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C. M. Herr, N. Gu, S. Roudavski, M. A. Schnabel, Circuit Bending, Breaking and Mending: Proceedings
of the 16th International Conference on Computer-Aided Architectural Design Research in Asia, 643-652.
©2011, Association for Computer-Aided Architectural Design Research in Asia (CAADRIA), Hong Kong
THE GARDENS REVISITED
The link between technology, meaning and logic?
GABRIELA CELANI,1 JOSÉ P. DUARTE2 and CARLOS V. VAZ3
1. FEC-UNICAMP, Campinas, Brazil, celani@fec.unicamp.br
2. FAUTL, Lisbon, Portugal, jduarte@fa.utl.pt
3. FEC-UNICAMP’s PhD Program, Campinas, Brazil, cevv00@
gmail.com
Abstract. The objective of this paper is to compare the computational
concepts present in three books published by Mitchell between 1987
and 1990: The art of computer-graphics programming (1987), which
has Robin Liggett and Thomas Kvan as co-authors, The logic of archi-
tecture (1990), probably his most inuential work, and The poetics of
gardens (1988), which has Charles Moore and William Turnbull as co-
authors. By looking at the concepts that are presented in the three books
and establishing a comparison between them, we expect to show that
The poetics of Gardens should not be seen as a detour from Mitchell´s
line of research, but rather as a key piece for understanding the relation-
ship between technology, meaning and logic in his very coherent body
of work.
Keywords. Computational design concepts; technology; meaning;
logic.
Introduction
The objective of this paper is to identify and inter-relate the computational
concepts that are present in three books published by late Professor William
Mitchell (two of them in collaboration with other authors) between 1987 and
1990. Two of these books are categorized in the eld of computational design:
The Art of Computer-graphics Programming: A Structured Introduction for
Architects and Designers (1987), which has Robin Liggett and Thomas Kvan
as co-authors, and The Logic of Architecture: Design, Computation and Cogni-
tion (1990), probably his most inuential work. Between them, Mitchell pub-
644 G. CELANI, J. P. DUARTE AND C. V. VAZ
lished a book that is usually found in a different section of the library: The
poetics of gardens (1988), which has Charles Moore and William Turnbull as
co-authors. By looking at the concepts that are presented in the later book and
establishing a comparison with the two other works cited above, we expect
to show that The Poetics of Gardens should not be seen as a detour from
Mitchell´s path on computational design, but rather as a key piece for under-
standing the relationship between meaning and logic in his very coherent body
of work.
The art of computer graphics programming
The Art of Computer-graphics Programming is much more than a Pascal pro-
gramming manual. In the Preface, Mitchell, Liggett and Kvan deliberately
afrm that they “are at least as concerned here with issues of design theory
and visual aesthetics as we are with computer technology” (p. vii). The book
introduces programming techniques along with computational design con-
cepts, through a number of shape generation concepts that can be implemented
in Pascal (as in any other computer language): variables that can take differ-
ent values, thus dening parametric shapes; symmetry and repetition, which
create different composition from the same vocabulary; conditionals, which
lead to environment-dependent solutions; encapsulation of shapes, which
creates hierarchic structures; and nally, transformation operations, which
carry objects from one state to another. The code examples and exercises
always establish a relationship to existing architectural examples, validating
the concepts presented as actual architectural design generation strategies.
The rst part of the book, “Introduction to the Medium”, presents informa-
tion about hardware and software - which was also the subject of Mitchell´s
previous book, Computer-Aided Architectural Design, from 1977 - as well as
computer-graphic principles - which would be more developed in Mitchell´s
book The Recongured Eye: Visual Truth in the Post-Photographic Era, from
1992. In Part 2, “Elementary Graphics Program”, after a brief introduction to
Pascal syntax basics, the authors start introducing computational design con-
cepts along with programming techniques.
Chapter 8, “Graphic Vocabularies”, introduces the “distinction between the
essential and accidental properties of an object” (p. 167), i.e., between the
general description of an object (its type) and its actual instantiation. The same
chapter describes the “Parameterization of Graphic Elements” (p. 166), includ-
ing a discussion about ranges of parameters, and the degrees of freedom of a
parameterized element. The authors illustrate the fact that the same element
may look different, depending on the parameters used in its instantiation, with
a grove of trees. The chapter ends with a section called “Dening vocabularies
645THE GARDENS REVISITED
of graphic elements”.
Chapter 9, “Repetition”, introduces “Principles of regular composition”
(p. 201), and proceeds with the “Use of Control Structures to Express Compo-
sitional Rules” (p. 202), which means looping through code with statements
such as For/Next, While/Do and Repeat/Until. This chapter ends with a dis-
cussion about generate-and-test-procedures.
Chapter 11, “Conditionals”, presents structures that allows “to vary con-
ditionally, according to context” (p. 273): If/Then/Else and Boolean varia-
bles. This concept is exemplied by many design situations, such as choosing
among many design alternatives (state-action diagrams), exterior and interior
conditions, conditional insertion of architectural elements to generate rythms,
and generate-and-test-procedures:
“Sometimes the designer knows the conditions that an instance of
some design element must satisfy, but does not know the parameter
values that will generate a satisfactory instance. The problem, then, is
to nd these parameter values… There are often formulas that can be
evaluated to yield the required value directly. In other cases, however,
there is no alternative to engaging in a trial-and-error process of gener-
ating candidate sets of parameter values for consideration and testing
these for compliance with the conditions” (p. 312).
Chapter 12, “Hierarchical structures”, shows how to create subsystems and
spatial relations by specifying “the relation between its constituent vocabulary
elements” (p. 324). It also introduces the concepts of recursion and recur-
sive subdivision. Finally, Chapter 14, “Transformations”, introduce Eucli-
dean operations and show how to combine them with hierarchical structures,
parameters and loops to generate symmetries:
“When transformation operators are applied within loops, symmetrical
patterns result. The graphic element to which they are applied becomes
the repeating element of the pattern, and different types of symmetry
result from using different combinations of transformation operators”
(p. 441).
The nal part of the book, again very technical, discusses graphic packages
for 2D and 3D-modeling, and for rendering still images and animations.
646 G. CELANI, J. P. DUARTE AND C. V. VAZ
The Poetics of Gardens
The Poetics of Gardens could be seen simply as a travel book for garden
lovers. The authors have certainly had a great time traveling around the world
to visit the more than forty gardens described. It could also be seen as a simple
garden design catalogue, in which gardens are grouped under certain catego-
ries. However, a careful reading reveals that the book includes many cognitive
aspects of the design process that are seldom addressed in landscape design
books. More than that, it establishes an unprecedented relationship between
design operations and meaning: Moore, Mitchell and Turnbull say that their
“concern is with the ways that places are given special meaning through
actions and rituals” (p. vii).
The rst part of the book (Chapters 1 and 2) describes the main ingredi-
ents (or vocabulary) for creating gardens, both tangible (topography, enclos-
ing, roong, connecting, watering, warming, cooling, lighting, scenting, fur-
nishing, etc.) and intangible (the genius loci, shan and shui, God and Cain,
memory and expectation, naming and meaning).
In the second part of the book (Chapter 3) a series of existing gardens from
all over the world are presented and analyzed, grouped under the following
categories: settings, collections, peregrinations and patterns. This categoriza-
tion is completely different from typical landscape design books, in which
examples are usually grouped by climate (such as tropical, Mediterranean,
temperate, arid, etc.), function (residential, public, recreational, etc.) or scale
(private house, housing development, urban square, park, etc.). The categories
proposed allow interpreting gardens according to the cognitive aspects of the
design process, which are also present in computational thinking.
The authors start Chapter 3 by saying that “gardens are rhetorical land-
scapes” that can be “read for content”, and that it is possible to “analyze [a
garden´s] devices of structure and gure and trope” in the same way that we
analyze a literary composition (p. 49). In other words, the reference to the
organization principles of visual compositions is explicit in the book, and it is
possible to infer that the categories proposed are related to cognitive strategies
in design and computation, such as shown in Table 1.
647THE GARDENS REVISITED
Table 1: Relationship between The Poetics of Gardens’s categories, cognitive aspects of the
design process and computer-programming techniques
Garden categoriesCognitive aspects of the design
process
Computer-programming
techniques
Settings Visual compositions Order of data in sets, data struc-
ture
Collections Vocabulary of shapes Mathematical sets
Peregrinations Steps or procedures in the design
process Procedural programming
Patterns Repetition according to rules, symme-
try, recursion
Loop, recursive functions, pa-
rameters
The relationship with computation is probably more explicit in the Pattern
Gardens section of the book. The authors start by saying that these gardens
“hold us … with their symmetries and repetitions and variations and com-
pletions” (p. 158). Persian gardens of the Mughul emperors from different
periods are used to introduce the concepts of symmetry and recursion. Some
of the gardens described here are the same as those that had been used by
Stiny and Mitchell (1980) as the corpus of analysis to develop “The grammar
of paradise”. The examples presented in this section show a progressive level
of complexity. When describing the Alhambra, the authors say that
“The compositional message of the Alhambra, surely, is that intricacy
is more satisfying if built in order, even simplicity, and that simplicity’s
pleasures can comfortably include the dazzlingly intricate” (p. 195).
The nal chapter of the book (Chapter 4) explicitly deals with the design
process, through a series of examples: a courtyard, a front yard, a backyard,
a side yard and a graveyard. The design process is literally described as a
conversation between different references from the past, which, translated to
the cognitive sciences jargon, is the same as afrming that design is a model-
based reasoning activity.
The Logic of Architecture
Mitchell’s The Logic of Architecture is a much more audacious work, aiming
to establish the theoretical bases of computer-aided architectural design and
to establish a computational theory of design. With Louis Sullivan’s maxim
“form follows function” as its starting point, the book is divided in three main
parts, each of them dening one of the words in the famous phrase. Thus,
648 G. CELANI, J. P. DUARTE AND C. V. VAZ
“form” is dened in terms of vocabularies and in terms of ways of organizing
elements, such as symmetries, proportions and repetitions. Next, “follow”,
i.e., action, is dened in terms of design reasoning, axioms, rules, and infer-
ence. Finally, “function” is dened in its physical, social and symbolic dimen-
sions, and meaning is explicitly presented as one of the expected functions of
a building.
Like the previous ones, this book is about the cognitive processes that
take place during the design activity, and Mitchell explicitly proposes, in the
Preface, to “elucidate the structure of design reasoning” (p. ix). Flemming
(1992), referring to the book as a “treatise”, clearly denes its objectives:
“The general idea underlying Mitchell´s treatment … is that of design
as computation, in which computation is not to be confused with num-
ber-crunching, but is to be understood in the general sense in which
the term is employed in computer science, namely, as an operation or
a sequence of operations performed on some symbolic representation”
(Flemming, 1992, p. 105).
Computational concepts applied to formal compositions are presented mainly
in Chapters 2 “Architectural form”, which includes a section called “Rhythm,
proportion and symmetry”, 3 “Design worlds”, 6 “Types and vocabularies”
and 7 “Design operations”. The concepts of vocabularies, types, parameters,
symmetry, repetition, variation, combination, transformation, conditions and
rules are thus reintroduced here, but within a much more formal framework,
with references to Articial Intelligence and Computer Science theories.
As stated by Flemming (1992), the book is not likely to be well-under-
stood by everyone: the concepts presented are extremely abstract and it relies
heavily on examples taken from classical architecture, “with its known regu-
larities and conventions” (p. 105). In other words, The Logic of Architecture is
a book for initiated researchers with at least some background in computation.
Comparison
In an implicit way, The Poetics of Gardens includes most of the computational
design concepts that had been previously introduced in The Art of Computer-
graphics Programming and that would be further developed in The Logic of
Architecture. Table 2 shows a summary of the main concepts that are pre-
sented in each book.
649THE GARDENS REVISITED
Table 2. Computational concepts presented in each book
The Art of Com-
puter-graphics
programming
The Poetics of Gardens The Logic of Architecture
parameters
symmetry
repetition/recursion
conditionals
hierarchy of parts
transformations
elements (vocabulary)
garden types (categories)
settings - metaphors
collections - nouns
peregrinations - verbs
patterns – verses
repetition
variation
combination
symmetries
descriptive methods
architectural form
rhythm, proportion,
symmetry
design worlds
points, lines, planes,
volumes
critic languages
design reasoning
types/vocabularies
design operations
transformation
combination
substitution
architectural languages
function
It is possible to say that the three books are inter-related and complement each
other. Yet, their character and target public are completely different. While
The Art of Computer-graphics Programming can be considered a technical
book, The Logic of Architecture is in the opposite end, and can be seen as a
philosophical treatise. The Poetics of Gardens is in between, not as technical
but also not as philosophical. While The Art of Computer-graphics Program-
ming can be easily read by both engineers and computer scientists (on top of
architects), The Logic of Architecture might be of interest to both philosophers
and logicians (maybe even more than to architects). The Poetics of Gardens,
on the other hand, is mostly interesting for architects and landscape architects,
but that is probably because the computational design community are still to
discover this book.
It is interesting to note how the same concepts are presented in each of
the books in a slightly different way. For example, the concept of essential
and accidental properties was introduced in The Art of Computer-graphics
Programming and further rened in The Logic of Architecture. However, the
concept was also used in The Poetics of Gardens, to explain how the chahar
bagh pattern could be instantiated in different ways. All the different chahar
bagh gardens were based on the same prototypical idea, but each of them
introduced particular characteristics (accidental properties) depending on
their physical extent, the availability of water, the topography and so on.
Similarly, the concept of parameters is initially introduced in The Art of
Computer-graphics Programming and further developed in The Logic of
650 G. CELANI, J. P. DUARTE AND C. V. VAZ
Architecture (Chapter 7, Design Operations, section Instantiating Primitives).
In The Poetics of Gardens, the different patios in the Alhambra are presented
as parametric variations of the same model, formed by a central open space
with a fountain and four vaulted spaces around it. Another example of how
parameters can receive different values depending on the designer’s intents
is William Kent’s planting scheme for Rousham, in which the landscape
designer uses a variation of tree heights to create different perspectives to the
river along the way:
“[Kent] indicated deliberate yet carefully controlled variations of the
characteristics of the woods along the paths, from high tree forests to
underwood and tall shrubs” (p. 129).
Types and vocabularies are also introduced in The Art of Computer-graphics
Programming and further developed in The Logic of Architecture, in which
Mitchell states that architectural styles can be dened in terms of their vocab-
ularies of shapes. In The Poetics of Gardens, the authors describe, in Chapter
2 - The designer’s place, an example of a clear denition of a vocabulary: the
eleven elements of a Japanese Garden.
The concepts of repetition and recursion, again introduced in The Art of
Computer-graphics Programming, are associated, in The Logic, to symmetry
and rhythm …: “in most buildings, there is a repetition of elements, such as
columns” (p. 27, Chapter 2 - Architectural form; section 3 - Rhythm, propor-
tion and symmetry). Recursion is seen as one of the possible design opera-
tions. In The Poetics of Gardens recursion is illustrated and given meaning
by different Mughul Garden designs. The gardens of the tomb of I’timad-ud-
Dula, for example, don´t need the same level of recursion as the bigger tombs
of the emperors. Being smaller, the canals along the main axes and the perim-
eter sufce for irrigating the ground.
The Poetics of Gardens is a link between The Art of Computer-graphics
Programming and The Logic of Architecture Theory and technology alone
are like water and oil; they do not mix easily. The architect must provide the
context to weave them together meaningfully. In this case, the context was
landscape design.
Discussion
Computational approaches have often been criticized for being unable to
handle subjective dimensions of design, such as meaning. Fleisher, for
example, has suggested that shape grammars fail to handle meaning because
in the traditional design process “one sketches to explore lexicon and seman-
tics. Neither words nor meanings are prior. They are assigned on trial, locally
651THE GARDENS REVISITED
and globally.” Meaning cannot be “entirely prescribed or anticipated” (p.
224). Still according to him, “Grammars for exploring [shapes] would invent
structure and meaning simultaneously, consistently.” (p. 224), but he believes
that “geometry is the only part of the architectural argument that is comput-
able” (p. 225).
The Poetics of Gardens shows that meaning in design can be the result of
the systematic application of shape rules through a series of built examples. In
the design of gardens, formal composition responds to symbolic requirements
in addition to pragmatic issues. For instance, in Persian gardens, symmetry
evolves with the type of political power hold by the emperor. Rules, thus, can
encapsulate meaning.
In summary, the analysis of The Poetics of Gardens allows concluding
that:
• The cognitive processes that take place during the development of
a design project include many computational operations, both for
establishing the visual composition and for dening its meaning;
• The book is about the computational and cognitive aspects of the
design process, rather than simply a catalogue of gardens;
• Among the three books analyzed, it is the less subject to obsoles-
cence, because it discusses very fundamental concepts of design,
without any explicit reference to technology.
After concluding this series of books about computational concepts in design,
which can be seen as a trilogy, Mitchell published many other titles, with
colleagues or by himself, always related to design, technology and meaning.
Some of his other books can also be grouped together by theme, such as:
Applications of the new technologies in the design process
• The Electronic Design Studio: Architectural Knowledge and Media
in the Computer Era (McCullough, Malcolm, William J. Mitchell and
Patrick Purcell, eds., 1990)
• The Recongured Eye: Visual Truth in the Post-Photographic (Mitch-
ell, William J., 1994)
• Digital Design Media: A Handbook for Architects and Design Profes-
sionals (Mitchell, William J. and Malcolm McCullough, 1996)
Impacts of connectivity in the urban space
• City of Bits: Space, Place, and the Infobahn (Mitchell, William J.,
1995)
• E-topia: Urban Life, Jim—But Not as We Know It (Mitchell, William
J., 1999)
652 G. CELANI, J. P. DUARTE AND C. V. VAZ
• Me++: The Cyborg Self and the Networked City (Mitchell, William
J., 2003).
Most of these books have been translated to other languages. E-topia, for
example, was translated to seven languages. On top of the books, Mitchell
published hundreds of papers in journals, magazines, newspapers and confer-
ence proceedings. This shows the relevance of his words and at the same time
the size of the legacy that he left us.
Revisiting this legacy, for example by publishing commented transla-
tions, can bring up new interesting discussions. The Portuguese version of
The Logic of Architecture (UNICAMP Press, 2009) includes a glossary about
rst order logic and articial intelligence concepts, and the Portuguese version
of The Poetics of Gardens (UNICAMP Press, scheduled for 2011), will have
hundreds of footnotes for the younger readers, who are not so knowledge-
able about British literature. One of the authors of the present paper plans to
translate The Art of Computer-graphics Programming, adapting the codes to
a more contemporary programming language. The new book will probably be
very useful as a programming manual for present days architecture students.
Even though Mitchell is not with us any more – he is probably enjoying
the most beautiful garden of all at this moment, with the other authors of The
Poetics of Gardens - we believe that the concepts present in his books still
have a great potential for teaching design and computation, and thus should
continue to be explored in many ways.
References
Fleisher, A.: 1992, Grammatical architecture? Environment and Planning B, v.19,
221-226.
Stiny G., Mitchell W. J,: 1980, “The grammar of paradise: on the generation of
Mughul gardens” Environment and Planning B 7(2), 209–226.
Flemming, U.: 1992, The logic of Architecture: Design, Computation and Cognition.
In: Journal of Architectural Education, v. 46, n. 2, nov. 1992, 104-106.
