Design by Grammar: Algorithmic Design in an Architectural Context
By
M. Birgul Colakoglu
M.S. Architectural Design (1990)
Yildiz Technical University
Submitted to the School of Architecture in Partial Fulfillment of the Requirements for the
Degree of Doctor of Philosophy in Architecture: Design and Computation
at the
Massachusetts Institute of TechnologyM
R511
September 2000
E
0 2000 Massachusetts Institute of Technology
All rights reserved
Signature of Author ........
...
Department of Architecture
September 15, 2000
Certified
by
.,/...................................
George Stiny
Professor of Design and Computation
Thesis Supervisor
I
Accepted by ...........
A
IL
I.................
Stanford Anderson
Chairman, Department Committee on Graduate Students
ROTCH
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
MAR
2R001
LIBRARIES_
Dissertaion Committee
George Stiny
Professor of Design and Computation
William J. Mitchell
Professor of Architecture and Media Art and Sciences
Terry
Knight
Associate Professor of Design and Computation
Design by Grammar: Algorithmic Design in an Architectural Context
By
M. Birgul Colakoglu
Submitted to the Department of Architecture on September 15, 2000
In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in
Architecture: Design and Computation
ABSTRACT
An experimental study was performed to explore the practical applicability of the rule
based design method of shape grammars. The shape grammar method is used for the
analysis and synthesis of the hayat house type in a particular context.
In the analysis part, the shape grammar method is used to extract basic compositional
principles of the hayat house. In the synthesis part, first the evolution of a new hayat
house prototype is illustrated. An algorithmic prototype transformation is considered.
This transformation is achieved in two ways: by changing the values assigned to the
variables that define the component objects of the form, and by replacing the vocabulary
elements of the form with new ones. Then, the application of the rule based design
method for housing pattern generation is explored. The design of a housing complex is
illustrated using this method.
Thesis supervisor: George Stiny
Title: Professor of Design and Computation
Acknowledgments
My gratitude goes to the following people:
My parents Asim and Suat Colakoglu for making me who I am, and for encouraging me
to follow my interes through life. My brother Gurhan and his wife Yesim Colakoglu for
their friendship and support. My cousin Guven Nil for his encouragement and financial
aid when it was most needed.
My dissertation committee for their friendship and support, especially:
Prof George Stiny for teaching me new ways of looking at design. His sense of the fun
of working with shapes made all these years of learning from him a pleasure and has been
a rewarding inspiration for a thesis centered on this theme. His critical rigor gave me
constant intellectual stimulation. I owe immense gratitude to my advisor for his
continuous support throughout my years at MIT.
Prof Terry Knight for encouragement and generosity in sharing her vaste knowledge for
continuous refinement of my thought.
Prof William Mitchell for his insightful comments and observations which helped me to
formulate my architectural motivations and my design concepts.
My thanks also go to my friends:
Carolyn Wood, David Fernandes,Jesse Khan and Ian Sue Wing for their friendship and
assistance.
Megan Yakeley for early discussions, and Michelle Woodward for proof reading my
thesis.
List of Figures
Figure 1.
Detached and semi-detached hayat houses in Sarajevo
Figure 2.
Hayat houses in Sarajevo
Figure 3.
Svirzina house birdseye view
Figure 4.
Svirzina house
Figure 5.
Semizova house
Figure 6.
Derzeleza house
Figure 7.
Partialmahala pattern
Figure 8.
The method of shape grammar development
Figure 9.
Vocabulary and spatial relations
Figure 10. Family of spatial relations and starting rules
Figure 11. Grammar rules
Figure 12. Grammar rules
Figure 13. Derivation of Prt. A
Figure 14. Derivation of Prt. B
Figure 15. Derivation of Prt. C
Figure 16. Different derivations of set 3 rules
Figure 17. Shape rules
Figure 18. Shape rules
Figure 19. Stagel
Figure 20. Stage 2, 3 and 4
Figure 21. Evolution of the first floor plan
Figure 22. Evolution of the first floor plan
Figure 23. Evolution of the first floor plan
Figure 24. Evolution of the first floor plan
Figure 25. Prt. A houses
Figure 26. House development rules
Figure 27. Room partition set
List of Figures Continued
Figure 28. Prt. Al house development
Figure 29. Prt. Al house development
Figure 30. Prt. Al house development
Figure 31. Prt. A2 house development
Figure 32. Prt. A2 house development
Figure 33. Prt. A2 house development
Figure 34. Prt. A3 and Prt. A4 house development
Figure 35. Prt. A3 house development
Figure 36. Prt. A4 house development
Figure 37. Prt. A5 development
Figure 38. Prt. A5 development
Figure 39. Set of articulated type A houses
Figure 40. Transformation rules for incline topography
Figure 41. Prt. A1.1 house transformation
Figure 42. Prt. A2.2 house transformation
Figure 43. Prt. A4.2 house transformation
Figure 44. Split level houses
Figure 45. Split level houses
Figure 46. Prt. Al.1
Figure 47. Transformation rules for Prt. A1.3
Figure 48. Transformation of Prt. A1.3
Figure 49. Transformation rules for TI
Figure 50. Transformation of Prt. T2 into T3
Figure 51. Transformation of Prt. T3 into T4
Figure 52. Transformation of Prt. Al.3
Figure 53 Transformation of Prt. A1.3
Figure 54. Transformation of Prt. Al.3
Figure 55. Evolution of Prt. Al.1
List of Figures Continued
Figure 56. Transformation of Prt. A1.1
Figure 57. Interpretation of Prt. A1.1
Figure 58. Transformation of Prt. T2
Figure 59. Block design generated with Prt. T2
Figure 60. House connection rules
Figure 61. Semi-detached houses
Figure 62. Adjacency relation between semi-detached houses
Figure 63. Adjacency relation between semi-detached houses
Figure 64. Row house layouts
Figure 65. Row houses
Figure 66. Housing pattern rules
Figure 67. Housing pattern generation
Figure 68. Substitution rules
Figure 69. Housing unit
Figure 70. Housing pattern rules for incline topography
Figure 71.
Spatial relations between different sites
Figure 72. Housing pattern on incline topography
Figure 73. Transformation of the site
Figure 74. Detached and row houses
Figure 75. Detached houses and semi-detached houses
Figure 76. Terrace houses
Figure 77. Housing complex
Table of Contents
1. Introduction
2. Shape Grammars
12
2.1 Shape Grammar Formalism
12
2.2 Shape Grammar Applications
13
3. Methodology
15
4. Hayat Houses
17
4.1 The Configuration of the Houses
18
4.2 Housing Patterns
19
5. Design by Grammar
5.1 House Prototype Generation
5.1.1
Primitive Prototype
5.1.1.1 The Application of the Rules to Designs
5.1.2
Prototype Instances
5.1.2.1 The Application of the Rules to Designs
5.1.3
Prototype Development
5.1.3.1 The Application of the Rules to Designs
5.1.4
Prototype Transformation
5.1.4.1 Transformation 1
5.1.4.2 The Application of theRules to Designs
20
21
21
25
27
29
31
33
5.1.4.3 Transformation 2
5.1.4.4 The Application of the Rules tos Designs
5.1.5
Prototype Compounds
5.2 Housing Pattern Generation
6.
49
5.2.1
Housing Patterns
49
5.2.2
The Application of the Prototypes
52
Discussion and Future Work
7. References
55
135
1. Introduction
This thesis explores the applicability of algorithmic design in a real-world architectural
context, through the use of the shape grammar formalism. This method is expressed as
an algorithm that describes the computational mechanism for composing shapes, utilizing
symbols, geometry, and algebraic operations. A shape grammar describes a vocabulary,
the relationships between vocabulary elements, and the rules for generating designs in a
particular style or design language.
Specifically, I use a parametric shape grammar. Rules in this grammar are defined by
assigning values to variables. Parametrically defined variables allow different geometric
properties of shapes, such as dimension, angle and position, to vary.2 By applying the
parametric shape grammar method in an informal manner, I illustrate how grammar rules
can be used to generalize the compositional design principles of a particular form within
a certain style. Shape grammars are primarily used in design analysis. My objective in
this thesis is to demonstrate their applicability to design synthesis in a real-world
architectural setting. I use this method for the analysis and synthesis of the hayat house.
(Figure 1) For my case study, I examine the specific hayat house type found in Sarajevo,
Bosnia and Herzegovina. The hayat is a large gallery open to a garden that occupies the
most important place in the house plan. Rooms are arranged around it on one, two, or
three sides. (Figure 2) It is from this key feature that the house derives its name.
Before proceeding to the shape grammar formalism, several terms need to be defined.
Beginning with the broadest category, a style is an aesthetic preference that manifests
itself in a variety of functional types. In the present context, a style possesses
characteristic features and can contain an indefinite number of types, all distinguished
and defined by their function within the style.
Type describes a group of objects characterized by the same formal structure. Types exist
Stiny, G., 1980, "Introduction to Shape and Shape Grammars," Environment and PlanningB, Vol. 7, pp.
343 -351.
2 Knight, T., 1996, Transformations in Design, Cambridge, Cambridge University Press.
physically in the material world and conceptually in the thinking and intellectual work of
the designer. They share the same characteristic features of the style and they can have
their own particular characteristics. A functional type is differentiated from similar
functional types by virtue of its style. For example, a hayat house is different from a
Victorian house or an Usonian house by virtue of its style. An extended discussion of
type can be found in Mitchell's The Logic ofArchitecture.3
A prototype describes the essential features of a type and represents generalized design
knowledge. It is an abstract form made of geometric parts, which can be described in
terms of shape grammar rules. This study illustrates a process by which the rule-based
design method of shape grammars can be used to generate prototypes of a hayat house.
An important aspect of type is that it permits modification and adaptation through
operations performed on the prototype. Changing the form of the prototype without
changing its function is called transformation. Transformation refers to changes in the
observable form of the object. It happens in three ways, by changing the configuration of
the form through Euclidean operations (scale, rotation, translation, and reflection), by
changing the values assigned to the variables that define the component objects of the
form, and by replacing the vocabulary elements of the form with new ones.
Transformation plays a dynamic role in a design language by generating instances of a
given prototype.
In an architectural context, the algorithmic (rule-based) design method is of little value
unless it can be applied to real design problems. Thus, this thesis examines the practical
viability of design by shape grammar methods. It demonstrates that the method has
potential to optimize layouts and reduce construction costs for housing projects while
constraining the design to match the existing stylistic characteristics in a given
architectural context.
3 Mitchell, W., 1996, The Logic ofArchitecture, Cambridge, The MIT Press.
2. Shape Grammars
Shape grammar is a method by which the application of principles to design can be
explored. In this context, principles correspond to rules. Rules are a way of desribing
designs, and they can be used to understand designs. A rule specifies some condition,
context, or an action that can be performed if certain prior conditions are met. Shape
grammars provide a means to formulate rules that deal with geometric objects and
properties in a design. In the context of shape grammar, design is interpreated as a set of
objects in a relation; here the objects are geometric -shapes- and the relations are spatial
compositions that are depicted by the rule, and they determine the way that shapes are
combined. The rules of a shape grammar do not have predefined structure. They can be
modified at every stage of design process.
Shape grammars provide a mechanism for form generation. The meaning associated with
these forms is not developed as part of the formalism. However, with insertion of
qualitative judgments and the integration of the other rule systems such as structural,
social, and environmental rules into the formalism, meaningful designs can be generated.
2.1 The Shape Grammar Formalism
Shape grammars allow for computation directly with shapes made up of points, lines,
planes, or solids, and symbolic items such as labels and weights.4 In computational work
in architecture and spatial design, shapes are typically comprised of labeled lines.
A shape grammar consists of rules of the form A -> B, where A and B are shapes. A rule
applies to a shape C whenever there is a transformation t such that t(A) is part of C. The
result is a new shape (C - t(A)) + t(B).
4
Stiny, G., 1980, "Introduction to Shape and Shape Grammars," Environment and PlanningB, Vol. 7, pp.
343 -351.
This computational mechanism can be generalized with rule schemas of the form x -+ y
where x and y are variables used to describe shapes.5 A schema x
-i
y applies to a shape
C whenever there is an assignment g of values to these descriptive variables such that
g(x) -> g(y) applies to C.
In this work shape rule schemas will be used throughout.
2.2 Shape Grammar Applications
Shape grammars have been used traditionally in two ways: for the analysis of historic
buildings, and for the generation of form from scratch. Both applications are constructive
in the form generation stage of the design process.
The first application has been widely used to understand and describe a diverse array of
architectural designs and to analyze different design styles. Work of this type includes:
the "Palladian Villa Grammar," 6 (Stiny and Mitchell, 1978); the "Mughul Garden
Grammar," 7 (Stiny and Mitchell, 1980); the "Japanese Tearoom Grammar"8 (Knight,
1981); the "Buffalo Bungalow Grammar," 9 (Downing and Flemming, 1981); the "Casa
Giuliani Frigerio Grammar,"' 0 (Flemming, 1987); the "Frank Lloyd Wright's Prairie
House Grammar""
(Koning and Eizenberg, 1981); and the "Queen Anne House
Grammar,"' 2 (Flemming, 1987). This work address different goals. For example, the
paper on Palladian villa designs is concerned with the definition of the Palladian style,
and applies rules in a two dimensional analysis to generate existing Palladian villas and
Ibid.
Stiny, G., Mitchell, B., 1978, "The Palladian Grammar," Environment and PlanningB, Vol. 5, pp.5-18.
G., Mitchell, B., 1980, "The Grammar of Paradise," Environment and PlanningB, Vol. 7, pp.
209-226.
8 Knight, T., 1981, "The Forty One Steps," Environment and Planning
B, Vol. 8, pp. 97-114.
9 Downing, F., Flemming. U., 1981, "The Bungalows of Buffalo," Environment and PlanningB, Vol. 8,
pp. 269-293
10Flemming, U., 1987, "The Architecture of Guiseppe Terragni," Environment and PlanningB,
Vol. 8, pp. 87-96.
" Koning, H., Eizenberg, J., 1981, "The Prairie Houses of Frank Lloyd Wright," Environment and
PlanningB, Vol. 8, pp. 295-323.
2 Flemming, U., 1987, "More than the sum of parts: Queen Anne Houses," Environment and PlanningB,
Vol. 14, pp. 295-323.
6
7Stiny,
new villas in the same style. The paper on Buffalo bungalows aims for a more general
grammar that could be expanded through additional schemata to generate a diverse
language of common houses. The paper on Queen Anne houses is concerned with
developing new design patterns compatible with historic precedents. The paper on Frank
Lloyd Wright's Prairie houses focuses on a three-dimensional analysis of Wright's
Prairie-style houses and their compositional principles, as well as the construction of new
house designs in the same style.
The second application of shape grammars is for the creation of new designs. Here twoand three-dimensional shapes are used to generate designs within the given rule set. This
13
method was first explored by Stiny (1976, 1980) and then developed and elaborated by
Knight (basic shape grammars and color grammars)
14
for use in design teaching and
practice. For example, shape gramars are used as a form generation method for the
projects: "Fallen Tower," museum in San Gimignano, Italy by Rand Brown, an Art
museum complex in Taipei, Taiwan by We Cheng Chang, and a housing complex in
Manhattan by Murat Sanyal.15 However, shape grammars have not been explored in
detail for everyday practice. It is the goal of this thesis to explore their transition into
everyday practice.
13
Stiny, G., 1976, "The Two Exercises in Formal Composition," Environment and PlanningB, Vol. 3,
pp. 187 - 210.
Stiny, G., 1980, "Kindergarten Grammars: Designing with Froebel's Building Gifts," Environment and
PlanningB, Vol. 7, pp. 409 - 462.
14
Knight, T., 1989, "Color Grammars: Designing with Lines and Colors," Environment and PlanningB,
Vol.16, 1989, pp. 41-449.
S Knight, T., 2000, "Shape Grammars in Education and Practice: History and Prospects," web paper,
3. Methodology
The goal of this study is to explore the applicability of the rule-based design method of
shape grammars in a real design setting. I use shape grammars as an exploratory design
tool for typological design analysis and synthesis. Specifically, I use a shape grammar to
generate prototypes that capture specific qualities of the hayat house type in Sarajevo. I
apply a simple parametric schema to generate three different hayat house prototypes and
select one of these (a house with a central hayat on both floors) for further elaboration by
the rule-based design method. Then I develop this prototype by applying shape rules and
by introducing different constraints. This method is also used to generate housing
patterns and row houses.
The shape rules that I use involve addition, subtraction, and union. Conceptually, shape
rule addition introduces new vocabulary elements into the design, subtraction deletes
existing vocabulary elements from the design and sum fuses shapes together in the
design. Constraints introduce relations to define the context of a specific design problem,
and limit the range of possible rule applications and design solutions.' 6 The constraints
can (1) indicate relations between variables (geometric, spatial, material, etc.) that
describe or define the object being designed and (2) express design knowledge in logical
(if-then) rules, guiding shape rule applications.
Architectural design variables are complex. Some of them are fixed and others are
dependent (values are determined by the values of other variables). Some are controlled
by the designer and some are determined by factors outside the designer's control. The
relationship between variables is subtle and highly non linear. Thus, they are complicated
to deal with in formal models. In this thesis, I apply only constraints that are within the
designer's control in order to produce architecturally acceptable forms.
1
http://www.mit.edu/tknight/IJDC/framset.html.
Gross, M., 1986, "Design as Exploring Constraints," Ph.D. Thesis, MIT, Department of Architecture.
Although I use a parametric shape grammar as a design tool, I do not elaborate its details
in full. That is, I do not define rules with assigned variables. I describe rules and
constraints with explicit drawings and give written descriptions of rules where needed.
4. Hayat Houses
The scope of the design analysis section of this study includes eight Sarajevo city houses
built between the
18 th
and
2 0
th
centuries. The traditional Bosnian house is based on the
classic Ottoman hayat house.
The hayat house is one of the four house types built in the Ottoman style in Sarajevo. It
consists of two main elements, the rooms and the hayat. The hayat is a large shaded
gallery open to the garden and it occupies the most important place in the composition of
the plan. It is the backbone of the overall spatial configuration of the house. Its shape and
size varies according to the geometries of the site and the size of the house. All variations
of the hayat house were arrived at by the displacement of axes according to the sizes of
the rooms and through rich compositions of recesses and kiosks (balconies). The house
grew around this core, rooms and a hall, and the plan of the house continuously changed.
The enlargement and development of the core pattern of the hayat house is based on the
additive principle of design.' 7 Thus, it is difficult to determine an exact style of this
domestic architecture. The simplicity of the basic schema of the hayat house allowed it to
be modified according to each plot of specific land and also gave it great flexibility for
future variations. In the
2 0 th
century the hayat was transformed into a central interior hall.
However, there are very few examples from this late period of central hall houses in
Bosnia.
The rooms generally have rectangular plans, which are divided, into two functional parts:
the entrance area and the sitting area. The size and shape of the rooms may be easily and
independently changed without altering their relationship to the other parts of the house.
The hayat space is expanded by adding kiosks at one or two ends. These areas have
slightly raised floors and sometimes are in the form of projecting bays supported by
brackets. All of these possibilities allow for a great variety of combinations, such as plans
17 Kuban,
D., 1995, The Turkish Hayat House, Istanbul, Eren Yayincilik.
17
with one or two L or U shaped wings. The hayat house is thus based on the dichotomy of
semi-open and covered spaces.
The main characteristics of the hayat house depend on its vertical and horizontal
functional divisions. The horizontal plan of the whole house is divided into public and
private spaces. The public space of the house is called the selamlik (men's quarter) and
the private space of the house is called the harem (women's quarter). The vertical plan of
the house is divided into two floors: the ground floor and the first floor. The ground floor
consists of a hayat, one or two rooms, a kitchen, and storage spaces. The geometry of the
ground floor is often modified according to the site's geometry. The first floor consists of
a hayat, kiosk, and rooms. Complete division between the men's and women's quarters
can be found only in a few large urban houses in Bosnia, particularly in Sarajevo. In these
larger buildings women's quarters and men's quarters are two separate buildings with
their own courtyard, staircase, and hayat as shown in figure 3. They are semi-detached
and united by a common roof. Although they stand as separate buildings they are
connected through a junction zone.' 8 The junction zone is a hallway or a room that has
two doors, one opening to the men's house and the other to the women's house.
There are two types of urban hayat houses, detached and semi-detached. Although both
have the same spatial configuration, the semi-detached hayat house integrates two houses
and two courtyards while the detached hayat house has only one courtyard. Figures 4, 5
and 6 illustrate the layout compositions of semi-detached hayat houses found in Sarajevo.
4.1 Configuration of the Houses
The house generally occupies the street side of the plot. The distinction of the street
facade from other facades is important in hayat houses. Ground floor walls merge with
courtyard walls to present a seamless continuum along the street. Another element of the
house that gives it a unique form is the bay. This feature is a prism with windows jutting
out from the first floor and hanging over the street. The overhanging elements are usually
rooms, and it is traditional for the largest one to occupy a corner of the house, and have
the best view of the street. The corner rooms are supported by brackets or stepped
cantilevered beams.
4.2 Housing Patterns
The house is the basic unit of the mahala (residential neighborhood) pattern.19 A mahala
consists of 40-50 houses along main and secondary roads. It is comprised of two areas;
one is private with houses, gardens, courtyards, and the other, dynamic and public, is
made up of streets and paths leading from one house to another. (Figure 7) Mahalas were
built on slopes and each has its own gently inclined main road or spine, plus three other
kinds of streets: sokaki, which are winding streets following the contour lines of the
topography; connecting sokaki; and dead-ends leading to the houses. The street pattern of
the mahala is similar to a branching tree.
" Gabrian, D., Neidhard, J., 1984, The Bosnian OrientalArchitecture in Sarajevo, Ljubljana, Univerzum
Ljubljana.
19 Hadrovic,
A., 1984, Gradska Kuca Orjentalnog Tipa u Bosni i Hercegovini, Sarajevo, Avicena.
19
5. Design by Grammar
In this thesis I use a parametric shape grammar as an analytical and conceptual tool for
typological design. Typological design studies form and spatial characteristics, and has
been developed to work in two ways, through analysis and synthesis.20 I explore the use
of the formal method of shape grammars for designing a housing project in a particular
context, by applying the method for both type analysis and synthesis.
Typological analysis provides opportunities to identify and clasify spatial and formal
characteristics, and to analyze the functional, contextual and morphological aspects
affecting these characteristics. The synthesis produces typological invention.
The typological design method has been widely used in different levels of design studios.
In some it has been used as an analytical tool and applied in order to understand context
and the formal, spatial qualities of architectural objects themselves, and in others as a
conceptual tool for design.'
Although the method investigates spatial and formal
qualities of architectural objects, it lacks any precise formal apparatus to do so. Studies in
this area often involve informal heuristics. In this study these are replaced with a formal
method of shape grammars.
In this section, I demonstrate two processes, first the generation of a hayat house
prototype (Prt) and then the generation of a new housing pattern. The first part both
generates and illustrates the development of house prototypes through the use of shape
rules and constraints. The second part consists of two steps, first generating house
patterns and then using prototype designs in a real setting.
20
Bandini, M., 1984, "Typology as a form of convention," AA Files, Vol. 6, pp.
73-82.
A., 1987, "Contextual Approaches to Typology at the Ecole des Beaux-Arts," Journalof
Architectural Education, pp. 45-48.
21 Gulgonen,
The house designs in the corpus illustrated in figure 2 show a marked sensibility for
spatial organization and formal composition. The primary qualities of the hayat house are
functionality and geometric simplicity. The aesthetic quality is expressed in the spatial
configuration of the hayat and the rooms. These features of the house are taken into
consideration in the house prototype generation.
Here, design is considered as a process that begins with prototypes and progresses to
specific design. Starting from a prototype to create the design emphasizes certain
relationships, while others become less important or are ignored as the design process
progresses. In this study, the generation, evolution, and transformation of the hayat house
prototypes are illustrated by the rule based design method of shape grammars. The
generic relationships that generate primitive prototypes are given in the prototype
formation stage. Then, the new relationships are inserted as the design progresses.
5.1 House Prototype Generation
I use five steps to generate hayat house prototypes:
5.1.1
Primitive prototypes: generates three primitive hayat house prototypes, Prt.A,
Prt.B, Prt.C.
5.1.2
Prototype instances: generates further instances of Prt.A.
5.1.3
Prototype development: articulates instances from 5.1.2.
5.1.4
Prototype transformation: illustrates two different transformations on prototypes
from 5.1.3.
5.1.5
Prototype compounds:
creates different house compounds by combining
articulated house designs from 5.1.3.
5.1.1
Primitive Prototypes
This first step illustrates the generation of hayat house prototypes. Here, I go through four
phases to define a shape grammar for primitive house prototypes:
Phase 1: definition of a vocabulary,
Phase 2: identification of the spatial relations between vocabulary elements,
Phase 3: creation of a family of spatial relations, and
Phase 4: definition of rules.
Figure 8 outlines the development of these phases.
Phase]
Phase 1 defines the vocabulary of the grammar as shown in figure 9a. The vocabulary
consists of seven elements: the overall room space, shown as a U shape and labeled RS,
can be used in both the ground and the first floor; the hayat, shown as a square and
labeled H for ground floor and FH for the first floor; the ground floor room space, shown
as a rectangle and labeled GR; the kiosk, shown as a small square and labeled K; the wall,
indicated by a line and labeled W, can be a part of a hayat or a ground floor room space;
the stairs, shown as a rectangle with a diagonal line in it and labeled S; the courtyard wall,
indicated by a line and labeled CW.
These vocabulary elements form component parts of the primitive hayat house prototype.
To actually construct prototype houses, the ways that vocabulary elements can be
combined with one another must be specified. The compositions of the vocabulary
elements are given with spatial relations in phase 2.
Phase 2
Phase 2 defines spatial relations between vocabulary elements. Spatial relations are
compositional ideas for making primitive hayat house prototypes. Six of these spatial
relations are illustrated in figure 9b. Spatial relations are defined in the following ways:
(1) Room / hayat compositions: a room (shown as a U shape) surrounds the hayat
(a square).
(2) Ground floor and stairs: defines where the stairs are situated on the ground floor. The
stairs are in relation to the wall, labeled, W that can be a part of the hayat or ground
floor room space.
(3) First floor hayat and stairs: describes the connection between the stairs and the first
floor hayat.
(4) Kiosk and first floor hayat: defines where the kiosk is attached to the first floor hayat.
(5) First floor hayats between two houses: defines the way in which houses can be
connected by their first floor hayats.
(6) Ground floor and courtyard wall: defines the way in which the ground floor of the
house is located in the courtyard, with respect to the courtyard wall.
Phase 3
Phase 3 organizes spatial relations with the same vocabulary elements but different
configurations into family groups as shown in figure 1Oa.
A spatial relation is an arrangement of vocabulary elements. The vocabulary elements can
be arranged in many different ways to form spatial relations. For example, in figure 10a in
the second family group, three spatial relations between the wall and the stairs are
illustrated. The first two spatial relations between the wall and stairs are the same.
Although the positions of the stairs in each relation are different, the relationship between
the wall and stairs in each relation is identical: the wall and stairs in both are adjacent and
the stairs are attached with one side to the wall. The third spatial relation is different.
Here the arrangement between the stairs and wall differs: the stairs are not attached to the
wall, however, they have another relation with the wall. For the sake of simplicity, spatial
relations with the same vocabulary elements, whether they are the same or different, are
categorized in groups and named as a family. These spatial relations are the basis for rules
of composition called shape rules,2 2 given in phase 4.
Phase 4
Phase 4 defines the initial shape and starting rules as shown in figure 10b, and shape rules
in terms of spatial relations as shown in figures 11 and 12. The starting rules define which
type of house is going to be generated and the shape rules specify the ways in which
vocabulary elements of each type of house are going to be put together. The shape rules
are defined in terms of a spatial relation. Each rule specifies different compositional
actions.
There are three different types of starting rules that define three different types of houses
extracted from the analysis: Prt.A (a house with a hayat at both the ground and first floor
levels), Prt.B (a house with no hayat, but only rooms, at the ground level), and Prt.C (a
house with no ground floor at all).
The shape rules used are divided into these six groups:
Group 1 rules specify the location of the overall room space around the hayat.
Group 2 rules define the location of the stairs on the ground floor. Rule 2.1 locates the
stairs at the corner of the wall, rule 2.2 at the mid-point of the wall, and rule 2.3 off the
wall. Different rules specify different compositional actions.
Group 3 rules define the compositions possible between the stairs and the first floor
hayat. Technically, group 3 rules operate on two different levels, the ground floor and the
first floor. The left side of the rule determines the location of the stairs on the ground
22
Knight, T., 1996, Transformation in Design, Cambridge.
floor and the right side of the rule shows the location of the first floor hayat in relation to
the stairs. The stairs belong to both levels and serve as a connecting element between the
two. Rule 3.1 locates the first floor hayat corner at the corner of the stairs, 3.2 off the
stairs, 3.3 on a diagonal from the corner of the stairs, 3.4 at the mid-point along the stairs
length, leaving part of the stairs out of the hayat, 3.5 off the stairs, leaving part of the
stairs out of the hayat. These rules determine the configuration of the first floor with
respect to the ground floor.
Group 4 rules define compositions between the first floor hayat and the kiosk. Rule 4.1
adds a kiosk to the mid-point of the hayat, 4.2 to the corner of the hayat, and 4.3 to the
inner side of the hayat.
The rules in groups 1, 2, 3 and 4 are derived from the analysis of hayat houses, and are
used to generate primitive hayat house forms.
Group 5 rules define connections between two first floor hayats. Rule 5.1 locates two first
floor hayats next to each other. Rules 5.2, 5.3, and 5.4 locate hayats in certain
configurations at a distance from one another. These rules are derived from the analysis
of semi-detached hayat houses. They are used to generate different house compounds.
Group 6 rules define the location of the ground floor with respect to the courtyard wall.
Rule 6.1 locates the ground floor of the house at the corner of the courtyard wall, and 6.2
at the middle of the courtyard wall. These rules are derived from the analysis of hayat
house and courtyard relations. They are used as the basis for housing pattern rule
generation.
5.1.1.1 The Application of the Rules to Designs
In each stage of the creation of the prototype houses, the sequence of rules and similarity
transformations through which rules are applied are defined according to the prototype
that is being introduced. The rules can be applied via different transformations to generate
different designs. Figures 13, 14, and 15 illustrate the derivation of the ground floor and
first floor plans of Prt.A, Prt.B, and Prt.C house designs. In each stage of the derivation,
the rule number indicates which group of rules is applied. The derivation begins with a
starting rule, which determines the type of house that is going to be generated. In the
process of derivation, for Prt.A and Prt.B in the second stage and for Prt.C in the first
stage, the derivation is divided into two levels allowing the ground floor and first floor
plans to be generated separately. The ground floor and first floor plans are distinguished
with different line thicknesses in the graphic representation of the designs. Once the
ground floor and the first floor plans of the same house are generated, then group 3 rules
are used to connect the two floors with the location of stairs. In order to articulate the
space, 3D representations of prototypes are shown as extruded plans.
The grammar rules are ordered so that each design generated in one stage is a part of the
design generated in the next. The grammar allows us to choose in each stage only one
rule from the group of rules defined in that stage.
Thus, a large number of design
prototypes can be generated by permutation of the rules.
Figure 16 shows different derivations using group 3 rules. Group 3 has five rules that
define the location of the first floor hayat with respect to the stairs. The application of
group 3 rules generates five different compositions between the ground floor and the first
floor hayats, which ultimately lead to five different house prototypes. This procedure is
illustrated for one prototype (Prt.A) in the following section.
5.1.2 Prototype Instances
The second step for generating hayat house prototypes consists of seven stages. First I use
group 3 rules from 5.1.1 to generate instances of Prt. A, then I introduce a group of new
shape rules to transform hayat houses for contemporary use. I use five groups of new
shape rules to generate elaborated instances of Prt. A. Some groups have multiple rules
while some have only one. The new shape rules are illustrated in figures 17 and 18.
The specifications for these new rules are as follows:
Group 7 rules are new rules, which I use instead of the kiosk rules. They modify the
house prototypes for contemporary use. By applying these new rules of addition, the
hayats on the first level are expanded. This is illustrated on the right side of the rule.
These new rules operate on multiple levels. The left sides of the rules illustrate the
composition of the hayats located on both the ground floor and the first floor. The
elements of the different levels are distinguished by different line thicknesses, so that the
square drawn with bold lines represents the first floor hayat and the square drawn with
thin lines represents the ground floor hayat. On the right side of the rules the new
extension (Ai) is added to the front of the first floor hayat, so that it covers the ground
floor hayat, and also extends beyond it a certain distance, creating an overhang. Here I am
concerned with transforming the first floor hayat for contemporary use. Therefore I create
a new group of shape rules which add an extended hayat to the first floor hayat,
transforming it into a central circulation hall. However the concept of the hayat continues
in the extended hayat which overlooks the garden and overhangs the entrance of the
house, creating a shaded protected area in front of the entrance.
The extended hayat is a new design element. By adding the extended hayat to the first
floor, I transform the hayat house for contemporary use, while maintanings its stylistic
characteristics.
Group 8 rules mark emergent shapes for further articulation of the houses. The left sides
of the rules show the first floor as well as parts of the ground floor that are not covered by
the first floor. The elements of the different levels are distinguished as above by different
line thicknesses. These ground floor parts are new emergent shapes derived from the
composition of the vocabulary elements in two layers. They are shown in the right side of
the rule by label Xi. These emergent shapes are used to expand the first floor layouts in
further stages of the design.
Group 9 has only one rule. This rule partitions the U shaped room space at the first floor
level into five sections, al, a2, bl, b2, and c. The reason for this rule comes from my
desire to generate different first floor layouts. By dividing the first floor room space into
five sections, I create a condition for modification of the first floor, so that each section
can be subtracted from the first floor to create different layouts.
Group 10 rules add emergent shapes, labeled Xi, to the first floor layouts, thus expanding
the total floor area. In order to apply these rules of addition, the emergent shapes have to
be defined first. Depending on the designer's conception of the form, a variety of addition
rules can be extracted. In these rules, although the emergent shapes are elements of the
ground floor layer, they are used as reference to expand the floor area of the first floor.
The left sides of the rules illustrate the first floor and emergent shapes labeled Xi. On the
right sides of rules the emergent shapes are added to the first floor, expanding the total
area of the first floor.
Groups 11 and 12 each have only one rule.
The group 11 rule, depending on the design intention, subtracts the section a1, a2, b 1, b2
or c, from the first floor plan, thereby generating different first floor layouts.
The group 12 rule sums the parts of the first floor plan. It is generalized to apply to all
first floor plans defined as: S + FH + RS + n (Xi), where S stands for stairs, FH for first
floor hayat, RS for room space, and n (Xi) for emergent shapes.
5.1.2.1 The Application of the Rules to Designs
In each stage of generating hayat house prototypes, a specified group of rules applies.
Stage ]
Stage 1 generates five instances of Prt. A through the application of group 3 rules as
shown in figure 19. Group 3 rules generate different configurations between the ground
floor and the first floor.
Stage 2
Stage 2 applies group 7 rules to five instances of Prt.A as shown in figure 20. Group 7
rules introduce a new concept of the hayat house by adding an extended hayat to the first
floor hayat. These rules transform the first floor hayat into a central hall, reassigning its
function to the extended hayat. In other words, the extended hayat takes over the function
of the hayat.
Stage 3
Stage 3 applies group 8 rules to five instances of Prt. A as illustrated in figure 20. In this
stage emergent shapes are defined for further elaboration of the first floor plans.
Stage 4
Stage 4 applies the group 9 rule to five instances of Prt. A. The rule partitions room
spaces into five sections as shown in figure 20. These partitions are used for modification
of the first floor layouts in further stages of the design.
Stage 5
Stage 5 applies group 10 rules to instances of Prt. A. These rules generate elaborated
instances of Prt. A, expanding the floor area of the first floors as shown in figures 21
through 24.
Stage 6
Stage 6 illustrates the further evolution of the first floor plans through the group 11
(subtraction) rule. This rule applies to parts al, a2, bI, b2, and c as shown in figures 21
through 24.
Stage 7
Stage 7 applies the group 12 (sum) rule. This rule generates footprints of the first floor
plans as shown in figures 21 through 24.
Figure 25 illustrates fourteen elaborated instances of Prt. A. These prototypes are
articulated by introducing new relationships and modifying existing ones in the following
section.
5.1.3 Prototype Development
The third step in the generation of hayat house prototypes illustrates the development of
Prt.A instances in four stages. I introduce three new groups of shape rules for prototype
development. The new shape rules are illustrated in figure 26.
The specifications of these rules are as follows:
Group 13 rules partition the U shaped room space in two steps. In the first step, rule 13.1
adds a wall to the corner of the hayat in eight different possible positions, and rule 13.2
adds a wall to the mid-point of one side of the hayat in four different possible positions as
shown in figure 27. Only a partial set of partitions is illustrated in figure 27.
In the second step, rule 13.3 replaces the hayat with a new hayat from the set. The type of
chosen partition is identified by a number (tpi) in the set. Rule 13.3 applies to both
ground and first floor hayats, partitioning the room space on both floors. Group 13 rules
generate rough room layouts. These layouts are used as templates for the further
articulation of inner spaces.
Group 14 rules modify the first floor hayat in accordance with a given condition 11 = /2
as shown in figure 26. The / indicates the width of the spaces (circulation areas) around
the stairs. The constraint, which requires all widths to be equal, derives from functional
concerns. Here, I am concerned with two things: creating functional circulation areas
around the first floor stairs, and providing an access to the extended hayat from the first
floor hayat. Therefore I create a rule which replaces the existing square shaped first floor
hayat with a rectangular shaped one that satisfies my concerns. The default square shaped
hayats are modified, depending on the location of stairs, and in accordance with the given
constraint.
Group 15 rules modify the form of the house through a set of constraints. Here I am
concerned with the configuration of the form and layout of the houses. Therefore, I
analyze the designs and make some qualitative judgments. Then, on the basis of these
judgments, I create rules that change specified parts of the designs, as explained below.
Rule 15.1 adjusts the uneven cantilevering portions of the first floor in relation to the
ground floor and is illustrated on the left side of the rule. The right side of the rule
extends the ground floor with respect to the first floor under the given constraint /I = 12,
as shown in figure 26. Here, the variable / indicates the size of the cantilevering portion
with respect to the ground floor. The rule generates even cantilevering portions on the
first floor creating a visually balanced house form.
Rules 15.2 and 15.3 modify the corner of the room into an architecturally acceptable form
as specified in figure 26. The left sides of the rules illustrate the adjacency relations
between any two rooms on the first floor. On the right sides of the rules, the adjacency
relations between the rooms are modified, creating clear-cut corners for each room.
Rule 15.4 adds the remaining part of the hayat that has been modified to the extended
hayat. In this rule, I am concerned with the use of the new emergent rectangular space
between the extended hayat and the original hayat. Thus, I add this space to the extended
hayat (Ai), expanding it.
Rule 15.5 elevates the extended hayat (Al) from the first floor level in accordance with
the rule illustrated in figure 26. In order to explain explicitly how this rule works, it is
generalized into a rule schema. Only one vertex of the extended hayat (Ai) and the first
floor hayat (FH) have assigned values (xi, yi, zi) to illustrate that the extended hayat is
elevated from the first floor hayat under a given condition z2>zI. This rule is derived
from the original hayat house designs in which the kiosks have elevated floors above the
hayats. By applying this rule, the extended hayat is separated from the first floor level,
creating a special space for family gathering. In other words, the concept of the original
hayat is transformed for contemporary use, while maintaning its stylistic characteristics.
Group 16 rules transform the schematic house designs into architectural representations.
Rule 16.1 splits the compact house designs into a ground floor and a first floor as shown
in figure 26. Rule 16.2 replaces a line with a wall in which the existing line is kept as the
axis of the wall, 16.3 erases the axis of the wall, 16.4 and 16.5 create clear vertical and
horizontal wall intersections by trimming the intersecting parts. Rules 16.7 and 16.8
move the stairs in relation to the generated wall. In both rules, the left side of the rule
shows the location of the stairs after the wall has been generated, while the right side of
the rule shows the new location of the stairs in relation to the wall, as illustrated in figure
26.
5.1.3.1 The Application of the Rules to Designs
In each stage of the development of the prototypes, a specified group of rules applies. In
figures 28 through 31, Prt. Al instances are articulated in four stages:
Stage ]
In stage 1, rule 13.3 applies to both the ground and first floor hayats and generates rough
room layouts. The number tpi shows the particular type of partitioning of each house.
The same type of partitioning is applied to both floors of a house.
Stage 2
In stage 2, rule 14.1 modifies the hayat, replacing the existing square hayat with a
rectangular one, to create functional circulation areas around the first floor stairs and
provide access to the extended hayat.
Stage 3
In stage 3, first rule 15.1 modifies the cantilevering parts of a house, to create a balanced
form, and then rule 15.2 modifies the corner of the room, to create a clear room finish.
Rule 15.5 elevates the extended hayat, differentiating it from the first floor hayat.
Stage 4
In stage 4, first rule 16.1 splits the prototype house into two floors, and then the remaning
rules are applied to both floors, transforming the simple schematic house design into a
more detailed architectural presentation. In order to illustrate room configurations in 3D,
the layouts of the floors are shown as extruded plans.
In figures 31 through 34, Prt. A2 instances are articulated in four stages:
Stage ]
In stage 1, rule 13.3 applies to both the ground and first floor hayats and generates rough
room layouts for both floors.
Stage 2
In stage 2, rule 14.1 modifies the hayat, satisfying functional constraints.
Stage 3
In stage 3, rule 15.1 modifies the cantilevered parts of the house, and then rule 15.5
elevates the extended hayat.
Stage 4
In stage 4, group 16 rules transform a simple schematic house design into a detailed
architectural presentation.
In figures 34 through 39, Prt. A3, Prt. A4, and Prt A5 are developed in four stages. Figure
39 illustrates a portfolio of fourteen typologically related two-story Prt.A houses. Once
the portfolio of house prototypes is generated, then each prototype can be further
elaborated depending on the context, site conditions, program, and user requirements.
The individuality of each prototype can be achieved through different layout
configurations and external details.
In this study, the house prototypes are described in terms of relations between the parts
rather than actual dimensions. However, the prototypes are parametric, which means that
the relations between the variables of the form can be mathematically defined. Thus, by
giving values to the variables, following the proportional rules, accurate designs can be
generated.
5.1.4 Prototype Transformations
The fourth step in the generation of hayat house prototypes illustrates two different
transformations on prototypes from 5.1.3. Transformation 1 occurs when the existing
vocabulary elements are replaced with the new ones. Transformation 2 occurs when the
values of the variables that define the component objects of the form are changed.
We describe or generate forms from other forms. In other words, we generate a new form
by transforming an existing one at hand. Therefore, the method that we use to generate a
form must be able to describe the transformation of the original form. The shape grammar
method provides the technical apparatus for the systematic description of this
transformation. In this fourth step of the generation of hayat house prototypes, I illustrate
the generation of new hayat house forms through the transformation of existing ones.
5.1.4.1 Transformation 1
Two-story house prototypes are transformed into split-level house prototypes by replacing
an existing vocabulary element (one flight of stairs, labeled Si) with new vocabulary
elements: three flights of stairs labeled Si, S2, S3 or two flights of stairs, labeled Si,
S2.
I
introduce three groups of new shape rules for prototype transformation. The first group of
rules replaces existing stairs with the new ones. The second group of rules splits the
floors into different levels. The third group of rules combines two floors into one, to form
a house. The shape rules are described with shape schemas in order to explain how they
work.
The specifications of the rules are as follows:
Group 18 rules replace the existing stairs with new stairs as shown in figure 40. Rule 18.1
replaces existing stairs (S) with new stairs Si, S2, S3, and rule 18.2 with stairs Si, S2. Here,
the new stairs are defined by spatial label schemas: for Si, I use A, B, C, D; for S2, I use C,
D, E, F; and for S3, I use A', B', C', D'. These labels have assigned variables (xi, yi, zi).
The house prototypes are modified with respect to this new vocabulary. Both rules define
the floor division in relation to the new stairs. The division line is a reference mark used
for splitting the ground floor and first floor into different levels, as shown in figure 40.
The stairs Si and S3 overlap in rule 18.1. However, the given condition Z3 > Z2> z > zI
indicates that the stairs are located at different elevations in the space. The variables of
the stairs (xi, yi, zi) differ depending on the slope of the site and the configuration of the
stairs.
Group 19 rules split the prototype house into different levels as shown in figure 40. Rules
19.1 and 19.2 split the house into four levels, joined by three flights of stairs. First, rule
19.1 splits the ground floor into two levels, labeled A and B, in relation to reference
points F and B. Reference points indicate the location of the floors in the space. Floor A
is located at elevation z and floor B is located at elevation zi. Then rule 19.2 splits the
first floor in two floor levels, labeled C and D, in relation to reference points D' and B'.
Floor C is located at elevation Z2 and floor D is located at elevation z3. Rules 19.3 and
19.4 split the house into three levels, joined by two flights of stairs. First, rule 19.3 splits
the ground floor into two floors, labeled A and B, in relation to reference points D and B.
Rule 19.4 leaves the first floor as it is.
In order to split a two-story house prototype into different levels, the shape rules have to
follow a given logical (if-then) rule ordering. For example, for splitting a two-story house
prototype into a four level prototype, the rule ordering is: "if 18.1 has been applied, then
apply first 19.1 and then 19.2." For splitting a two-story house prototype into a threelevel prototype the rule ordering is: "If 18.2 has been applied, then apply first 19.3 and
then 19.4."
Rule 19.5 modifies the ground floor and 19.6 modifies the first floor hayat - stairs spatial
relation as shown in figure 40. Rule 19.5 extends the ground floor hayat such that both
flights of stairs, one going up and the other down, are accessed from the ground floor
hayat. Rule 19.6 is described with shape schema in order to explain how it works. Here,
the spatial relation between the first floor hayat and stairs is defined by spatial label
schema: A, B, C, D, E, F, G, H, K, and L. These labels have assigned variables (xi, yi, zi).
The interpretation of this rule depends on the introduced prototype, and the designer's
intentions. Some possible interpretations are illustrated in figure 40.
Group 20 has only one rule. It combines the ground and the first floor into one to form a
house with respect to the location of the stairs as shown in figure 40.
5.1.4.2 The Application of the Rules to Designs
Figures 41 and 42 illustrate the transformation of two-story house Prt. Al .1 and Prt. A2.2
into four-level house prototypes in five stages.
Stage ]
In stage 1, rule 16.1 from 5.1.3 deconstructs the house into two floors in order to illustrate
transformations on both floors.
Stage 2
In stage 2, rule 18.1 replaces existing stairs with the new vocabulary elements (three
flights of stairs).
Stage 3
In stage 3, several rules are applied at the same time. First rules 19.1 and 19.2 split the
prototype house into four levels, labeled A, B, C and D. Then rules 19.5 and 19.6 replace
the hayat-stairs compositions with the new ones on both floors.
Stage 4,
Stage 4 applies a set of wall generation rules, transforming the schematic prototype
designs into architectural representations.
Stage 5
Stage 5 combines the ground and first floors to form a house, using rule 20.
In figure 43, Prt. A4.2 is transformed into a three-level house in five stages.
Stage ]
In stage 1, rule 16.1 deconstructs the original house into two floors.
Stage 2
In stage 2, rule 18.2 replaces an existing vocabulary element (stairs) with two flights of
stairs.
Stage 3
In stage 3, rule 19.5 replaces the hayat on the ground floor with the new one, expanding
its floor area.
Stage 4
In stage 4, rule 19.3 splits the ground floor into two levels, labeled A and B. Rule 19.4
keeps the first floor as it is, labeled C. Then a set of wall generation rules from 5.1.3 is
applied.
Stage 5
In stage 5, rule 20 composes the separate floors of the prototypes into one house.
Figure 44 illustrates a portfolio of fourteen split-level house prototypes. The prototypes in
the portfolio have similar layouts. However, the individuality of prototypes can be
achieved by modifying layouts and external details. Figure 45 illustrates an interpretation
of these house prototypes with possible roof structures.
5.1.4.3 Transformation 2
The form of the prototype is transformed in two steps by first modifying the relations
between vocabulary elements of the first floor in relation to the ground floor, and then
modifying the ground floor in relation to the first floor. The transformation rules derive
from the prototype itself and can be applied only to that particular prototype. This type of
transformation is illustrated for a specific prototype (Prt. A1.3) in figure 46.
Step ]
Step 1 modifies the relations between vocabulary elements of the first floor using group 1
rules with given constraints k = k2 and 11 = /2 = /3 as shown in figure 47. Here, k
represents the length and / the width of the cantilevered portion of the room. The
constraint k1 = k2 requires the lengths and li = /2 = /3 the widths of the cantilevered
portions of the first floor plan to be equal. Rule 1.1 shortens a cantilevered rectangular
room on the right side of the first floor plan such that the length of the room does not
exceed the length of the ground floor. Rule 1.2 modifies a rectangular room on the left
side of the first floor plan into the L shaped cantilevered room. The rules operate on two
layers, which are distinguished with different line thicknesses. The first floor is the active
layer, where changes are made. The ground floor serves as a reference for these changes.
The reason for the first floor transformation comes from my analysis of the hayat house
form. Most of the hayat houses have cantilevered bays on their front fagades, which
overlook the street. With this in mind, I decided to change the first floor into a crossshaped form with equal sized cantilevered portions on three sides as shown in figure 48.
Therefore, I created a set of rules to realize my intentions.
Step 2
Step 2 modifies the ground floor according to the first floor using group 2 rules as shown
in figure 47. Here, the active layer is the ground floor, and the reference layer is the first
floor. Rule 2.1 refines the relation between the two floors, erasing the room partition lines
from the first floor. It is generalized to apply to all first floor plans defined as: S + FH +
Ai + (RS + tpi), where S stands for stairs, FH for the first floor hayat, Al for an extended
hayat, and (RS + tpi) for a partitioned room space. Rule 2.2 expands the ground floor,
stretching it from its four corners in accordance with the first floor. In this rule, my
intention is to change the form of the ground floor, keeping it visually balanced with the
first floor. Rule 2.3 modifies the front side of the ground floor by adding a small rectangle
to its center. In this rule my intention is to create an entrance niche. Therefore, I add a
rectangle to indicate the niche location at the ground floor. The size of this rectangle is
the same as the cantilevered portion of the extended hayat. Rule 2.4 illustrates the
transformed form of the ground floor by erasing the reference layer (first floor) from the
design. The new ground floor has three niches on three sides of the house. Rule 2.5
subtracts the small rectangle that has been added in rule 2.3 from the ground floor,
creating an entrance niche under the extended hayat.
The reason for the ground floor transformation comes from my continuous search for a
new hayat house form. Here, my intention is to generate a new hayat house form out of
an existing one.
1.5.4.4 The Application of Rules to Designs
Figure 48 illustrates the transformation of Prt. Al.3 in two steps. The first step generates
Prt. TI, and the second Prt T2. In the first step, Prt. A1.3 is transformed into Prt. TI in
two stages modifying the first floor. In the second step, Prt. TI is transformed into Prt. T2
in four stages, modifying the ground floor. The transformation of Prt. Al.3 into Prt. T2
happens in six stages as illustrated in figure 48.
In the first step of the transformation, I modify the first floor of Prt. A1.3 in two stages as
shown in figure 48.
Stage ]
In stage 1, rule 1.1 modifies the room on the right hand side, shortening its length with
respect to the ground floor.
Stage 2
In stage 2, rule 1.2 modifies the room on the left-hand side, transforming it into a
cantilevered L shaped room. By applying these two transformation rules, the form of the
first floor is transformed into a cross-shaped form that has equal size cantilevered
portions on three sides. The sequential transformation of the first floor of Prt. Al.3 is
illustrated in figure 48. The new prototype, labeled TI, has a different first floor but the
same ground floor as Prt. Al.3.
In the second step of the transformation, I modify the ground floor of Prt. TI in four
stages as shown in figure 48.
Stage 3
In stage 3, rule 2 refines the relation between the ground and the first floors, erasing the
room partition lines from the first floor. The point of this rule is to illustrate clearly the
relationship between the two floors.
Stage 4
In stage 4, first rule 2.2 expands the corners of the ground floor with respect to the first
floor, enlarging its floor area. Then rule 2.3 marks the location for the entrance niche at
the ground floor.
Stage 5
In stage 5, rule 2.4 erases the first floor from the design, illustrating the re-modified
ground floor.
Stage 6
In stage 6, rule 2.5 subtracts the small rectangle from the fagade of the ground floor,
creating an entrance niche at the ground floor.
Further transformation of Prt. T2 continues by repeating the two steps of the
transformation. The first step modifies the relations between vocabulary elements of the
first floor. The second step modifies the ground floor in relation to the first floor. Group 3
and group 4 shape rules which transform Prt. T2 into Prt. T3 are derived from the analysis
of Prt. T2 and can be applied only to Prt. T2.
Step 1
Step 1, modifies the first floor of Prt. T2 through group 3 rules illustrated in figure 49.
Here I am concerned with generating a visually balanced form: a form that has certain
proportional rules, coherent with the original hayat form. Therefore, I introduce
conditions that satisfy my concerns. Rule 3.1 enlarges the L shaped cantilevered room on
the left side of the first floor plan by extending its length. Rule 3.2 enlarges the
rectangular shaped cantilevered room on the right side of the first floor plan according to
the given conditions ki = k2,
1=
/4, and /2=
/3.The
first condition requires the lengths of
the cantilevered portions of the rooms to be equal, the second requires the cantilevered
portions of the rooms on two sides to have equal width, and the third requires the
cantilevered portions of the back sides of the rooms to have equal width. Rule 3.3
modifies the adjacency relation between the two rooms.
Step 2
In step 2, group 4 rules modify the ground floor with respect to the first floor as shown in
figure 49. Rule 4.1 enlarges back corners and 4.2 front corners, expanding the floor area
of the ground floor. Figure 50 illustrates the step-by-step transformation of the Prt. T2
form into a new Prt. T3 in five stages.
Stage 1
In stage 1, rule 3.1 enlarges the room on the right side.
Stage 2
In stage 2, rule 3.2 enlarges the room on the left side.
Stage 3
In stage 3, rule 2.1 refines the relation between the ground floor and the first floor.
Stage 4
In stage 4, rules 4.1 and 4.2 expand the corners of the ground floor, enlarging the floor
area.
Stage 5
In stage 5, rule 2.6 erases the reference layer of the first floor from the design, showing
the modified ground floor.
Figure 51 illustrates the step by step transformation of Prt. T3 into the split-level Prt. T4
in five stages.
Stage 1
In stage 1, rule 16.1 separates a compact house into two floors, the ground floor and the
first floor, to illustrate a transformation on both floors.
Stage 2
In stage 2, rule 18.1 replaces one flight of stairs with three flights of stairs.
Stage 3
In stage 3, group 19 rules split the ground floor and first floor into different levels and
modify the hayats on both floors.
Stage 4
In stage 4, group 16 rules transform schematic designs into more elaborate architectural
presentations.
Stage 5
In stage 5, the group 20 rule composes different levels of the house prototype into one
house.
Figures 52, 53, and 54 illustrate new prototypes Prt. TI, Prt T2, Prt. T3, and Prt. T4
generated through the sequential transformation of Prt. A1.3. Figures 55 and 56 illustrate
the development of Prt. A1.1 from a primitive prototype into a more elaborate house.
The grammar rules generate rough layouts of the houses. These layouts serve as
references for the actual configurations of the houses. Figure 57 illustrates the implicit
reconfiguration of the Prt. Al .1 layout into an architecturally acceptable configuration.
The prototype houses can be further elaborated in many different ways, as illustrated in
figure 58. Here, Prt. T2 is transformed into a larger building to accommodate new
requirements by adding new spaces to the ground and first floors. By enclosing the
courtyard with walls the house is transformed into the smallest urban unit. Figure 59
illustrates a block design generated by combining these units.
By applying the same transformation method to each prototype in the same portfolio a
large number of new hayat house prototypes can be generated. Once the prototype is
generated, the next step is to select specific values for the variables and generate accurate
designs, according to program and user requirements.
In this fourth step of the generation of hayat house prototypes, I illustrate the evolving
intentions of my designs. My intentions were not fully established at the beginning of the
design process, but evolved through my appreciation and qualitative judgments of
designs. In each stage of the design, I analyze what the rule has produced and apply a new
rule in relation to it, transforming the design. This sequential process of analysis, rule
application, and further analysis enabled me to both transform the design algorithmically
and manage the complexity of it.
5.1.5 Prototype Compounds
The fifth step illustrates the generation of house compounds. Figure 60 illustrates the
composition rules from step 5.1.1.
These rules define the compositional principles
between two houses with respect to their first floor hayat locations. The distance ()
determines the relation between the two hayats, and whether the houses can be adjacent
or intersect. For example, in figure 61, example 1, Prt. A3.3 and Prt. A4.1 are combined
according to rule 5.3, which creates adjacent semi-detached houses. The houses are
adjacent on their first floors but detached on the ground floor, the passageway as shown
in figure 62. Since the houses are topologically related, their compositions create visually
coherent forms. The passageway between the houses is an emergent space whose creation
was not specifically intended when these two houses were put together. Emergent spaces
provide new opportunities for the designer to enrich the spatial quality of the designs.
One of the most striking features of shape grammars is that they generate unintended
spaces. These discovered spaces are not part of the original design intention, nevertheless
the designer can find desirable qualities in them that provide material for subsequent
elaborations.
In example 2, Prt. A3.3 and Prt. A4.1 are combined according to rule 5.3, creating
overlapping semi-detached houses. The overlapping occurs on the first floors of the
houses as shown in figure 62. This creates a new design condition that has to be solved
depending on the programs of the houses. For example, if Prt. A3.3 is a house for a
couple and Prt. A4.1 is a four member family house, then the overlapping part will belong
to Prt. A4.1 and will be subtracted from Prt. A3.3. Once the decision about the
overlapping part is made then the next step is to modify the layouts of the houses
according to the new constraints.
In example 3, the same houses as above are combined under different transformation
conditions using rule 5.2. Here, the overlap occurs on the ground floors of the houses, as
shown in figure 62. Depending on the programs of the houses the overlapping part will be
added to one prototype and subtracted from the other as above, creating new design
conditions.
In example 4, Prt. A4.1 and Prt. A4.2 are combined according to rule 5.3, creating
overlapping semi-detached houses with balconies. The overlap occurs on the ground
floors of the houses as shown in figure 62 and 63.
In example 5, the same houses are combined according to rule 5.5. The composition rules
can be applied under different transformation conditions to generate different compound
house designs. These houses are contemporary interpretation of semi-detached hayat
houses. However, they are not internally connected. They are separate units, each serving
one family.
A set of fourteen houses can be combined in accordance with a set of six composition
rules to generate eighty-four different combined house prototypes. Recursive application
of the rules under different transformation conditions generates linear designs, which in
our example correspond to row houses.
Figure 64 and 65 illustrates two different row house compositions: the first is generated
through two connection rules and the second through a series of connection rules both
creating crossings underneath the houses.
Once the prototype houses are combined, the next step is to specify the values of the
variables and generate accurate layouts according to the new constraints, which have
emerged. The prototypes used to generate block designs are instances of Prt. A. They
have similar forms. Therefore, when they are put together they create repetitive fagade.
The repetitiveness of this linear fagade can be broken by creating different external
details, and roof configurations.
5.2 Housing Pattern Generation
In the first section of this chapter, I illustrate the generation of two hypothetical housing
patterns. In the second section, I illustrate the implicit generation of housing complexes
composed of detached, semi-detached, and terrace houses of the same style.
5.2.1. Housing Patterns
In this section, I illustrate the generation of two hypothetical housing patterns, one for
flat, and the other for an inclined topography.
Housingpatternfor aflat topography
I generate the housing pattern for a flat topography in four stages as shown in figure 66.
Stage 1
In stage 1, I illustrate courtyard rules extracted from the analysis. The shaded rectangle
indicates the location of the house in the courtyard. Rule 1 locates the house at the corner
of the courtyard, rule 2 at the mid point of the courtyard wall. I use these rules as a
reference for generating new housing site configurations.
Stage 2
In stage 2, I generate three new house sites with three rules. Rule 1 locates a house at the
corner of a rectangular site labeled A, creating an L shaped courtyard. Rule 2 locates a
house at the comer of an L shaped site labeled B, creating two separate courtyards; one
attached to the front and the other to the side of the house. Rule 3 locates a house at the
mid-point of an I shaped site labeled C, creating two separate courtyards, one attached to
the front and the other to the rear of the house.
Stage 3
In stage 3, I illustrate six spatial relations between house sites A, B and C as shown in
figure 66.
Step 4
In stage 4, I illustrate housing pattern rules. The rules specify the way in which house
sites can be put together.
Figure 67 illustrates the derivation of a housing pattern and its interpretation. Different
interpretations will lead to different avenues of exploration. Figure 68 illustrates
substitution rules. These rules insert two-story prototype hayat houses from a portfolio
into the pattern. The portfolio of two-story hayat houses is shown in figure 39. The label
Prt. Ai indicates the inserted house. Figure 69 illustrates the neighborhood design
generated by the rule-based design method. The design looks very rigid, however its hard
line geometry and repetitiveness can be easily broken by introducing different design
constraints and parameterizing the individual designs in different ways.
Housingpatternsfor an inclined topography
I generate a housing pattern for an inclined topography in three stages by modifying the
courtyard vocabulary A, B, and C, from the previous section.
Stage ]
In stage 1, 1transform the house sites A, B, and C into split-level house sites with respect
to the split-level houses, as shown in figure 70. The left sides of the rules illustrate flat
house sites with two-story houses. The right sides of the rules replace the two-story
houses with split-level houses and the flat courtyard with one that is split into two
different levels according to the split ground floor. In this way courtyard B is accessible
from the B level of the house and courtyard A is accessible from the A level of the house.
Stage 2
In stage 2, I define spatial relations between courtyards as shown in figure 68.
Stage 3
In stage 3, I define pattern generation rules. The rules can be applied to different house
sites. For example CA can be in relation with CB, which belongs to the Al or BI or Cl
house sites as shown in figure 71. The parametric relations between two courtyards vary
depending on the topography of the site. Thus, each inclined site is a new design
challenge constrained by topographic characteristics. The site-specific topographic
constraints guide the selection and application of the rules for generating housing patterns
that are feasible for that particular site.
In a real design setting the number of constraints for generating housing patterns will
increase depending on the site's topography, external forces, program requirements, and
the designer's intentions. Figure 72 illustrates two hypothetical housing patterns generated
through constrained pattern rules.
The pattern rules are constrained by the given
statement: the houses cannot be adjacent and the distance between two houses must be at
least one courtyard.
In these two examples, I illustrate the rule based design method for housing pattern
generation. I do not make any qualitative judgments either for the rules or the final
designs. Because of the absence of qualitative judgments, the designs are mechanical and
repetitive. In order to create meaningful designs, the qualitative judgments about the rules
and final designs such as the quality of the outdoor spaces, the light that the house
receives, and adjacency relation between the houses should be integrated into the design
process.
Therefore, design by rules requires many cycles through which qualitative judgments that
inform further rule applications can be inserted.
5.2.2 The Application of the Prototypes
This section illustrates the design of a single-family housing project on a hypothetical
site, using the two Prt. A house portfolios, shown in figure 39 and 44.
The view that designing can be understood as a dialogue of prototype and site was
expressed by Donald Schon. "According to this view, designers have access to a
repertoire of prototypes, derived from their earlier experiences. Faced with a particular
site and design task, the designer selects one or more prototypes from his repertoire,
seeing the site in terms of the prototype carried over to it, seeing the prototype in the light
of the constraints and possibilities discovered in the site. This reciprocal transformation
of prototype and site suggests a further sense of what it means to say that designing is
reflective conversation with a design situation."23
In the design of a housing complex, I illustrate the reciprocal transformation between
prototype and site. In order to illustrate possible site constraints on a hypothetical site, I
transform the steep sloping site and create three different sites with flat, inclined and
cascaded terrain as shown in figure 73. Then I select one or more prototypes from the
portfolios and according to the constraints and possibilities of the sites, I combine them to
generate housing blocks appropriate to site conditions.
For example, I situate on the
cascaded terrain the split-level house prototypes (A1.1, A1.3, A2.2, A2.4, A3.1, A2.3,
A5.2, A4.1, A4.2, and T3), as shown in figures 74, 75 and 77. Then for the flat terrain, I
combine two story house prototypes A3.1, A1.1, and A1.3 according to the connection
rules from 5.1.5 and create semi-detached and row houses with crossings underneath as
shown in figures 75 and 77. On the sloping terrain I locate the terrace houses made up of
split-level prototypes of Al.2, A1.1, and Al.3 as shown in figure 76 and 77. The attached
and terraced houses are special cases because of their overlapping parts. Thus, the layouts
Schon. D., 1992, " Designing as Reflective Conversation with the Materials of a Design Situation,"
Research in EngineeringDesign, Vol: 3, pp. 131-147.
23
of these houses have to be modified depending on the constraints derived from their
specific configurations.
All prototype houses in the complex have similar outlines (a central hall surrounded by
rooms). However, the layouts of the houses can vary depending on their location on the
site, scale, user profile, and designer decisions.
The house forms are parametric. That is, the relations between the variables of the form
of the house are mathematically defined. Thus, they are suitable for design optimization
models such as layout, structure, light, construction, and automated customization
through which different cost ranges can be obtained. An extensive discussion of
optimization in architecture can be found in Gero and Radford's Optimization in
Architecture and Construction.
The design by shape grammar method utilizes the generation of a portfolio of
standardized house types. Once the house types for a housing complex are determined
then they can be combined in many different ways to generate a complex of multiple
dwelling units relevant to the topography of the site as illustrated in figure 77. The
individuality of the houses can be achieved by customizing layouts and external details of
the houses according to the constraints imposed by the user.
In this thesis, I demonstrate the practical applicability of the shape grammar design
method. Shape grammars generate languages of form, providing a technique to generate
different configurations of the form. Formal languages have always been part of
architecture. Most architects have worked within the discipline of accepted formal
languages. In my opinion, it is impossible for an architect to move from the starting point
of a set of requirements to the end point of their translation into form without a set of
rules for the making of the form.
Shape grammars provide a technique for describing such form-making rules in essence
making the design process explicit and codifiable. These rules can be related to other rule
systems such as structure, light, or whatever conditions bear on form. Depending on the
architect's ability, the use of this technique may help to enhance form generation skills
and ultimately the quality of architects' designs.
24
Gero.J., Radford.A., 1988, Optimization in Architecture Building, and Construction, New York, Won
Nostrant Reinhold.
6. Discussion and Future Work
Architectural design does not spring from rules, but rather rules evolve from design, and
therefore there are as many rules as there are designers. As designers, we build our
repertoire of rules by analyzing existing functional types and extracting their rules
heuristically. However, as soon as we grasp the construction of a design, we use rules
implicitly to build new designs. Thus, the rules of design never become explicit but
remain embedded in the design. It is not a common practice in the tradition of
architectural design to externalize and record the rules of the design. However, their
existence and use in the design process is undeniable. Donald Schon points out that a
designer's ability to apply a rule depends on having familiarity with the underlying type.
"An individual designer may, in a project or series of projects, break apart objects and
relations inherent in a type she has developed or adapted. She may live for a time in a
design world made up of these objects and relations, exploring its limits and its potentials
for generating new forms."25
We express the concept of type with prototypes in the design world. In the context of
vernacular architecture, the problem, its constraints, and the set of acceptable solutions
are defined in terms of prototypes. In this context we start our design with a generalized
prototype whose parts have clear relations and are defined as a whole. Then gradually we
articulate the relations between the parts and develop the existing prototype or we add
new parts, and by changing the relations between the parts, we generate new prototypes
that ultimately lead to the new types. All of this is done intuitively. Although we may
record development stages with sketch drawings, we do not externalize each step of the
design. In other words, we do not externalize the rules of the design.
In this thesis, I applied the rule-based design method of shape grammar as a design tool
for typological analysis, as well as synthesis, of the hayat house type in a specific
vernacular architectural context. There are certain limitations to what can be expressed
2
Schon, D., 1985, "Rules, Types and Worlds," Design Studies, Vol. 9, pp. 18 -190.
55
using this rule-based method in architectural design. Therefore, this method is not a
substitute for the actual design process, but is one of many design methods that can be
used in the preliminary stages of design. Therefore, the present work makes no claim to
completeness.
The usefulness of this computational design method lies in the ability of architects to
employ its mechanism and use it for their own purposes, whether for education or
practice. Shape grammars have been used in three ways in education: as an apparatus for
the formal analysis and synthesis of form, as has been illustrated in this thesis; as a
constructive and pedagogical design tool for training students to create their own design
language or style; and as an intermediate computational tool for teaching programming
concepts to design students.
The shape grammar method as a design tool provides a constructive mechanism to teach
the concept of a design language. In this method, any relation between the input and
output states of the design can be defined by rules. In an architectural context, this
corresponds to the program and the designer's intentions (input state) and the actual
design (output state). Between the two there are different computational procedures
(rules) that will produce the design that satisfies both the program and the designer's
intentions. In other words, any design can be constructed in many ways. However, each
designer will have his/her own set of rules (design language) that distinguishes him/her
from other designers. This aspect of design has been dealt with in education in varied
elective graduate courses and compulsory undergraduate studios. For example, T. Knight
at UCLA and MIT has taught the synthesis and creation of completely new designs with
shape grammars in "Computational Design" courses. These courses are based on design
exercises with grammars through which students are taught explicitly compositional
skills. 26
26
Knight,T., 1991, CAADfeatures 91 edited by Schmitt. G.
56
Further examples of shape grammars being used in design education are the lecture
course and "Architectural Design Composition" studio taught by U. Flemming at
Carnegie Mellon University.27 Flemming, (1991) describes the structure of the course:
"The approach is to introduce students to a series of architectural languages characterized
by a vocabulary of elements and a grammar whose rules indicate how these elements can
be placed in space."
The shape grammar method provides an apparatus for teaching
design languages in a structured and constructive way, and allows the student to enhance
his/her repertoire of design rules.
The shape grammar method can be used as an intermediate computational design tool that
builds a bridge between programming and design. In visualizing the rules of computation,
it utilizes an understanding of algorithmic design procedures. Recent work on shape
grammar computer applications has been based on creating stand-alone software capable
of shape recognition and manipulation. The problem of compatibility between these
programs with Computer Aided Design (CAD) currently prevents the use of shape
grammars in more complex architectural software platforms. Thus, as a design tool, the
future of the shape grammar lies in its integration with CAD. The inherent structure of
CAD systems restricts the design exploration. Emergent sub-shapes that are recognized
by designers in design computation are unrecognizable from computer's viewpoint. The
shape grammar method has the potential to change the nature of CAD programs in two
ways: by providing a technique for emergent shape recognition and manipulation, and by
providing a mechanism for interaction between the user and the program through its
visual programming techniques. The shape grammar method has developed a formal
mechanism that can be implemented as a plug-in for CAD software and could ultimately
change it from being static and closed to a dynamic, interactive, and parametric design
tool. However, this also requires interdisciplinary study between CAD programmers and
architects who have sufficient knowledge of CAD programming concepts.
Flemming U., 1991, "Syntactic structure in architecture: Teaching Compositions with Computers," in The
Electronic Design Studio, edited by Mitchell, W, Purcel, P., The MIT Press.
27
57
In practice, shape grammars utilize the generation of standardized designs, while
respecting the existing stylistic characteristics in a given architectural context. They
provide a formal mechanism for optimization and automated customization models.
However, the integration of design models with mathematical models requires complex
data and variable management and can be handled only through the use of computer
technologies. Shape grammars provide a formal apparatus for communication between
the two. The integration of these models creates a new research area, which requires
interdisciplinary collaborative work between the disciplines of mathematics, computer
aided design, and design.
Figure 1: Detached and semi-detached hayat houses in Sarajevo
F -iT
w
Ground floor
a
First floor
DZENETICA HOUSE
DERZELEZ HOUSE
SABANOVICA HOUSE
SEMIZOVA HOUSE
KAJTAZOVA HOUSE
Courtyards
)
THE HOUSE IN POTOKLI
STREET
Women's house hayat
m
SVIRZINA HOUSE
Figure 2: Hayat houses in Sarajevo
Men's house hayat
SABURINA HOUSE
Division between public and
private quarters
Figure 3: Svirzina house, birdseye view
OWN'S COUF
WOMENS COURTYARD
MEN'S COURTY ARD
FIRST FLOOR
GROUND FLOOR
R- ROOM
H-
IIAYAT
S- STAIRS
K- KITCHEN
10E
-HOUS
R
H
ST- STORAGE
WOMEN'S
C.R- COFFEE ROOM
COURTYARD
R
KI- KIOSK
C.H- CONNECTION HALL
SK
C- COURTYARD
WOMEN'S QUARTER
ST
ST
T
WOMEN'S QUARTER
j
SMEN'S
COURTYARD
R
MEN'S QUARTER
MEN'S QUARTER
Figure 4: Svirzina house
R
R- ROOM
MEN'S
QUARTER
H- HAYAT
K- KITCHEN
S- STAIRS
C- COURTYARD
KI- KIOSK
FIRST FLOOR
GROUND FLOOR
ST- STORAGE
C.H- CONNECTING HALL
IK
R
R
R
H
R
MEN'S
QUARTER
R
C
WOM EN'S
QUARTER
Figure 5: Semizova house
R- ROOM
H- HAYAT
S- STAIRS
K- KITCHEN
GROUND FLOOR
FIRST FLOOR
ST- STORAGE
C- COURTYARD
KI- KIOSK
ST
R
K
KC
C.R- COFFEE ROOM
CC
KK
IKC
WOMEN'S QUARTER
MEN'S QUARTER
WOMEN'S QUARTER
Figure 6: Derzeleza house
MEN'S QUARTER
Courtyards
Hayats
Figure 7: Partial Mahala Pattern
VOCABULARY
a b c d e
SPATIAL RELATIONS
3
ab
@ aa
2
ac
D bb
3) bd
V
FAMILY OF SPATIAL
RELATIONS
© ac
ab
2.1
1.1
T
bd
3.1
aa
(4
4.1
1.2
2.2
3.2
4.2
1.3
2.3
3.3
4.3
1.4
2.4
3.4
4.4
GRAMMAR RULES
o
1.1
2.1
3.1
a ->a+a
4.1
1.2
2.2
3.2
4.2
1.3
2.3
3.3
4.3
1.4
2.4
3.4
4.4
a-> a+b
a
->
a+c
b
PROTOTYPE DESIGNS IN THE
LANGUAGE
Figure 8: The method of shape grammar development
b d
@
Figure 9: Vocabulary and spatial relations
FAMILY OF SPECIFIC VOCABULARY ELEMENTS
F,
I
-I
-
L
H
a
0.1~F*H
TY E
-
STARTING RULES
o[G
H_
TYPE A
A housewith havat atboth levels.
0.2 G.2
b
0.3-
TYPE B
A housewith no havat but only roomsat ground floor
level.
TYPE C
A housewithout ground floor atall.
Figure 10: Family of spatial relations and starting rules
GRAMMAR RULES
GROUP
GROUP
GROUP
GROUP
4.1
xx4.2
s
3.2
2.3
1.2
'
II
'I'D
3.3
3.5
H
-
FH --
-
G1-
RS
>
Fi
RS
W -
W
S
Figure
S
11: Grammar rules
->S 4 F11
FH
-
FH-
K
III
K
GRAMMAR RULES
53I-
11 - -
1 +i t
GI -
>
Figure 12: Grammar rules
( :+ (
Figure 13: Derivation of Prt. A
GR
62
GR
2.2
(R
GROtIND FLOOR
GROtUND FLOOR+FIRST FLOOR
3.2
42
1.2
RS
FH
FIRST FLOOR
GR +
S
S f
Fi+
K + RS
Figure 14: Derivation of Prt. B
GROUND FLOOR
GROUND FLOOR
3.1
6.1
1.2
4.2
FH
K
FIRSI FLOOR
S
FI
K +
RS
Figure 15: Derivation of Prt C.
FlRSI FLOOR
GH
GH
Li
L~LEZI
w
w
GH
s
F
w
W
w
j
I
Figure 16 : Different derivation of set 3 rules
GROUP
li i
>
211
7A
I
x
F
LLJ
GH 4 S
S
GH
+ F1
S
s 4 ( FH4 +Ai)
Figure 17: Shape rules
1
UI~EZ
I.?
108
J,
110
1010
10.
11
Figure 18: Shape rules
LI
I
(ROUND FLOOR
(ROUND FLOOR + FIRST FLOOR
FIRST FLOOR
421
2
3
ZIBI~
LIES
4
5
(ill
S
RS
S+- Fi
STAGE I
Figure 19: Stage I
RS
c
bI
b2
a2
L
,
XJ,
2
x
3
r
Flx,
_j
4
L :1
5
GH
- S
S
+
RS
FH + RS
GH 4
S
S
+
GH
RS
( FH
4 A,
)-
RS
STAGE 2
+
S
S--
-
GH
RS
FfH+ Ai )+ RS
+n(X,)
STAGE 3
Figure 20: Stage 2, 3 and 4
4
S
S
p
I(
RS
+ A, ) + ( al + bl + c + a2+b2)
STAGE 4
n ( X)
L~i1
l
Eh2
~;ii
1
-14
STAGE I
STAGE 2&3
STAGE 4
bl
c
h2
FT21
I--I ,,L
1 - .1
ly
LU77
S + (
s--I II'
STAGE 5
+
R
-R
S 4
(
(
(ill +
(ill + S
+ K
S - (I1if+
A,)t (RS-b)+
STAGE 6
Figure 21: Evolution of the first floor plan
n(
RS
X)
STAGE 7
LL,
I
P2
STAGE I
STAGE 2 &3
STAGE4
L-L-j-j
LW
>
STAGE 5
STAGE 6
Figure 22: Evolution of the first floor plan
-- EJ
STAGE 7
STAG E
I
STAGE 2&3
STAG E4
->
.1.
11 "1
STAGE 5
STAGE 6
Figure 23: Evolution of the first floor plans
STAGE 7
'.~
STAGE I
F:91
x,
STAGE 2&3
STAGE 4
LI
STAGE 5
STAGE I
STAGE 2&3
STAGE 6
STAGE 7
STAGE 4
L~~~1i~zl"
STAGE 5
STAGE 6
Figure 24: Evolution of the first floor plans
STAGE 7
Prt.Al
1.1
1.2
Prt.A2
Prt.A2
2.1
3.1
3.2
.2
1.3
1.4
Q
)
Figure 25: Prt.A houses
Prt.A4
4.1
4.2
Prt.A5
5.
5.2
P
U
H
Di
L
DU
Fw
>
1D
i} )UP
1( )UP
ROUP
ti,
114
III
4
-F
166
L
16.7
155
I'l
16.S
l-fl
A,
|
:
xy,
.
x.,y,
|
14.1
Figure 26: House development rules
-
EIGHT PART ITIONS ARE GENERATED FROM RULEI
h
q
H F,
-D
-1
FOUR PARTITIONS ARE GENERATED FROM RULF 2
±
--1]
PARTIAL PARTITION SET GENERATED FROM COMBINATION OF RULF AND RULE 2
-EF -I--
H
(1,1
,[1
11,8
III
(jp7
2
1,1
[PI
Figure 27: Room partition set
,pll
II,I4
w
Prt Al
15.1, 15.3, 15.5
tp3
tp.9
tp.2
GH +S+ RS
S + (FH + Ai) + RS
GH + S + (R., R2,......R.)
S + (FH + Ai) + (R,, R2,...... R.)
STAGE I
STAGE 2
Figure 28: Prt. A l house development
STAGE 3
16.1
FIRST FLOOR
16.2, 16.3, 16.4,..
GROUND FLOOI
STAGE 4
Li
L
Figure 29: Prt.A I house development
Fri[]
STAGE 4
00
L.
STAGE 4
Figure 30: Prt. A l house development
Prt. A2
tp.2j
15.1, 15.5
14.1
tp.2
tp.2
tp.14
STAGE I
Figure 31: Prt.A2 development
STAGE 2
STAGE 3
STAGE 4
STAGE 4
Figure 32: Prt. A2 development
L
-
STAGE 4
>
r
E-L:ILEMI
STAGE 4
Figure 33: Prt. A2 development
Prt. A3
tp.15
141
15.4, 15.5
tp. 14
3.2
>
STAGE
>
STAGE2
STAGE3
Prt. A4
14.2
-p2
>.3
4.1
STAGE I
STAGE2
Figure 34: Prt. A3 and Prt.A4 development
STAGE 3
3. 1
16.1
16.2, 16.3, 16.4,
Lb]i
STAGE 4
3.2
STAGE 4
Figure 35: Prt. A3 development
ELnU
STAGE 4
L]
IF
IF
IL
STAGE 4
Figure 36: Prt. A4 development
Prt. A5
15.1, 15.5
14.2
1
tp.
8
STAGE I
15.
STAGE 2
Figure 37: Prt. A5 development
1,15.2,15.5
STAGE3
16.1
---
6.2, 16.3,..
STAGE 4
STAGE 4
-11
-A-1
Figure 38: Prt.A5 development
Prt. Al
Prt. A2
Prt. A3
3.
Prt. A4
1
4.
Prt. A5
I
L.2
4.2
3. 2
1. 3
1.4
2. 3
2. 4
4
4
Figure 39: Set of articulated type A houses
.1
I
GIROU
P
NI WVOCAlBULARY
20.
(iROUP
ORW tI
191
i>sosi
B
--L9 -----
D
A
>
6
-9
A
iNI RAT I) 1'
liAYAT STAIRSNCOMPOSITIONSO
IN
ASSIININ(VALIETOITIl VARIAlLIS
19,3
l(
B
19.4
C
Figure 40: Transformation rules for an inclined topography
IIM
A
f~
HlFN[
I)
IN
NRl
lI.
TIll
1)
6,
I)>
16 1
LT
>
-A-
Ix
91 19.2 19SI
62 16
ELF' 1K
L IT
STAGE I
STAGE 2
TRA N SFORMATION
TRA N SFORMATION
STAGE 3
STAGES
STAGES
Figure 41: Prt.AI.1 house transformation
STAGE 4
STAGE 5
FIRST FLOOR
D
19.1, 192, 19 5,19.6
1181
L>
6 2,
F
>
L
GROUND FLOOR
STAGEI
CT
STAGE 2
163
2)
LI
B
A
STAGE 3
TRANSFORMATION S AGES
TRANSFORMA IION STAGES
Figure 42: Prt.A2.2 house transformation
STAG E 4
STAGE 5
F IRSTI L(X)R
16,1
18
7>
>
LB
195
B
L
2-o>
1136194
13
A
A
1
(;ROUNID II UOXR
STAGE I
STAGE 2
STAGE I
TRANSFORMATION ST AGES
IRANSFORMATION STAGES
Figure 43: Prt A4.2 house transformation
STAGE 4
STAGE
5
Prt.A
Prt.A 22
1
Prt.A 1I
Prt.A. 5
Prt.A. 5
Prt.A.4
Prt.A.4
Prt.A 3
Prt.A 3
L
1.2
1.3
F
2.1
4.1
2.2
4.2
2.3
2.4
Figure 44: Split -level houses
5.1
5.2
Figure 45: Split -level houses
GROUP
GROUP
>1
.1
2.1
->
2A4
-
FIRST
FLOOR
2.2-
FLOOR
GROUND
TPAl.
IHOUSE
Figure 46: Prt.A 1.3
CONDMON:
>
il - k2
II=12=13
Figure 47 Transformation rules for Prt.A 1.3
)
V
A.1.3
STEPI
6L
R
R3
FIRSTFLOOR
II
1
R4
1.1
1.2
STAGEI
2.1
STAGE2
GROUNDFLOOR
STAGE3
2.5
24
2.2,2.3
STAGE5
STAGE4
STEP2
Figure 48: Transformation of Prt.A1.3
STAGE6
GROUP
GROUP
ki
3.1
3.2
I/= 14
12= 13
ki= k2
3.3
Fr-
Figure 49: Transformation rules for Prt. T2
STEP I
3.1~
3.2
STEP I + STEP 2
STAGE I
STAGE2
-- I
L I
>
r-
2.6
4.1,4.2
I
STAGE3
STAGE4
STEP 2
Figure 50: Transformation of Prt.T2 into Prt.T3
STAGE5
w
ILLW
ThJ~
16.1
STAGE 1
2.19.,19.616.2.
131
STAGE 2
STAGE 3
Figure 51: Transformation of Prt.T3 into Prt. T4
16.3
STAGE 4
STAGE 5
- ww
TRI
Prt.A1.3
Figure 52: Transformations of Prt.A1.3
4-
Prt. A1.3
TR I
Figure 53: Transformation of Prt.A1.3
Prt.A. 1.3
T2
T3
Figure 54: Transformation of Prt.Al.3
T4
Prt. A1.1
Figure 55: Evolution of PRT. Al .1
Figure 56: Transformation of Prt. Al.1
111111111M
11111111M
Figure 57: Interpretation of the Prt.A1.1 house
T2
Figure 58: Transformation of prototype T2
Figure 59: Block design generated with Prt. T2
Eli
FH
_
Eli
5.1-
5.2 -
FH
[H
5.3
[H
-
[FH
FHF
5.4
-
[H
5.6
Ei
-[I]
-
Figure 60: House connection rules
HE
H
Prt.A3.3, Prt. A4. 1
Prt. A4. 1, Prt. A4.2
_LL__E
5
Prt. A3.3, Prt. A4.1
VJ
Prt. A3.3, Prt. A4.1
Prt A4. 1, Prt. A4.2
Figure 61: Semi-detached houses
Figure 62: Adjacency relation between semi-detached houses
Prt. A4.1
Prt. A4.2
Figure 63: Adjacency relation between semi-detached houses
77r
kL1Lf
-ik
I
Prt. A3.3
Prt. A 3.3
Prt. A.4.1
Prt. A
1.1
Prt. A. 1.1
Prt. A4.1
Prt. A.3.3
Prt. A4.2
Figure 64: Row houses
Prt. A4.1
Prt. A. 3.3
Figure 65: Row houses
COURTYARD RULES
HOUSING PATTERN RULES
SPATIAL RELATIONS BETWEEN
SITE VOCABULARY ELEMENTS
NEW SITE RULES
HZ,,TA.
IHZ
A+A
jE'
71
B.
F-FIH
A+B
C.
3.
7.
B+C
B +C
5.
B+B
5.
LI~Z
6.
B+B
STAGE I
STAGE2
STAGE3
STAGE4
Figure 66: Housing pattern rules
1- DERIVATION OF HOUSING PATTERN
1,2,3
0
HOUSING PATTERN
1, 2, 3, 5, 3,4, 3, 5,. ..
3- INTERPRETATION
Figure 67: Housing pattern generation
TP Ai
(A
Figure 68: Substitution rules
Figure 69: Housing unit
TOPOGHRAPHY
PATTERNRULESFOR INCLINED
HOUSING
SPATIALRELATIONS
SPLIT SITEVOCABULARY
BETWEEN
GENERATION
OF SPLIT SITE
VOCABULARY
RULES
HOUSING PATTERN GENERATION
FOR INCLINETOPOGRAPHY
CB
7,
CH
2.
C
A
CE
CI.
4.
1CA
11
CA
6.
STAGEI
C
CB
STAGE2
Figure 70: Housing pattern rules for an incline topography
STAGE3
00
CB
CA
CB
Figure 71: Spatial relations between different sites
CB
CB
Figure 72: Housing pattern on an incline topography
A
4 73:
Figure73
rnfnaio
ftest
Figure 74: Detached and row houses
131
Figure 75: Detached houses and semi-detached houses
132
0
1-4
Figure 76: Terrace houses
133
Figure77: Housing complex
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