Architectural Morphology: An introduction to the geometry of building plans

148 Pages·1983·59.78 MB·English

by  Philip Steadman

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Architectural
Morphology
J PSteadman
Architectural Morphology
J P Steadman
Contents
Introduction
2 The 'dimensionless' representation
of rectangular plans
3 The symmetries of rectangular plans
4 Generating and counting rectangular
arrangements: dissection and additive
methods
5 Generating and counting rectangular
arrangements: tilings and colourings
on grids
6 Graphs of plans and their arrangement
7 Embedded, coloured, and weighted graphs
of plans
8 Properties of rectangular arrangements,
and their classification
9 Floor plan morphology in design
10 Plan morphology and building science
11 Plan morphology and architectural history
12 Afterwords: prospects for an architectural
morphology
Appendix:
Diagrams of rectangular dissections up ton = 7
with tabulations of their properties
References
Index
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r
Architectural
Morphology
J PSteadman
An introduction to the geometry
of building plans
Preface and acknowledgements
p
Pion Limited, 207 Brondesbury Park, London NW2 SJN "If something like a theory of architecture will ever be developed, then one of its
first chapters will deal with the theory of cell configurations ... "
H Rittel (I 970)
© 1983 Pion Limited
This book provides an introduction to an area of architectural research
All rights' reserved. No part of this book may be reproduced in any form
which has been emerging over the last ten years, and which has gone under
by photostat microfilm or any other means without written permission
the name, variously, of 'architectural morphology' or 'configurational
from the publishers.
studies' in architecture. It is concerned centrally with the limits which
ISBN O 85086 086 5 geometry places on the possible forms and shapes which buildings and
their plans may take. The use of the term 'morphology' alludes then to
Goethe's original notion, of a general science of possible forms, covering
not just forms in nature, but forms in art, and especially the forms of
architecture.
This research work has been published up to now in scattered papers,
many of them so technical as to be inaccessible to the general reader.
The material is here brought together for the first time, put into order,
and, together with the necessary mathematical foundations, set out in a
self-contained treatment for the nonspecialist student of architecture. The
last three chapters of the book explore in a more speculative way the
broader implications of the work for design, for building science, and for
architectural history.
The hope is that the book may be of interest to practising designers and
architectural students. But it is directed most specifically to theoreticians:
to building scientists, understood in the most general sense of that
term; to historians of architecture who have interests in the description
and explanation of the basic underlying forms of buildings, and their
methods of composition; and to those working on computer aids for the
representation and manipulation of building form in design.
Much of the work described here is that of my own immediate colleagues
and students in three university departments: the Martin Centre at the
Cambridge School of Architecture, the School of Architecture and Urban
Planning at the University of California, Los Angeles, and the Centre for
Configurational Studies at the Open University. Of these colleagues I should
like to name specifically, at Cambridge, Leonardo Combes and Cecil Bloch;
at UCLA, Bill Mitchell, Robin Liggett, and George Stiny; and at the Open
University, Lionel March, Chris Earl, Ray Matela, and Ramesh Krishnamurti.
I owe a great deal to the many discussions which I have had with these
individuals and others in these three places; and I hope I have dbne justice
to their work where I have presented it, in necessarily highly summarised
form, here.
A glance at the references will show how a very large proportion of the
entries refer to a single source- the journal Environment and Planning B.
Quite apart from his own protean contributions, Lionel March in his
editorial capacity has promoted this field of research to an international
audience with such enthusiasm and vigour that everyone working on these
Printed in Great Britain by Page Bros (Norwich) Limited
Preface and acknowledgements
subjects must be greatly in his debt. If this book can introduce the field For Leonardo:
to readers unfamiliar with Environment and Planning B, and lead them on another exhibit for Dubuffet's museum?
into the fuller and more technical discussions of the journal itself, then it
will have served much of its purpose.
Outside these immediate circles, I must mention the intellectual stimulus
and challenge continuously provided by the morphological work of Bill
Hillier and of his colleagues and students at University College London.
Some of the arguments recounted here have been raised and debated in an
interuniversity seminar series held jointly between the Open University,
Cambridge, and University College groups.
I would like to thank Chuck Eastman, as editor of this series, and also
Chris Earl, for reading the manuscript, for making many helpful suggestions,
and for saving me from at least some of my errors. I am especially
grateful to Cecil Bloch for his kindness in allowing me to reproduce part
of his catalogue of rectangular dissections as an appendix. The manuscript
was typed by Sue Ayers and the diagrams drawn by Sarah Couch.
Thanks are due to the following publishers, for their kind permission to
reproduce copyright material:
Cambridge University Press, Cambridge, for figures 2.3 and 2.4;
Petrocelli/Charter, New York, for figure 2.8;
Artemis Verlag, Zurich, for figure 8.12(a);
Macmillan, New York, for figures 8.12(c) and (d);
MIT Press, copyright Massachusetts Institute of Technology, Cambridge, MA,
for figure 9. I ;
Oxford University Press, London, for figures 9 .2 and I I .9(a);
Granada, St Albans, for figure 10.7;
Faber and Faber, London, for figure 11.1;
Manchester University Press, Manchester, for figures 11.S(a) and 11. 7;
Architectural Press, London, for figure 11.11 (a).
Contents
Introduction
2 The 'dimensionless' representation of rectangular plans 6
3 The symmetries of rectangular plans 20
4 Generating and counting rectangular arrangements: 31
dissection and additive methods
5 Generating and counting rectangular arrangements: 46
tilings and colourings on grids
6 Graphs of plans and their arrangement 61
7 Embedded, coloured, and weighted graphs of plans 79
8 Properties of rectangular arrangements, and their classification 112
9 Floor plan morphology in design 140
IO Plan morphology and building science 171
11 Plan morphology and architectural history 209
12 Afterword: prospects for an architectural morphology 247
Appendix: Diagrams of rectangular dissections up to n = 7 250
with tabulations of their properties
References 269
Index 277
1
Introduction
"It seems very unaccountable that the generality of our late architects dwell so
much upon [the) ornamental, and so slightly pass over the geometrical, which is the
most essential part of architecture."
Sir Christopher Wren (1750)
In I 975 William Mitchell, Robin Liggett, and I developed a computer
program which generated architectural plans of a certain type automatically
(Mitchell et al, 1976). These were plans consisting of rectangular rooms,
set together to form arrangements with a rectangular shape overall- the
sorts of plans typical of many small houses and flats. Constraints could
be specified on the topology of the plan, requiring that certain rooms be
adjacent, or not be adjacent to each other, and on the dimensions of the
rooms, limiting their areas, lengths, widths, or proportions. The method is
explained in more detail here in chapter 9. The special and novel character
of the program was its capacity to produce exhaustively all possible plans
in which the given constraints were satisfied.
This work provoked some strange reactions. Mitchell outlined the
system to an architect acquaintance in Los Angeles, and was told flatly
"That's impossible". Later, Mitchell and I submitted a paper describing
the work to the British Architects' Journal. The article was refused by the
then editor in a letter of scarcely concealed hysteria: "This work is
strictly non-architectural, ... it has nothing to do with architecture".
I tell these anecdotes not out of any sense of grievance (our feelings at
the time were more ones of surprise and amusement), but in recognition
of the fact that any book which treats architectural subjects from a
mathematical point of view, and even more so one which mentions
computers, is bound immediately in the present climate of ideas to come
up against preconceptions in the minds of many readers.
There is a widespread reaction today, and for good reasons, against the
architectural functionalism of the modern movement. That functionalism,
to speak very generally, took two forms, one more benign and less
dangerous than the otherOl. The functionalism of Sullivan, or of Lethaby,
(I) Two of the best and most succinct discussions of these distinct meanings of
'functionalism' are to be found in Summerson (1949, page 149), and in Goodman and
Goodman (1947, pages 8-9). As the Goodmans say, 'Form follows function'" ... in
the original statement of Louis Sullivan ... meant that the form is not given by the
function but is appropriate to the function; in his words 'a store must look like a
store, a bank must look like a bank'. This is an aesthetic principle; for it includes
certain ideas, the genres of buildings, whose unity is formal over and above the utility;
they are given by the sensibility of the culture ... But in the more radical interpretation
of the Bauhaus the formula means that the form is given by the function: there is no
addition to the arrangement of the utility, but it is presented just as it works. As such,
this is not an aesthetic principle at all ..." . (See also Steadman, 1979, chapter 13.)
2 Chapter I Introduction 3
involved an aesthetic belief that buildings should 'explain themselves', None of these limitations force the designer's hand. Rather they serve to
should present in their design a rational argument about their function and determine the extent of the field of possibilities within which his choice
means of construction. By contrast the functionalism of, say, Hannes must be exercised. As he restricts himself to a geometrical discipline, to a
Meyer, or more recently of some adherents of the 'design methods' set of formal elements, to some dimensional constraints, so his choice is
movement, tended towards a much more radical doctrine: that functional further narrowed.
considerations could, if subjected to sufficiently precise analysis, be made Other authors have adopted the terminology of ,linguistics in this
to define the form of a building in a necessary and automatic way- what context, and have referred to the syntax (Frank Lloyd Wright spoke of
has been called 'functional determinism'. 'grammars') of architectural form. We might pursue this analogy with
It is popularly assumed that any architectural research of a mathematical language a little farther. The academic study of architecture can be seen
nature must have functionalist aims in this second sense: that it seeks to as being divisible into three areas or disciplines. There is the professional
devise ways in which the design of a building can be formulated as a training of designers, in architectural schools. The analogy here is with
mathematical 'problem', and mathematically 'solved'. learning to speak a language. There is the study of architectural history,
This book aims to provide an introduction to an area of research which, from a critical and aesthetic point of view. This must correspond to the
though mathematical in nature, and although computers are certainly used, study of literary history and literary criticism. And, third, there is what I
has quite different aims and is based on a very different conception of the would suggest is the architectural counterpart to the discipline of linguistics:
nature of architectural design. It takes the view that design is, always has that is, an architectural science, devoted to a general investigation of the
been, and always will be concerned at its central core with the manipulation cultural and technological systems within which all architects work, and all
of form, with composition, understood as the putting together of two buildings are produced.
dimensional and three-dimensional components, either spaces or material This 'architectural linguistics' is itself divisible into two parts. There is
elements, in arrangements or configurations. that part which deals with the syntax of possible architectural forms and
The architect's choice of forms is made according to his artistic purpose, arrangements. And there is that part which deals with the semantics, the
and is directed towards the satisfaction of (though not by any means systems of meaning, which the syntactic forms and structures come to
uniquely determined by) his client's tastes, desires, and utilitarian support. (For example, see Norberg-Schulz, 1974; Bonta, 1979; Broadbent
requirements, as well as being limited by technical and structural possibility. et al, I 980.) The present book is confined entirely to the subject of
But whatever is expressed or signified by an architectural work, whatever architectural syn tax.
practical functions it might serve, and however it is constructed, this It is in many ways a sequel to The Geometry of Environment which
choice of form in design is constrained above all by limits on what is Lionel March and I published just twelve years ago (March and Steadman,
geometrically and topologically possible. It is the purpose of this whole 1971) . (In fact the material presented in the two books overlaps to an
book to demonstrate the detailed nature of some of these limits. As an extent, especially that on symmetry, and graph theory.) One of our
example, and speaking generally, if it is required that a number of rooms slightly hidden motives in writing The Geometry of Environment was a
be laid out on a single floor level such that specified pairs of rooms are or belief that learning to understand geometrical limitations and geometrical
are not adjacent (without consideration of their shape or size) then there possibility formed a valuable, and at that time neglected, part of the
exists only a finite number of possible such arrangements (perhaps none at general education of the designer<2>.
all). Such limitations are of a topological nature. Not that this knowledge would be applied necessarily in specific
Again there exist choices for the overall geometrical discipline according mathematical techniques or methods, but that it could constitute part of
to which plans may be laid out, for instance with their walls aligned on a the broad intellectual makeup of the designer, part of the mental apparatus
rectangular or some other form of grid; for the geometrical elements from which he brings to bear in design. There was admittedly a short presentation
which the plan is to be made up- for example, rectangles or other shapes in The Geometry of Environment of some computerised 'design methods'
corresponding perhaps to rooms; and for conditions on the assembly of
those elements- for example, that they should pack closely without gaps. <2> It is perhaps worth recalling that we felt it necessary, in the introduction to The
that they should not overlap, and so on. Limits on the variety of possible Geometry of Enviro11me11t, to apologise for our "total disregard in this book for any
arrangements of such elements under such conditions can then be expressed but the most simple functional requirements". Thus we could have been more
justifiably accused on that count of formalist rather than functionalist tendencies. For
in terms of well-defined rules for their composition. The introduction of
coverage of functional aspects we referred readers, among other works, to Alexander's
dimensional constraints will reduce this variety of arrangement still further. ( 1964) Notes on the Synthesis of Form, which as George Stiny has said, should more
properly have been called Notes on the Analysis of Function.
I.
4 Chapter 1 Introduction 5
intended for generating supposedly 'optimal' architectural layouts on the 'infinitude of possibilities' which paralyses the imagination. Thus Stravinsky
basis of a circulation-minimising criterion. Such methods had been (I 970, page 85) says:
formulated very much in a 'functional determinist' spirit, and were "What delivers me from the anguish into which an unrestricted freedom
criticised in the book on those grounds. plunges me is the fact that I am always able to turn immediately to
Some similar methods are described briefly here at the beginning of the concrete things that are here in question. [He is referring to such
chapter 9; but the purpose is most emphatically not to endorse the view acoustic and physiological facts as the nature of the octave, its chromatic
of architectural design which they embody. They are introduced because intervals, and their perception, etc.) Let me have something finite,
they make use of some of the mathematical ideas and techniques which definite- matter that can lend itself to my operation only insofar as it is
are described here; and more importantly because they led the way commensurate with my possibilities. And such matter presents itself to
towards the development of methods for enumerating all permutations of me together with its limitations. I must in turn impose mine on it. So
plan arrangement within given constraints, and hence of exploring the here we are, whether we like it or not, in the realm of necessity. And yet
'outer limits' of geometrical possibility in design, as already described. which of us has ever heard talk of art as other than a realm of freedom?
Some designers are strangely unwilling to acknowledge the fact of the This sort of heresy is uniformly widespread because it is imagined that art
existence of such geometrical limitations at all- witness the reaction of is outside the bounds of ordinary activity."
Mitchell's acquaintance- and adopt evasive tactics in discussion. When one In architecture too there are individuals whose creativity might be
makes the argument that, say the number of rectangular plans with so credited at least in part to their knowledge of geometry as a subject;
many rooms is (in a certain sense, defined in chapter 2 in terms of either explicit, as in the case of Wren, or of a more intuitive and informal
topological equivalence) strictly finite, then the response tends to be kind, such as that of Wright, who is well known to have made much of his
"Ah well, but you haven't included triangular plans ... " or "What about education from an early age in the constructive appreciation of abstract
circular plans? ... or 'free-form' plans? ... ". By moving the ground of the pattern and form.
discussion, by trying to step outside the system, the architect attempts
A final word should be said about the mathematical treatment. For
vainly to escape this geometrical prison, as he sees it, in an effort to
many people, I know, the mere sight of a mathematical symbol is sufficient
reassert his creative freedom.
to make the eyes glaze over and the brain go numb. This, however, is an
But this supposed freedom is illusory; and anyone who denies the
irrational phobia, and like all phobias it is treated by urging the sufferer to
existence of geometrical limitations in design is only doomed to stumble
face and handle the feared object, to discover for himself that it is by no
against them blindly. The fact is that for many good geometrical and
means as frightening as he had always believed.
practical reasons, as will be clear from later chapters, architects do choose
If you are a mathematophobe, you should be reassured that the prior
to confine themselves to a rectangular discipline in design. And where
knowledge of mathematics required is no more than basic arithmetic and a
they do so, then certain limitations on geometrical possibility must
few simple algebraic concepts. The mathematics is very informally
necessarily apply. They have perfect freedom, certainly, to reject the
presented, most equations are spelled out in words, and frequent examples
discipline of the right-angle if they so wish, and adopt say a triangular or a
are given, illustrated with explanatory diagrams. Do not be put off by
curvilinear geometry. But of course these disciplines in their turn impose
algebraic formulations (of which there are few). You should expect to
their own limits on possibility- in some respects more severe, as we shall
read mathematics slowly in any case: and more is learned by doing rather
see, than those of rectangular geometry.
than just reading- so exercises are included at the end of several of the
It might be objected that architects have been managing to compose
chapters. All the treatment here is self-contained; but in some of the
forms in design very satisfactorily for a couple of thousand years or so,
topics covered, background textbooks have been cited for those who want
without any conscious knowledge of such limitations. In terms of our
to prepare more widely around the subject.
earlier analogy, a person can certainly achieve fluency in a language
For the mathematically equipped reader, on the other hand, I should
become a poet indeed- without any formal knowledge of the science of
apologise for the absence of formal definitions and proofs, and for any
linguistics. Perhaps there is no call for the practical training of designers
possible tedium which the repetition of explanations or illustrations might
to include any formal geometrical education in these subjects.
cause. References are given to the specialised literature in which formal
On the other hand it is possible to point to some undeniably creative
treatment of the mathematical issues may be found.
practitioners of other arts, who have argued that a mastery of the formal
'rules of composition' serves precisely to liberate, rather than to enslave,
the artist; that it is exactly the dizzying (and deceptive) notion of an
2 The 'dimensionless' representation of rectangular plans 7
The 'dimensionless' representation of rectangular plans
All the faces are made from essentially the same drawing, from the same
set of curved lines joined in an unvarying arrangement; but squeezed or
stretched, so to speak, as the grid dimensions are altered. It is as though
"The splitting into something discrete and something continuous seems to me a the drawing were made on a sheet of rubber.
basic issue in all morphology, and the morphology of ornaments and crystals In other illustrations, Diirer encloses the head in an oblique grid of
establishes a paragon by the clearcut way in which this distinction is carried out." equal parallelograms (figure 2.2). The grid is again transformed, this time
Hermann Wey! (1952) by altering the angle between the coordinates- so subjecting the drawing
to a shear transformation- to generate a different kind of series of related
There are some famous drawings by Albrecht Diirer ( 1528), in which he profiles.
uses a particular geometrical method to describe the proportions of the The same idea is developed by D'Arcy Wentworth Thompson (1961) in
human head and face. The method consists in drawing a square or one of the best-known chapters "On the theory of transformations, or the
rectangle to enclose the head, and dividing this rectangle up into a grid of comparison of related forms", in his book on biological morphology On
lines which mark the positions of the various features- brow, eyes, nose, Growth and Form. Thompson's purpose here is to compare the shapes of
chin, and so on. Diirer shows how a series of different faces may be animals which belong to the same zoological class. To do this he makes
produced by altering the relative spacing of the lines of the grid (figure 2.1 ).
m
m m
n n n
Geryon Para lorn is
I, l\s
~ttw
,I I
I I,
m
m r- I
m I ,
n " n Lupa Corystes
Figure 2.1. Different faces produced by assigning varying dimensions to the intervals
of the superimposed grid (from Dilrer, 1528).
Scyramathia Chorinus
Figure 2.2. Different faces produced by changing the angle between the coordinates of Figure 2.3. Carapaces of various crabs, related together in shape by D' Arey Thompson's
the superimposed grid, in a shear transformation (from Dnrer, 1528). 'method of coordinates' (from Thompson, 1961, figure 142).