters Average Sunlight hours = 2hrs - 4 hrs / day

Average Solar Radiation

= Minimizing the Solar Radiation

Climatic Comfort

Optimum Wind Speed = 5 m/s

Climatic Comfort

Average Visibility > 30%

108 | Cellular Automata

Extracted Parameter

Density Parameters Volumetric Density of Cells = Occupied Area Circulation & Semi Open Area Void Area

= 40 % - 50 % = 25 % - 35 % = 20 % - 25 %

Continuity of Void = 20% - 25 %

Ratio of Occupied Area : Circulation Area = 2:1

Built Up Area & Built Up Area / person = 9 m2 - 36m2 & 3 m2 - 6m2

No. of people / Unit = 3 people / 9 m2 = 6 people / 18 m2- 36 m2 9 m2

18 m2

36 m2

Circulation Area / person =

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110 | Cellular Automata

06 CA RULE IMPLEMENTATION

6.1

OVERVIEW

6.2

CA RULE IMPLEMENTATION FOR HOUSING

6.3 CONCLUSION

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112 | Cellular Automata

6.1 Overview

Extracted Parameters Volumetric Densities Black

= 40% - 50%

Grey

= 25% - 35%

White

= 15% - 25%

Continuity of Void

= 15% - 20%

Similarity of cell organization

= 80% - 90%

The environmental and spatial analysis of the different housing typologies conducted in chapter 05 have helped us derive various parameters for evaluating the various rules of 2D Cellular Automata explored in Chapter 04. The table 8 shows the permissible values for volumetric densities, void and cell organization essential for spatial organization of low cost housing.The table 9 gives a comparative volumetric analsis of all the 6 rules explored in Chapter 03 and the parameters extracted from the case studies in Chapter 04. The analysis aimed at evaluating the rule with permissible range of values for volumetric densities, voids and cell organization.

table 8 : Extracted Parameters for spatial organization

Rule 1

Rule 2

Rule 3

Rule 4

Rule 5

Black

27% - 28%

32% - 34%

37% - 39%

34% - 37%

35% - 39%

30% - 31%

Grey

25% - 28%

35% - 37%

42% - 44%

32% - 36%

36% - 39%

11% - 12%

White

43% - 53%

27% - 32%

19% - 20%

28% - 32%

24% - 28%

57% - 58%

Continuity of Void

2.4% - 4.9%

20% - 21%

20% - 25%

18% - 24%

Similarity of cell organization

85% - 95%

85% - 90%

15% - 27%

Rule 6

Volumetric Densities

table 9 : Comparative Analysis of the different CA Rules

From the above analysis it is observed that volumetric densities, ratio and the void achieved by the application of Rule 04 and 05 are within the permissible range of densities required for spatial planning of low cost housing. Furthermore environmental and spatial analysis are conducted for Rule 04 and 05 and strategies are developed for incremental groeth. The fig x demonstrates the strategies for linkage, access and circulation.

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Black cell Linkage - Clustering of Cells

Evaluation

The occupied areas at each level can be clustered to form different unit typologies. The clustering of cells is based on the parameters and unit typologies extracted from the case studies.

The various combination of unit types that can be achieved at each level. The BUA, SOA the number of people/ unit are defined. As a result, the clustering of black cells enables us to determine the number of units, density, ratio of built, open and semi open spaces that can be achieved at each level.

The number of Units and the typologies at each level are defined by different iterations of clustering of cells. The diagrams below show the various possibilities of clustering cells and developing unit typologies. Strategy 01

Maximize : Total density of the volume Create semi - open, social spaces at each level.

The clustering of the cells should be such that each unit has an adjacent grey cell which functions as an access to the unit. Strategy 02 If a cell does not have an adjacent grey cell, clustering of cells can be done vertically and the access is from other level.

Level

t=0

Possible Iteration for Units by clustering of Cells

Iteration 01 No. of Units = 11

Iteration 02 No. of Units = 14

fig. 26 : Strategies for linkage

114 | Cellular Automata

Iteration 03 No. of Units = 14

Grey cell Access & circulation

Evaluation

As per the parameters extracted from the case studies, access to each unit is through a semi open space. Strategies are developed to define the grey cell which provides access to the unit.

Maximize : Number of units with access from grey cell along the edges ( ease of circulation to the service core ).

Strategy 01

Maximize : One grey cell should have access for one unit, hence each unit get 50 % of semi open space.

Grey cell = Access to Unit = 50 % Semi Open Area + 50 % circulation Strategy 02 Grey cell = Internal Courtyard + 50 % Semi Open Area + 50 % circulation Strategy 03 Continuity of Circulation path : The access and courtyards should be located such that there is not discontinuity of the circulation path.

Strategy 01 + 03

Possible access for the units

Strategy 02 + 03

Iteration 01

Iteration 01 No. of unit with Internal courtyard = 4

fig. 27 : Strategies for Circulation & Access

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6.2 CA Rule Implementation for Housing 6.2.1 Experimental Setup Rule No. =4&5

The CA rule no. 4 & 5 have the volumetric densities and ratios which when further explored and analyzed

Initial State = Random

As the initial state is random, 3 experiments were conducted and the volumetric densitites, continuity of void, ratios of black and grey cells are compared to evaluate the similarities between the volumes achieved

Grid Size =9x 6

Based on the case studies and the extracted parameters, the grid for the floor area under consideration is 9x x 6x. The service core is excluded and strategies for the same can be developed.

Size of each cell = 3m

Number of Levels =9

116 | Cellular Automata

Each cell was assigned a spatial function and considering 9m2 as a minimum area for accommodation, the size of each cell is 3m x 3m. As per the Mumbai, DCR, the maximum travel distance is 30m. The maximum travel distance for the floor area under consideration = 9 x 3m = 27m

6.2.2 Evaluation Method 6.2.2a CA Rule Exploration The aim of first set of experiments conducted was to analyze if volumetric densities and ratios are constant for any given initial state and the strategies developed for one iteration can be applicable to all the iterations derived by the application of the rule. Further, the strategies are developed and conducted for one of the iteration. 6.2.2b Environmental Analysis The environmental analysis were conducted for the circulation and semi open areas at each level. The aim of the analysis is to evaluate and obtain the area with optimum sunlight hours, solar radiation, visibility and wind flow to develop strategies for incremental growth. 6.2.2c Neighborhood Analysis The neighborhood analysis were conducted for each level and the aim of the analysis is to determine the number of units, unit type, density, access and circulation, relation between built, open and semi open spaces at local, regional and global level. 6.2.2d Possibilities for Incremental growth Based on the environmental analysis and neighborhood analysis - Possible areas for incremental growth are proposed. The aim of the analysis was to determine the percent of increment that can be achieved at local and global level. 6.2.2e Incremental State _ Analysis The incremental state was evaluated for the increment in the percent of occupied area and its corresponding effect on the wind flow

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118 | Cellular Automata

6.2.2a CA Rule Exploration Rule 4 (R4) Current state of Cell

Loneliness - Death

Black

State of Cell in Next Level

Sum of Neighbors

White

<=3 White

Grey

Overpopulation - Transformation

<=3

Black

Grey >4

Grey

Black >4

White

Black

Birth

=3 White

Grey =4

The state of other cells remain constant

fig. 28a : Diagram explaining 2D CA Rule 4

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Experiment 4D _Iteration 01

t4d.1 = 00

t4d.1 = 01

t4d.1 = 02

t4d.1 = 03

t4d.1 = 04

t4d.1 = 05

t4d.1 = 06

t4d.1 = 07

t4d.1 = 08

Inference Volumetric Density

Volumetric Packing

120 | Cellular Automata

Black Cell

= 38 %

Grey Cell

= 39 %

White Cell

= 23 %

Volumetric Ratio (B:G)

=1:1

Volumetric Continuity of Void (Open to Sky )

= 19 %

fig. 28b : Rule 4d _ Iteration 01 Plans for each levels and volumetric packing

Experiment 4D _Iteration 02

t4d.2 = 00

t4d.2 = 01

t4d.2 = 02

t4d.2 = 03

t4d.2 = 04

t4d.2 = 05

t4d.2 = 06

t4d.2 = 07

t4d.2 = 08

Inference Volumetric Density

Volumetric Packing

Black Cell

= 39 %

Grey Cell

= 40 %

White Cell

= 21 %

Volumetric Ratio (B:G)

=1:1

Volumetric Continuity of Void (Open to Sky )

= 15 %

fig. 28c : Rule 4d _ Iteration 02 Plans for each levels and volumetric packing

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Experiment 4D _Iteration 03

t4d.3 = 00

t4d.3 = 01

t4d.3 = 02

t4d.3 = 03

t4d.3 = 04

t4d.3 = 05

t4d.3 = 06

t4d.3 = 07

t4d.3 = 08

Inference Volumetric Density

Volumetric Packing

122 | Cellular Automata

Black Cell

= 40 %

Grey Cell

= 40 %

White Cell

= 20 %

Volumetric Ratio (B:G)

=1:1

Volumetric Continuity of Void (Open to Sky )

= 15 %

fig. 28d : Rule 4d _ Iteration 01 Plans for each levels and volumetric packing

Conclusion From the above set of 3 experiments, it can be observed that the volumetric density, volumetric ratios and percentage of continuous void are similar for all the experiments. Hence it can be inferred that the strategies demonstrated and explored for one iteration can be applicable for all iterations. All the further analysis and the strategies that were developed, were demonstrated for Iteration 01

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6.2.2b (R4) Environmental Analysis

Levels

Surface Area receiving more then 2 hrs of direct Sunlight 21st June

22nd Dec

33 %

48 %

47 %

42 %

41 %

54 %

46 %

38 %

46 %

t4d.1 = 00

t4d.1 = 01

t4d.1 = 02

t4d.1 = 03

t4d.1 = 04

124 | Cellular Automata

Surface Area receiving more then 1 kWh/m2 of Solar Radiation

Surface Area with more then 30% of Visibility

21st June

22nd Dec

36 %

41 %

42 %

37 %

26 %

46 %

39 %

34 %

54 %

41 %

29 %

52 %

41 %

40 %

50 %

CFD Analysis

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6.2.2b (R4) Environmental Analysis

Levels

Surface Area receiving more then 2 hrs of direct Sunlight / day 21st June

22nd Dec

52 %

40 %

36 %

41 %

68 %

46 %

97 %

86 %

t4d.1 = 05

t4d.1 = 06

t4d.1 = 07

t4d.1 = 08

Inference From the above set of analysis it was observed that the internal areas receive less then 1kw/m2 of solar radiation due to self shading and the wind speed is 1.5 - 2.25 m/s . The continuity of void across the volume and the semi open spaces enables the movement of wind throughout the volume ( Refer Appendix I for the movement of wind throughout the volume). It also creates a visual connection between different levels. As a result the internal circulation areas can be proposed as social spaces which can be utilized even during the day time.

126 | Cellular Automata

Surface Area receiving more then 1 kWh/m2 of Solar Radiation

Surface Area with more then 30% of Visibility

21st June

22nd Dec

38 %

25 %

46 %

35 %

34 %

50 %

60 %

39 %

55 %

100 %

89 %

59 %

CFD Analysis

fig. 29 : Rule 4d Environmental analysis

The areas receiving optimum sunlight hours, solar radiation and visibility are located along the edge and can be proposed for further incremental growth. Furthermore strategies for increment are developed based on environmental and neighborhood analysis.

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128 | Cellular Automata

6.2.2c Neighborhood Analysis 6.2.2c.1 Unit Typology 8 Unit typologies are extracted from the case studies that were evaluated in Chapter 04. The clustering of cells and the linkages are defined as per based on these unit typologies.

6.2.2c.2 Access _ Strategy 01 + 03 The black cell has access from the adjacent grey cell. Grey Cell = 50 % circulation = 50 % semi open space for the occupied Continuity of Circulation path : The access and courtyards should be located such that there is not discontinuity of the circulation path.

Linkage _ Strategy 01 + 02 The clustering of the cells should be such that each unit has an adjacent grey cell ( access to the unit ). If a cell does not have an adjacent grey cell, clustering of cells can be done vertically and the access is from other level.

6.2.2c.3 Density Analysis The density analysis evaluates the density of people, BUA, CA and CA / person at regional and global level.

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6.2.2c.1 (R4 & R5 ) Unit Typology 8 Unit types were defined based on housing case studies that were evaluated in Chapter 05. The number of linked black cells, BUA / unit, no. of people/ unit for each unit are defined based on the extracted parameters. Size of cell = 3m x 3m Built Up Area / cell = 9 m2 The fig. 30 on the next page demonstrates various clustering options that can be achieved by these defined 8 unit types at each level.

Occupied Surface Area ( OA ) |

130 | Cellular Automata

Semi Open Area ( SOA )

No. black cells OA SOA Total area No. of people

=1 = 9 m2 = 4.5 m2 = 13.5 m2 =3

No. black cells OA SOA Total area No. of people

=2 = 18 m2 = 4.5 m2 = 22.5 m2 =6

No. black cells OA SOA Total area No..of people

=3 = 27 m2 = 4.5 m2 = 31.5 m2 =6

No. black cells OA SOA Total area No. of people

=3 = 27 m2 = 4.5 m2 = 31.5 m2 =6

No. black cells OA SOA Total area No. of people

=4 = 36 m2 = 4.5 m2 = 40.5 m2 =6

No. black cells OA SOA Total area No. of people Unit level

=3 = 27 m2 = 4.5 m2 = 31.5 m2 =6 =2

No. black cells OA SOA Total area No. of people Unit level

=4 = 36 m2 = 4.5 m2 = 40.5 m2 =6 =2

No. black cells OA SOA Total area No. of people Unit level

=4 = 36 m2 = 4.5 m2 = 40.5 m2 =6 =2

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6.2.2c.2 (R4) Linkage , Access & Circulation

Levels _ Iteration 01

Option 1

t4d.1 = 00

No. of units = 11

t4d.1 = 01

No. of units = 9

t4d.1 = 02

No. of units = 11

t4d.1 = 03

No. of units = 9

t4d.1 = 04

No. of units = 10

132 | Cellular Automata

Option 2

Option 3

No. of units = 13

No. of units = 14

No. of units = 11

No. of units = 12

No. of units = 13

No. of units = 10

No. of units = 11

No. of units = 13

No. of units = 12

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6.2.2c.2 (R4) Linkage , Access & Circulation

Levels _ Iteration 01

Option 1

t4d.1 = 05

No. of units = 9

t4d.1 = 06

No. of units = 11

t4d.1 = 07

No. of units = 9

t4d.1 = 08

No. of units = 10

Inference Number of Units / Level ( Range ) Total no. of Units Unit Typology Access

134 | Cellular Automata

Option 01

Option 02

Option 03

= 9 - 11 = 89 = Mixed unit typologies = All units have individual access

= 10 - 13 = 106 = Mixed unit typologies = All units have individual access

= 11 - 14 = 111 = Maximum number of single units = 91 % units have individual access

Option 2

Option 3

No. of units = 11

No. of units = 13

No. of units = 14

No. of units = 10

No. of units = 11

No. of units = 13

No. of units = 14

fig. 30 : Rule 4d _ Linkage , circulation and access

From the above set of clustering options - 01, 02 and 03, it was observed that there is a flexibility in number of units and the unit types that can be achieved at each level by defining the linkages for black cell. Further, as observed in fig x, the BUA and the no. of people for each unit type are defined hence, density analysis enables us to determine the following : Total no. of Units | Total BUA | Total no. of people | Total CA & CA / person at regional and global levels. All the further density analysis and strategies for incremental growth are demonstrated for Option 01.

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6.2.2c.3 (R4) Density Analysis

BUA (m2)

Total no. of people

BUA / person (m2)

4.5

Total no. of Units

Total BUA ( m )

Total no. of people

Total no. of Units

Total BUA ( m2 )

Total no. of people

Total no. of Units

Total BUA ( m2 )

Total no. of people

Total no. of Units

Total BUA ( m2 )

Total no. of people

Unit

t=0

Total CA

CA / person ( m2 )

Total CA t=1

( m2 )

CA / person ( m2 )

Built Up Area ( BUA ) | Circulation Area ( CA )

136 | Cellular Automata

( m2 )

CA / person ( m2 )

Total CA t=3

( m2 )

CA / person ( m2 )

Total CA t=2

(m ) 2

4.5

2 54

189 51

158 3.09 2

9 0

189 48 142 2.95 11

162 39 176 3.45

3 81 18

198

48 149 3.10

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6.2.2C.3 (R4) Density Analysis

Total no. of Units

Total BUA ( m2 )

Total no. of people

Total no. of Units

Total BUA ( m2 )

Total no. of people

Total no. of Units

Total BUA ( m2 )

Total no. of people

Total no. of Units

Total BUA ( m2 )

Total no. of people

Total no. of Units

Total BUA ( m2 )

Total no. of people

Total CA

( m2 )

CA / person ( m2 )

t=4

Total CA

( m2 )

CA / person ( m2 )

t=5

Total CA t=6

( m2 )

CA / person ( m2 )

Total CA

( m2 )

CA / person ( m2 )

t=7

Total CA t=8

( m2 )

CA / person ( m2 )

Built Up Area ( BUA ) | Circulation Area ( CA )

Inference Volumetric Density ( Global ) Total no. of Units Total BUA Total CA

138 | Cellular Automata

= 111 = 1554 m2 = 1460 m2

Total no. of people Total BUA / person Total CA / person

= 368 = 4.22 m2 = 3.49 m2

1 27

162 45

178 3.95 1

9 0

132 42 153 3.64 11

135 39 171 4.38

4 108

1 0

198 48

162 3.37 1

10 0

189 48 171 3.56 table 10 : Rule 4d.1 _ Density Analysis

From the above analysis it was observed that varying unit types and densities can be achieved at different levels. It is also observed that alternate levels, t = 0, 2, 4, 6 & 8 have higher number of single unit typology ( U1 ) but overall, the number of units at each level range between 9 - 11 units. The density analysis enables us to determine the number of unit types, density of people, circulation area / person at local, regional and global level. Thus each level is a combination of different unit types and densities creating various social and semi open spaces at local and regional level.

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6.2.2d (R4) Possibilities for Incremental Growth Optimum surface

t4d.1 = 00

t4d.1 = 01

t4d.1 = 02

t4d.1 = 03

t4d.1 = 04

140 | Cellular Automata

Wind movement Analysis

Optimum surface

Wind movement Analysis

t4d.1 = 05

t4d.1 = 06

t4d.1 = 07

t4d.1 =08

fig. 31 : Rule 4d _ Possibilities for Incremental Growth

Inference From the environmental analysis, fig 29, it was observed that the circulation and semi open areas, with optimum sunlight, visibility and solar radiation are located along the edges. The grey cells which function as access to units were excluded from the areas with possibility for increment. Furthermore, the cells which are in windward direction are strategically developed as occupied areas and semi open spaces to avoid the obstruction of wind flow in the internal open and semi - open spaces. Based on the above mentioned strategies, the next set of analysis demonstrate the increment state and the percent of increment achieved at every level.

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6.2.2e (R4) Incremental Growth Analysis

Level

t4d.1 = 00

t4d.1 = 01

t4d.1 = 02

t4d.1 = 03

t4d.1 = 04

Occupied Surface Area ( OA ) | Semi Open Area ( SOA ) |

142 | Cellular Automata

Possibilities for Increment

Inital State

SOA

Circulation Area ( CA )

CA 32

% Increment of Occupied Area

Incremental State

t4d.11 = 00

t4d.11 = 01

t4d.11 = 02

t4d.11 = 03

t4d.11 = 04

SOA

13 %

9 %

11 %

All values are in percentage

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6.2.2e (R4) Incremental Growth Analysis

Level

Possibilities for Increment

Inital State

t4d.1 = 05

t4d.1 = 06

t4d.1 = 07

t4d.1 = 08

SOA

Inference From the above set of analysis, it was observed that 9% - 11% of increment can be achieved at maximum number of levels, by developing the circulation areas as occupied and semi - open areas. The increment can be achieved by extending the already existing units or by developing new units. Thus the increment is user defined and can be executed over time as per the requirement. Furthermore it was also observed that inspite of the increment, the social spaces are retained. Occupied Surface Area ( OA ) | Semi Open Area ( SOA ) |

144 | Cellular Automata

Circulation Area ( CA )

% Increment of Occupied Area

Incremental State

t4d.11 = 05

t4d.11 = 06

t4d.11 = 07

t4d.11 = 08

SOA

11 %

fig. 32a : Rule 4d _ Incremental Growth Analysis

It is important to determine the effect of additional built form on the wind speed within the internal open and semi open spaces. As a result CFD analysis was conducted on the volume achieved after increment and the wind speed within the internal areas were evaluated.

All values are in percentage

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6.2.2e (R4) Incremental State Analysis

Incremental State

CFD Analysis

t1 = 00

Analysis

IOA 13%

t1 = 01

t1 = 02

t1 = 04

% Increment of Occupied Area ( IOA ) | Wind Speed in Internal Open & Semi Open Spaces ( WS )

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1.5 - 2

IOA

WS (m/s)

2 - 2.5

IOA

WS (m/s)

11%

t1 = 03

WS (m/s)

1.5 - 2

IOA

WS (m/s)

2 - 2 .5

IOA

WS (m/s)

1.5 - 2

Incremental State

CFD Analysis

t4d.11 = 05

t4d.11 = 06

t4d.11 = 07

Analysis

IOA

WS (m/s)

2 - 2.5

IOA

WS (m/s)

1.5 - 2

IOA

WS (m/s)

11%

IOA

t4d.11 = 08

11%

1.5 - 2

WS (m/s) 2 - 2 .5

fig. 32b : Rule 4d _ CFD Analysis for Incremental Growth

Inference The average increment is 10 % and the overall wind speed in the internal open and semi open space is maintained at 1.5 - 2.5 m/s ( Refer Appendix I for the movement of wind throughout the volume). Thus we can conclude that the strategic increment does not compromise the ventilation of internal open and semi open spaces.

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148 | Cellular Automata

6.2.2a CA Rule Exploration Rule 5 (R5)

Current state of Cell

Loneliness - Death

Black

State of Cell in Next Level

Sum of Neighbors

White

< 2 Black

Grey

Overpopulation - Transformation

< 2

Black

Grey > 3

Grey

Black > 3

Death

Black

White =3

Grey

White =3

White

Grey

Birth

=3 White

Black =4

The state of other cells remain constant

fig. 33a : Diagram explaining 2D CA Rule 4

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Experiment 5D _Iteration 01

t5d.1 = 00

t5d.1 = 01

t5d.1 = 02

t5d.1 = 03

t5d.1 = 04

t5d.1 = 05

t5d.1 = 06

t5d.1 = 07

t5d.1 = 08

Observation Volumetric Density

Volumetric Packing

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Black Cell

= 39 %

Grey Cell

= 38 %

White Cell

= 23 %

Volumetric Ratio (B:G)

=1:1

Volumetric Continuity of Void (Open to Sky )

= 19 %

fig. 33b : Rule 5d _ Iteration 01 Plans for each levels and volumetric packing

Experiment 5D _Iteration 02

t5d.2 = 00

t5d.2 = 01

t5d.2 = 02

t5d.2 = 03

t5d.2 = 04

t5d.2 = 05

t5d.2 = 06

t5d.2 = 07

t5d.2 = 08

Observation Volumetric Density

Volumetric Packing

Black Cell

= 38 %

Grey Cell

= 38 %

White Cell

= 24 %

Volumetric Ratio (B:G)

=1:1

Volumetric Continuity of Void (Open to Sky )

= 19 %

fig. 33c : Rule 5d _ Iteration 02 Plans for each levels and volumetric packing

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Experiment 5D _Iteration 03

t5d.3 = 00

t5d.3 = 01

t5d.3 = 02

t5d.3 = 03

t5d.3 = 04

t5d.3 = 05

t5d.3 = 06

t5d.3 = 07

t5d.3 = 08

Observation Volumetric Density

Volumetric Packing

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Black Cell

= 39 %

Grey Cell

= 39 %

White Cell

= 22 %

Volumetric Ratio (B:G)

=1:1

Volumetric Continuity of Void (Open to Sky )

= 19 %

fig. 33c : Rule 5d _ Iteration 01 Plans for each levels and volumetric packing

Conclusion From the above set of experiments, it can be observed that the volumetric density, volumetric ratios and percentage of continuous void are similar for all the experiments. Hence it can be inferred that the strategies demonstrated and explored for one iteration can be applicable for all iterations. All the further analysis and the strategies that are developed, are demonstrated for Iteration 01

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6.2.2b (R5) _ Environmental Analysis

Levels

Surface Area receiving more then 2 hrs of direct Sunlight 21st June

22nd Dec

30 %

48 %

37 %

44 %

31 %

49 %

35 %

30 %

29 %

48 %

t5d.1 = 00

t5d.1 = 01

t5d.1 = 02

t5d.1 = 03

t5d.1 = 04

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Surface Area receiving more then 1 kWh/m2 of Solar Radiation

Surface Area with more then 30% of Visibility

21st June

22nd Dec

37 %

38 %

29 %

36 %

41 %

32 %

39 %

38 %

28 %

24 %

30 %

29 %

38 %

35 %

CFD Analysis

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6.2.2b (R5) _ Environmental Analysis

Levels

Surface Area receiving more then 2 hrs of direct Sunlight 21st June

22nd Dec

35 %

30 %

29 %

48 %

45 %

37 %

95 %

62 %

t5d.1 = 05

t5d.1 = 06

t5d.1 = 07

t5d.1 = 08

Inference From the above set of analysis it was observed that the internal areas receive less then 1kw/m2 of solar radiation due to self shading and the wind speed is 1.5 - 2 m/s . The continuity of void across the volume and the semi open spaces enables the movement of wind throughout the volume ( Refer Appendix I for the movement of wind throughout the volume). It also creates a visual connection between different levels. As a result the internal circulation areas can be proposed as social spaces which can be utilized even during the day time.

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Surface Area receiving more then 1 kWh/m2 of Solar Radiation

Surface Area with more then 30% of Visibility

21st June

22nd Dec

28 %

24 %

30 %

29 %

38 %

35 %

38 %

36 %

31 %

89 %

67 %

45 %

CFD Analysis

fig. 34 : Rule 5d Environmental analysis

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6.2.2c.2 (R5) Linkage , Access & Circulation

Levels _ Iteration 01

Option 1

t5d.1 = 00

No. of units = 11

t5d.1 = 01

No. of units = 11

t5d.1 = 02

No. of units = 11

t5d.1 = 03

No. of units = 12

t5d.1 = 04

No. of units = 12

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Option 2

Option 3

No. of units = 13

No. of units = 12

No. of units = 13

No. of units = 15

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6.2.2c.2 (R5) Linkage , Access & Circulation

Levels _ Iteration 01

Option 1

t5d.1 = 05

No. of units = 9

t5d.1 = 06

No. of units = 11

t5d.1 = 07

No. of units = 9

t5d.1 = 08

No. of units = 10

Inference Number of Units / Level ( Range ) Total no. of Units Unit Typology Access

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Option 01

Option 02

Option 03

= 9 - 12 = 96 = Mixed unit typologies = 88.55% units have individual access

= 10 - 13 = 110 = Mixed unit typologies = 80.91% units have individual access

= 11 - 15 = 117 = Maximum number of single units = 78.64 % units have individual access

Option 2

Option 3

No. of units = 11

No. of units = 13

No. of units = 15

No. of units = 10

No. of units = 11

No. of units = 13

No. of units = 15

fig. 35 : Rule 5d _ Linkage , circulation and access

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6.2.2C.3 (R5) Density Analysis

Unit BUA (sq. mt)

Total no. of people

BUA / person

Total no. of Units (m )

Total no. of people

Total BUA

t5d.1 = 00

Total CA

Total no. of Units

Total BUA

( m2 )

Total no. of people

Total no. of Units

Total BUA

( m2 )

Total no. of people

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( m2 )

CA / person ( m2 ) Total no. of Units

Total BUA

( m2 )

Total no. of people

Total CA t5d.1 = 03

( m2 )

CA / person ( m2 )

Total CA t5d.1 = 02

(m ) 2

CA / person ( m2 )

Total CA t5d.1 = 01

( m2 )

CA / person ( m2 )

4.5

108

216

54 79 1.46

11 0

144 42 135 3.21

207

51 106 2.07

12 0

162 48 185 3.85

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6.2.2C.3 (R5) Density Analysis

Total no. of Units

Total BUA

( m2 )

Total no. of people

Total CA t5d.1 = 04

( m2 )

CA / person ( m2 ) 8

Total no. of Units (m )

Total no. of people

Total BUA Total CA t5d.1 = 05

(m ) 2

CA / person ( m2 ) Total no. of Units

Total BUA

( m2 )

Total no. of people

Total CA t5d.1 = 06

( m2 )

CA / person ( m2 ) Total no. of Units ( m2 )

Total no. of people

Total BUA Total CA t5d.1 = 07

( m2 )

CA / person ( m2 ) Total no. of Units

Total no. of people

Total CA

( m2 )

CA / person ( m2 )

Inference Volumetric Density ( Global ) Total no. of Units Total BUA Total CA

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= 96 = 1728 m2 = 1.46 - 3.85 m2

( m2 )

Total BUA

t5d.1 = 08

Total no. of people Total BUA / person Total CA / person

= 462 = 3.74 m2 = 2.72 m2

225

57 119 2.08

12 0

162 48 185 3.85

225

57 119 2.08

12 0

162 48 185 3.85

225

57 119 2.08 table 11 : Rule 5d.1 _ Density Analysis

From the above density analysis it was observed that varying unit types and densities can be achieved at each level . It is also observed that the number of single units are more then other unit types thus accommodating high densities. Each level is thus a combination of different unit types and densities creating various social and semi - open spaces at local and regional level. Furthermore, based on environmental and neighborhood analysis, strategies for incremental growth are proposed and analysis are conducted for the same.

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6.2.2b (R5) _ Environmental Analysis _ Evaluation Optimum surface

t5d.1 = 00

t5d.1 = 01

t5d.1 = 02

t5d.1 = 03

t5d.1 = 04

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Wind movement Analysis

Optimum surface

Wind movement Analysis

t5d.1 = 05

t5d.1 = 06

t5d.1 = 07

t5d.1 = 08

fig. 36 : Rule 5d _ Possibilities for Incremental Growth

Inference From the environmental analysis, fig 34, it was observed that the circulation and semi open areas, with optimum sunlight, visibility and solar radiation are located along the edges. The grey cells which function as access to units are excluded from the areas with possibility for increment. Furthermore, the cells which are in windward direction are strategically developed as occupied areas and semi open spaces to avoid the obstruction of wind flow in the internal open and semi - open spaces. Based on the above mentioned strategies, the next set of analysis demonstrate the increment state and the percent of increment achieved at every level.

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6.2.2d (R5) Incremental Growth Level

t5d.1 = 00

t5d.1 = 01

t5d.1 = 02

t5d.1 = 03

t5d.1 = 04

Occupied Surface Area ( OA ) | Semi Open Area ( SOA ) |

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Possibilities for Increment

Inital State

SOA

Circulation Area ( CA )

CA 37

CA 31

% Increment of Occupied Area

Incremental State

t5d.11 = 0

t5d.11 = 1

t5d.11 = 2

t5d.11 = 3

t5d.11 = 4

SOA

4 %

All values are in percentage

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6.2.2d (R5) Possibilities for Incremental Growth Level

Possibilities for Increment

Inital State

t5d.1 = 05

t5d.1 = 06

t5d.1 = 07

t5d.1 = 08

SOA

Inference From the above set of analysis, it was observed that 2% - 4% of increment can be achieved at maximum number of levels, by developing the circulation areas as occupied and semi - open areas. The increment can be achieved by extending the already existing units or by developing new units. Thus the increment is user defined and can be executed over time as per the requirement. Furthermore it was also observed that inspite of the increment, the social spaces are retained. Occupied Surface Area ( OA ) | Semi Open Area ( SOA ) |

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Circulation Area ( CA )

% Increment of Occupied Area

Incremental State

t5d.11 = 5

t5d.11 = 6

t5d.11 = 7

SOA

t5d.11 = 8

OA 48

fig. 37a : Rule 5d _ Incremental Growth Analysis

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6.2.2e (R5) Incremental State Analysis Incremental State

CFD Analysis

t5d.11 = 0

t5d.11 = 1

t5d.11 = 2

t5d.11 = 3

t5d.11 = 4

% Increment of Occupied Area ( IOA ) | Wind Speed in Internal Open & Semi Open Spaces ( WS )

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Analysis

IOA

WS (m/s)

1.5 - 1.75

IOA

WS (m/s)

2 - 2.5

IOA

WS (m/s)

1.5 - 1.75

IOA

WS (m/s)

2 - 2.5

IOA

WS (m/s)

1.5 - 1.75

Incremental State

CFD Analysis

t5d.11 = 5

t5d.11 = 6

t5d.11 = 7

t5d.11 = 8

IOA

WS (m/s)

2 - 2.5

IOA

WS (m/s)

1.5 - 1.75

IOA

WS (m/s)

2 - 2.5

IOA

WS (m/s)

1.5 - 1.75

fig. 37b : Rule 5d _ CFD Analysis for Incremental Growth

Inference The average increment is 2.7 % and the overall wind speed in the internal open and semi open space is maintained between 1.5 - 2.5 m/s ( Refer Appendix I for the movement of wind throughout the volume). Thus we can conclude that the strategic increment does not compromise the ventilation of internal open and semi open spaces.

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6.3 Conclusion - Comparative Analysis

Regional - Evaluation at each levels ( Range of values )

Rule 4

Rule 5

Environmental

Initial State Void

19% - 20%

19 % - 33 %

Wind Speed ( Internal Open & Semi open spaces )

1.2 - 1.5 m/s

1.5 - 2.5 m/s

Incremental State Wind Speed ( Internal Open & Semi open spaces )

1.5 - 2.5 m/s

Density

Initial State No. of units

9 - 11

9 - 12

No. of Single Units

2-5

5-8

CA / person

2.95 - 4.38 m2

2.08 - 3.85 m2

Total no. of People

39 - 48

42 - 57

Neighborhood

Initial State Occupied Area

35 % - 39 %

33 % - 46 %

Semi Open Area

6 % - 10 %

7 % - 11 %

Circulation Area

31 % - 37 %

31 - 37 %

Incremental State Occupied Area

44 % - 52 %

48 % - 50 %

Semi Open Area

7 % - 13 %

7 % - 11 %

Circulation Area

20 % -25 %

27 % - 35 %

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Global - Evaluation for the entire Volume ( Average values )

Rule 5

Rule 4

Environmental

Initial State Continuity of Void

19 %

Wind Speed ( Internal Open & Semi open spaces )

1.5 m/s

2 m/s

Incremental State Wind Speed ( Internal Open & Semi open spaces )

2 m/s

Density

Initial State Total no. of units

Total no. of Single Units

CA / person

3.49 m/s

2.72 m/s

Total no. of People

368

462

Occupied Area

37 %

39.33 %

Semi Open Area

8.44 %

8.66 %

Circulation Area

33.22 %

33.55 %

Neighborhood

Initial State

Incremental State Occupied Area

42.66 %

42 %

Semi Open Area

9.33 %

8.66 %

Circulation Area

21.77 %

31 %

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176 | Cellular Automata

07 CONCLUSION

7.1

OVERVIEW

7.2

A WAY FORWARD

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178 | Cellular Automata

7.1 Overview Cellular Automata (CA) has been used as a design tool by architects to achieve organization of patterns at various scales. The exploration and implementation of CA as a design tool within the architectural context requires certain modification of the basic rules of CA. As the rules are based on adjacencies, the spatial organizations achieved are emergent, self-organized patterns. Such patterns based on local iteration are prevalent in bottom up approach. This research dwells on developing and adopting this tri-parta approach, where the relations are established at local, regional and global scale to achieve spatial volumes. It also helps us to understand the various alterations that can be performed on the basic rules of 2D CA to establish these relations and achieve configuration of cells specific to a context. The research helps us the understand the design process that can be adopted to achieve different patterns of spatial organization. The design process adopted is a bottom up approach where the spatial configuration achieved is result of interaction of cells at local, regional and global levels. The different state of cells correspond to the defined spatial function and their inter-relation, which once established, the rules for over population, loneliness and birth can be explored. Thus, by altering the state of cell and relation between them, different volumes can be iterated. The research also helps us to understand that, the input parameters, evaluation method and the fitness criteria necessary for the application of CA, when extracted from the set of case studies, builds a volume which is more context sensitive and user driven. From the set of spatial and environmental analysis conducted in chapters 06, It can be concluded that the organization system and the volumes iterated by the application of 2D CA achieve high density and defines relation between built, open ans semi - open spaces at every level, thus enhancing the quality of life within low cost, high density housing.Furthermore, different strategies can be developed to define various housing typologies for low cost housing. The figure 38. on the next page demonstrates strategy for clustering of cells, which creates social spaces at local and regional level.

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7.2 A Way Forward Housing Type _ Scenario 2 It is observed from Chapter 06 - CA rule implementation that varying densities can be achieved by defining the unit type and number of people/unit. The diagram below demonstrates an alternate strategy for defining the unit type.This type of unit can be proposed to develop an alternate housing typology with medium density. Unit Type = The single unit is linked to another single or double celled unit with an adjacent grey cell, which functions as an internal courtyard. Access to the unit is through a grey cell which functions as a semi open space and circulation Grey Cell

= Internal Courtyard

Grey Cell

= Access = 50 % Semi Open Space + 50 % Circulation Area

Unit Type 01 Black cells = 2 OA = 18 m2 SOA = 9 + 4.5 = 13.5 m2 Total area = 31.5 m2 No. of people = 6 Unit Type 02

fig. 38 : Strategy 2 _ Unit Typology

Black cells = 3 OA = 27 m2 SOA = 9 + 4.5 = 13.5 m2 Total area = 40.5 m2 No. of people = 6

Linkage + Access + Circulation Initial State

= The Layout achieved by application of the above mentioned strategy for clustering of cells, creates social spaces at unit level and floor level. An inter - relation between the built, open and semi open spaces is established.

Total no. of Units = 8 OA = 33% SOA = 17% CA = 30% Total no. of people CA / person

fig. 39 : Strategy 2 _ Linkage + Access + Circulation

180 | Cellular Automata

= 48 =

CA Rule Exploration _ Scenario 2 State of Cell = Each state of cell corresponds to a function and the cell organization achieved by the application of the rule can be evaluated based on various fitness criteria. By defining more states of cell, the sum total of the neighboring cell increases, thus increasing the possibility for rule exploration.

White = 0

Grey = 2

Black = 1

Blue = 3

For the given state of cells, the minimum total of the neighboring cells = 1 the maximum total of the neighboring cells = 24

Sum of neighboring cells = 1

= 10

= 17

= 24

fig. 40 : State of Cell

Grid size _ Layout = The number of cells at each level i.e the size of the grid and the layout can be defined based on the context. In this research we have explored the square and rectangular grid sizes of 12 x 12, 9 x 9, 9 x 18 & 9 x 6.

fig. 41 : Grid Layout

The fig x, show the examples of different layouts, for which 2D CA can be explored

Domain = The rules of 2D CA can be explored and implemented for various context where the spatial organization system is determined by the inter-relation of spaces and functions. Each spatial function can be determined by the state of cell and the relation between the spaces can be explored by defining the rules of neighborhood. Furthermore, the organization pattern and the volume achieved can be optimized by defining the input parameters, strategies and evaluation methods, that are derived from the context.

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08 APPENDIX

Appendix I

Rule 4d.1 _ Initial State

Wind Speed within Internal Courtyards = 1.5 -2.25 m/s The continuity of voids and the semi open spaces facilitate the movement of the wind through out the volume

Rule 4d.1 _ Incremental State Wind Speed within Internal Courtyards = 2 -2.5 m/s The continuity of voids and the semi open spaces facilitate the movement of the wind through out the volume . The wind speed within the internal courtyards is maintained.

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Rule 5d.1 _ Initial State

Wind Speed within Internal Courtyards = 1.5 -2.5 m/s The continuity of voids and the semi open spaces facilitate the movement of the wind through out the volume

Rule 5d.1 _ Incremental State Wind Speed within Internal Courtyards = 2 -2.5 m/s The continuity of voids and the semi open spaces facilitate the movement of the wind through out the volume . The wind speed within the internal courtyards is maintained.

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184 | Cellular Automata

09 REFERENCE & BIBLIOGRAPHY

Andel, F. V. (2015). DASH : global housing : affordable dwellings for growing cities. Rotterdam: nai010 publisher. Batty, M. (2005). Cities and Complexities : Understanding cities with cellular Automata, agent based models, and fractals. Massachusetts, Cambridge: MIT Press. Jacobs, J. (1992). Death and Life of Great American Cities. New York: Vintage Books. Krawcyk, R. (2002). Architectural Interpretation of Cellular Automata . The 5th International Conference on Generative Art (pp. 7.1 - 7.8). Milan, Italy : Generative Design Lab, DiAP: Politecnico di Milano University. Negroponte, N. (1970). The Architecture machine : Towards a more human environment. Cambridge: Mass : MIT Press. Padora, S. (n.d.). In the name of Housing : a study of eleven projects in Mumbai. Mumbai: Urban Design Research Institute. Thoma, H. C. (2005). Using Cellular Automata to Generate High Density Building Form. In M. B. A., Computer Aided Architectural Design Futures 2005 (pp. 249 - 258). Springer, Dordrecht. Thomas, H. C. (2005). Using Cellular Automata to Generate High- Density Building Form. In B. A. Martens B., Computer Aided Architectural Design Futures 2005 (pp. 249 - 258). Hongkong: Springer, Dordrecht. Voon, P. C. (1996). The Use of Cellular Automata to Explore Bottom Up Architectonic Rules. Eurographics UK Chapter 14th Annual Conference at Imperial College. London. Wolfram, S. (2002). New Kind of Science. Wolfram Media, Inc.

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186 | Cellular Automata

List of Figures

Figure 1 :

Rule 250 - Diagram showing the rules of neighborhood for 1D CA

Figure 15a :

Diagram explaining 2D CA Rule 2

Figure 2 :

Recreated frame from Conway’s ‘ Game of Life ‘

Figure 15b :

Rule 2 _ 12 x 12 Plan for each level and Volumetric Packing

Figure 3 :

Diagram showing rules of Game of Life

Figure 15c :

Rule 2 _ 9 x 9 Plan for each level and Volumetric Packing

Figure 4 :

Patterns achieved by varying rule - set of GOL for same initial state

Figure 15d :

Rule 2 _ 9 x 18 Plan for each level and Volumetric Packing

Figure 5 :

Diagram showing the rules of Game of Life - 2D Spatial Layering

Figure 6 :

Map showing the increase and projected growth in world city population

Figure 16a :

Diagram explaining 2D CA Rule 3

Figure 16b :

Rule 3 _ 12 x 12 Plan for each level and Volumetric Packing

Figure 7 :

Low cost, SRA building in Mumbai

Figure 8a :

Aranya Housing, Indore, India

Figure 16c :

Rule 3 _ 9 x 9 Plan for each level and Volumetric Packing

Figure 8b :

Incremental growth of units

Figure 9 :

State of Cell

Figure 16d :

Rule 3 _ 9 x 18 Plan for each level and Volumetric Packing

Figure 10 :

Possible state of cell in next level

Figure 11 :

Demonstration of Rule 1_ Rule set 1

Figure 17a :

Diagram explaining 2D CA Rule 4

Figure 12 :

Rule of adjacencies from Rule 1 _ Rule set 1

Figure 17b :

Figure 13 :

Rule of adjacencies from Rule 5 _ Rule set 2

Rule 4 _ 12 x 12 Plan for each level and Volumetric Packing

Figure 17c :

Figure 14a :

Diagram explaining 2D CA Rule 1

Rule 4 _ 9 x 9 Plan for each level and Volumetric Packing

Figure 14b :

Rule 1 _ 12 x 12 Plan for each level and Volumetric Packing

Figure 17d :

Rule 4 _ 9 x 18 Plan for each level and Volumetric Packing

Figure 14c :

Rule 1 _ 9 x 9 Plan for each level and Volumetric Packing

Figure 18a :

Diagram explaining 2D CA Rule 5

Figure 18b :

Rule 5 _ 12 x 12 Plan for each level and Volumetric Packing

Figure 14d :

Rule 1 _ 9 x 18 Plan for each level and Volumetric Packing

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Rule 5 _ 9 x 9 Plan for each level and Volumetric Packing

Figure 23a :

Typical Floor Plan

Figure 23b :

Unit Plan

Rule 5 _ 9 x 18 Plan for each level and Volumetric Packing

Figure 23c :

Volumetric Plan

Figure 23d :

Volumetric Unit Plan

Figure 19a :

Diagram explaining 2D CA Rule 6

Figure 24a :

Typical Floor Plan

Figure 19b :

Rule 6 _ 12 x 12 Plan for each level and Volumetric Packing

Figure 24b :

Unit Plan

Figure 24c :

Volumetric Plan

Rule 6 _ 9 x 9 Plan for each level and Volumetric Packing

Figure 24d :

Volumetric Unit Plan

Figure 25a :

Typical Floor Plan

Rule 6 _ 9 x 18 Plan for each level and Volumetric Packing

Figure 27 :

Strategies for Linkage

Figure 28a :

Diagram explaining 2D CA Rule 4

Figure 20a :

Typical Floor Plan

Figure 28b :

Figure 20b :

Unit Plan

Rule 4d _ Iteration 01 Plan for each level and Volumetric Packing

Figure 20c :

Volumetric Plan

Figure 28c :

Figure 20d :

Volumetric Unit Plan

Rule 4d _ Iteration 02 Plan for each level and Volumetric Packing

Figure 21a :

Typical Floor Plan

Figure 28d :

Figure 21b :

Unit Plan

Rule 4d _ Iteration 03 Plan for each level and Volumetric Packing

Figure 21c :

Incremental Plan

Figure 29 :

Rule 4d _ Environmental Analysis

Figure 21d :

Volumetric Plan

Figure 30 :

Figure 21e :

Volumetric Unit Plan

Rule 4d _ Linkage, circulation and access

Figure 22a :

Typical Floor Plan

Figure 31 :

Rule 4d _ Possibilities for Incremental growth

Figure 22b :

Unit Plan

Figure 32a :

Rule 4d _ Incremental growth analysis

Figure 22c :

Incremental Plan

Figure 32b :

Figure 22d :

Volumetric Plan

Rule 4d _ CFD Analysis for Incremental growth

Figure 22e :

Volumetric Unit Plan

Figure 33a :

Diagram explaining 2D CA Rule 5

Figure 18c :

Figure 18d :

Figure 19c :

Figure 19d :

188 | Cellular Automata

Rule 5d _ Iteration 01 Plan for each level and Volumetric Packing

table 1a :

Rule 1 - Cell Density at Individual Level

table 1b :

Rule 1 - Volumetric Evaluation

Rule 5d _ Iteration 02 Plan for each level and Volumetric Packing

table 2a :

Rule 2 - Cell Density at Individual Level

table 2b :

Rule 2 - Volumetric Evaluation

Rule 5d _ Iteration 03 Plan for each level and Volumetric Packing

table 3a :

Rule 3 - Cell Density at Individual Level

table 3b :

Rule 3 - Volumetric Evaluation

Figure 34 :

Rule 5d _ Environmental Analysis

table 4a :

Rule 4 - Cell Density at Individual Level

Figure 35 :

Rule 5d _ Linkage, circulation and access

table 4b :

Rule 4 - Volumetric Evaluation

Figure 36 :

Rule 5d _ Possibilities for Incremental growth

table 5a :

Rule 5 - Cell Density at Individual Level

table 5b :

Rule 5 - Volumetric Evaluation

Figure 37a :

Rule 5d _ Incremental growth analysis

table 6a :

Rule 6 - Cell Density at Individual Level

Figure 37b :

Rule 5d _ CFD Analysis for Incremental growth

table 6b :

Rule 6 - Volumetric Evaluation

Figure 38

Strategy 2 _ Unit Typology

table 7 :

Unit Type

Figure 39 :

Strategy 2 _ Linkage + Access + Circulation

table 8 :

Extracted parameters for spatial organization

Figure 40 :

State of Cell

table 9 :

Comparative Analysis of different CA Rules

Figure 41 :

Grid Layout

table 10 :

Rule4d.1 - Density Analysis

table 11 :

Rule 5d.1 - Density Analysis

Figure 33b :

Figure 33c :

Figure 33d :

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