'Watch those scrollbars or you might miss most of what must be the world's longest Web page'
UK Gaurdian, 2nd February 95
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Copyright notice
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Copyright notice
(c) the authors and owners, 1995
Copying for commerical reasons is strictly forbidden without the permission of the authors and owners
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A natural model for architecture
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A natural model for architecture
'... a typical seed with two cotyledons. The cotyledons are specialised rudimentary leaves containing a supply of nourishment sufficient for the initial stage in the development of the germ. The germ is the real thing; the seat of identity. Within its delicate mechanism lies the will to power: the function of which is to seek and eventually to find its full expression in form. The seat of power and the will to live constitute the simple working idea upon which all that follows is based... '
Louis H. Sullivan, A System of Architectural Ornament, 1924
An Evolutionary Architecture investigates fundamental form-generating processes in architecture, paralleling a wider scientific search for a theory of morphogenesis in the natural world. It proposes the model of nature as the generating force for architectural form. The profligate prototyping and awesome creative power of natural evolution are emulated by creating virtual architectural models which respond to changing environments. Successful developments are encouraged and evolved. Architecture is considered as a form of artificial life, subject, like the natural world, to principles of morphogenesis, genetic coding, replication and selection. The aim of an evolutionary architecture is to achieve in the built environment the symbiotic behaviour and metabolic balance that are characteristic of the natural environment.
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A natural model for architecture
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A natural model for architecture
Space, structure and form are the traditional outward expressions of an architectural concept which has developed in the mind of the architect. This idea is taken further in our work. Architectural concepts are expressed as generative rules so that their evolution may be accelerated and tested. The rules are described in a genetic language which produces a code-script of instructions for form-generation. Computer models are used to simulate the development of prototypical forms which are then evaluated on the basis of their performance in a simulated environment. Very large numbers of evolutionary steps can be generated in a short space of time, and the emergent forms are often unexpected.
These techniques have previously been limited to easily quantified engineering problems. Only now is it becoming feasible to apply them to the complex problems associated with our built environment. To achieve this, we have to consider how structural form can be coded for a technique known as a 'genetic algorithm', how ill-defined and conflicting criteria can be described, how these criteria operate for selection, and how the morphological and metabolic processes are adapted for the interaction of built form and its environment. Once these issues are resolved, the computer can be used not as an aid to design in the usual sense, but as an evolutionary accelerator and a generative force.
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The proposition
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The proposition
This text introduces the concept of an evolutionary architecture, indicates the nature of the biological and scientific analogies, and relates the idea to the wider context of present scientific discourse. In the process, it relies heavily on natural science and the newer sciences of cybernetics, complexity and chaos.
This Introduction advances the general proposition and describes the background to our work. Section 1 describes the creation and implementation of tools to assist in developing the model. Section 2 establishes the theoretical proposition and describes one possible way of achieving these principles. Overall, this text will describe the emerging field of architectural genetics. It will explore at least one possible future based on artificial design life, suggesting a new form of designed artefact interacting and evolving in harmony with natural forces, including those of society. It will explain a new computer-based technique for design which models inner logic rather than external form, and it will afford a brief glimpse of a future as yet evolving only in the imagination of a computer.
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The nature of the analogy
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The nature of the analogy
Architecture has frequently drawn inspiration from nature - from its forms and structures, and, most recently, from the inner logic of its morphological processes. It is therefore necessary to be clear as to where architecture is literally considered as part of nature, where there are analogies or metaphors, and where nature is a source of inspiration.
We can say that architecture is literally part of nature in the sense that the man-made environment is now a major part of the global eco-system, and man and nature share the same resources for building. In turn, our description of an architectural concept in coded form is analogous to the genetic code-script of nature. Analogies, particularly biological, bedevil architectural writing. Sullivan, Wright and Le Corbusier all employed biological analogies and the concept of the organic is central to the twentieth century. In our case, the primary inspiration comes from the fundamental formative processes and information systems of nature.
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The problem of the blueprint
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The problem of the blueprint
Architecture's use of biological analogies has a counterpart in the use of architectural analogies in science. There is an abundance of books with titles like The Cosmic Blueprint (by Paul Davies) or Blueprint for a Cell (by the Nobel Laureate Christian de Duve). These, however, are quick to point out that an architect's blueprint is a specific one-off set of plans whereas the 'blueprint' in nature is a set of instructions which are dependent on a particular environmental context for their interpretation. Our present search to go beyond the 'blueprint' in architecture and to formulate a coded set of responsive instructions (what we call a 'genetic language of architecture') may yield a more appropriate metaphor. It may provide at least a model of how such a form-generating process might work, even if it is not a direct parallel of the way in which nature itself generates form.
Examples of the architectural analogy turn up in every field. For botanists, too, the concept of the architectural model has provided a powerful tool for studying plant form and structure:'The architectural model is an inherent growth strategy which defines both the manner in which the plant elaborates its form and the resulting architecture'.It is ironic that architectural theory actually lacks the methodological incisiveness which these reverse analogies imply.
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Intentionality
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Intentionality
Although evolution operates without preknowledge of what is to come - that is, without design - the seemingly purposeful construction of living things makes it tempting to apply the idea of 'design' to natural forms. On this basis, Bishop William Paley argued that since the existence of something as complex as a watch implied the existence of a watchmaker, the infinitely greater complexity of nature had necessarily to imply the existence of a creator. Richard Dawkins countered with the 'Blind Watchmaker' argument, contending that the blind forces of Darwinian natural selection alone were sufficient explanation for the complexity of natural forms. But Dawkins in turn has resorted to anthropomorphism, attributing 'selfish' tendencies to genes.
The tendency to invest nature with vitalist forces is common in both science and poetry. In the framework of our analogy, we will sometimes apply the word 'design' to nature for convenience of expression: we will also apply it to our new model with purposeful intent. To us the connotations of the term 'design' are very different from the norm: when we 'design', we are clear in our intentions, but perhaps 'blind' to the eventual outcome of the process that we are creating. This 'blindness' can cause concern to those with traditional design values who relish total control. It can alarm those who feel that what we are proposing might get out of control like a computer virus. However, we remain convinced that the harnessing of some of the qualities of the natural design process could bring about a real improvement in the built environment.
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Sources of inspiration
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Sources of inspiration
A clear distinction is intended between sources of inspiration and sources of explanation. When natural science is used for explanation or illustration, it is essential that the science is correct and that the analogy is valid. But when it is used for inspiration and as a take-off point for thought experiments, it matters less, and misunderstood or even heretical ideas can provide much imaginative stimulus.
It is important to differentiate between the nature of different kinds of theories. Lionel March has written: 'Logic has interests in abstract forms. Science investigates extant forms. Design initiates novel forms. A centeric hypothesis is not the same thing as a design hypothesis. A logical
proposition is not to be mistaken for a design proposal. ln this context, ours is not a theory of explanation, but a theory of generation.
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The inspiration of nature.
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The inspiration of nature.
The perfection and variety of natural forms is the result of the relentless experimentation of evolution. By means of profligate prototyping and the ruthless rejection of flawed experiments, nature has evolved a rich biodiversity of interdependent species of plants and animals that are in metabolic balance with their environment. Whilst vernacular architecture might occasionally share some of these characteristics, the vast majority of buildings in our contemporary environment most certainly do not.
Our analogy of evolutionary architecture should not be taken just to
imply a form of development through natural selection. Other aspects of evolution, such as the tendency to self-organization, are equally or even more significant. Natural processes such as metabolism and the operation of the laws of thermodynamics are central to our enquiry, as are the general principles of morphology, morphogenetics and symmetry-breaking, which are introduced in the next section.
Charles Darwin established a new world which broke away from the Newtonian paradigm of stability - a world in a continuous process of evolution and change. Modern physics now describes a world of instability. Ilya Prigogine has discovered new properties of matter in conditions that are far from equilibrium, revealing the prevalence of instability which is expressed by the phenomenon of small changes in initial conditions leading to large amplifications of the effects of the change
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Natural and artificial models
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Natural and artificial models
The modelling of these complex natural processes requires computers, and it is no coincidence that the development of computing has been significantly shaped by the building of computer models for simulating natural processes. Alan Turing, who played a key role in the development of the concept of the computer (the Turing Machine), was interested in morphology and the simulation of morphological processes by computer-based mathematical models. The Church-Turing hypothesis stated that the Turing Machine could duplicate not only the functions of mathematical machines but also the functions of nature. Von Neumann, the other key figure in the development of computing, set out explicitly to create a theory which would encompass both natural and artificial biologies, starting from the premise that the basis of life was information.
A significant example of this dual approach in terms of our genetic model is John Holland's Adaptation in Natural and Artificial Systems. Holland starts by looking for commonality between different problems of optimization involving complexity and uncertainty. His examples of natural and artificial systems range from 'How does evolution produce increasingly fit organisms in highly unstable environments?' to 'What kind of economic plan can upgrade an economy's performance in spite of the fact that relevant economic data and utility measures must be obtained as the economy develops?'
Although Holland suggests that such problems have no collective name, they seem to share a common concern with questions of adaptation. They occur at critical points in fields as diverse as evolution, ecology, psychology, economic planning, control, artificial intelligence, computational mathematics, sampling and inference. To this list we must now add architecture.
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Artificial life
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Artificial life
In nature it is only the genetically coded information of form which evolves, but selection is based on the expression of this code information in the outward form of an organism. The codes are manufacturing instructions, but their precise expression is environmentally dependent. Our architectural model, considered as a form of artificial life, also contains coded manufacturing instructions which are environmentally dependent, but as in the real world model it is only the coded script which evolves.
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Generative systems
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Generative systems
An essential part of this evolutionary model is some form of generative technique. Again this is an area charged with problems and controversy. The history of generative systems is summarized by William Mitchell, who maps out a line from Aristotle to Lull through the parodies of Swift and Borges. After tracing back the use of generative systems in architectural design to Leonardo's study of centrally planned churches and Durand's Precis des Lecons d'Architecture, he outlines the concept of 'shape grammars', or elemental combinatorial systems.
From our point of view, there are several problems with this approach. All of these generative systems are essentially combinatorial or configurational, a problem which seems to stem from Aristotle's description of nature in terms of a kit of parts that can be combined to furnish as many varieties of animals as there are combinations of parts. Fortunately, nature is not actually constrained by the limitations implied by Aristotle.
Mitchell regards architectural design as a special kind of problem-solving process. This approach has limitations which he recognizes in principle. First, it assumes we can construct some kind of a representation which can achieve different states that can be searched through for permutations corresponding to some specified criterion (the criterion of the problem). Unfortunately for this goal-directed approach, it is notoriously difficult to describe architecture in these terms, except in the very limited sense of an architectural brief to which there are endless potential solutions. The other problem is that any serious system will generate an almost unmanageable quantity of permutations.
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Problems with industrialization
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Problems with industrialization
A problem arose in the sixties when architecture started toying with new design processes, taking up a particular form of component-based rationalization and methodology which embraced a generic approach, modular coordination and a perception of construction as a kit of parts. For despite rhetoric to the contrary, the architectural profession - and the construction industry as a whole - have failed to learn from developments in the aircraft, automotive and shipbuilding industries. Construction remains labour-intensive: it has never made the transition to a capital-intensive industry with adequate research and development capabilities. It has been left largely to individual architects to take the risk of performing experimental and innovative prototyping in an uncoordinated and romantic or heroic manner. The ensuing (inevitable) failures have been catastrophic for both society and the architectural profession. The nostalgic inclinations of some to return to a previous era are an equally inadequate response, at every level, to the current predicament. The archetypes of the past do not reflect the changing demands of society, the realities of the construction industry, or the pressing need for environmentally responsible buildings.
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Post-industrialization
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Post-industrialization
Architecture is not the only field to be concerned with these problems. In industrial design the all-embracing concept of mass production for a homogeneous international market has given way to a search for a new flexibility in design and manufacture. The distinguishing characteristic of this approach is that it focuses on the dynamic processes of user experience rather than on physical form. Or, in John Thackara's words, design is now 'beyond the object'.
Industrial production used to be associated with high tooling costs and very large production runs. This is now changing because the computer has paved the way for what I have called 'the electronic craftsman'. The direct relationship between the designer at the computer console and the computer-controlled means of production potentially means not just a dramatic reduction in the production costs of the tools for mass production, and thus shorter economic runs, but a one-to-one control of production and assembly equipment. This is effectively a return to one-off craft technology, but with all the capability of the precision machine tool.
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Post-industrialisation
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Post-industrialisation
As Charles Jencks describes it: 'The new technologies stemming from the computer have made possible a new facility for production. This emergent type is much more geared to change and individuality than the relatively stereotyped productive processes of the First Industrial Revolution. And mass production, mass repetition, was of course one of the unshakeable foundations of Modern Architecture. This has cracked apart, if not crumbled. For computer modelling, automated production, and the sophisticated techniques of market research and prediction now allow us to mass produce a variety of styles and almost personalized products. The results are closer to nineteenth-century handicraft than the regimented superblocks of 1965.'
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The environmental case
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The environmental case
Natural ecosystems have complex biological structures: they recycle their materials, permit change and adaptation, and make efficient use of ambient energy. By contrast, most man-made and built environments have incomplete and simple structures: they do not recycle their materials, are not adaptable, and they waste energy. An ecological approach to architecture does not necessarily imply replicating natural ecosystems, but the general principles of interaction with the environment are directly applicable.
The construction industry is a significant consumer of raw materials and of the energy required to process, transport and assemble them. Buildings in use are even more significant consumers of energy for heating and cooling. An ecological approach would drastically reduce construction energy and materials costs and allow most buildings in use to export energy rather than consume it.
While there is a growing awareness of the importance of environmentally and ecologically sound design amongst both architects and enlightened clients there is still no comprehensive design theory and few built examples of an ecological architecture. The solution to our environmental problems may lie in relating architecture to the new holistic understanding of the structure of nature.
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Responsive environments...
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Responsive environments...
Another important issue for our model of an evolutionary architecture is that it should be responsive to evolving in not just a virtual but a real environment. In his article, 'The Design of Intelligent Environments', Warren Brodey proposed an evolutionary, self-organizing, complex, predictive, purposeful, active environment. He asked: can we teach our environments first complex, then self-organizing intelligence which we can ultimately refine into being evolutionary? These issues preoccupy us too.
...and soft architecture
Brodey went on to describe in enthusiastic terms some of the hypothetical implications of intelligent environments, and to introduce the concept of 'soft architecture'.
The idea of a soft, responsive architecture also preoccupied Nicholas Negroponte who suggested that the design process, considered as evolutionary, could be presented to a machine, also considered as evolutionary, to give a mutual training resilience and growth. Negroponte placed high expectations first on computer hardware, then on software through artificial intelligence. Neither delivered any answers.
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The role of the computer
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The role of the computer
Christopher Alexander dismissed the use of computers as a design aid: 'A digital computer is, essentially, the same as a huge army of clerks equipped with rule books, pencil and paper, all stupid and entirely without initiative, but able to follow exactly millions of precisely defined operations... In asking how the computer might be applied to architectural design, we must, therefore, ask ourselves what problems we know of in design that could be solved by such an army of clerks ... At the moment, there are very few such problems.
Our evolutionary approach is exactly the sort of problem that could be given to an army of clerks - the difficulty lies in handing over the rule book. Much of this text concerns the nature of these rules and the possibilities of developing them in such a way that they do not prescribe the result or the process by which they evolve.
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The electronic muse
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The electronic muse
I see computers not as an army of tedious clerks who will thwart all creativity with their demands for precise information, but as slaves of infinite power and patience. However, computers are not without their dangers. If used unimaginatively, they have a tendency to: dull critical faculties, induce a false sense of having optimized a design which may be fundamentally ill conceived, produce an atmosphere where any utterance from the computer is regarded as having divine significance, distort the design process to fit the limitations of the most easily available program, distort criticism to the end-product rather than to an examination of process, and concentrate criticism and feedback on aspects of a problem which can be easily quantified.
'Imaginative use' in our case means using the computer - like the genii in the bottle - to compress evolutionary space and time so that complexity and emergent architectural form are able to develop. The computers of our imagination are also a source of inspiration - an electronic muse.
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The Role of Human Creativity
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The Role of Human Creativity
One of the world's leading exponents of neural networks, Igor Aleksander, is also very conscious of the unique capabilities of the human brain. He reminds us that it is extraordinarily good at making guesses based on experience, at retrieving knowledge from memory without the need for exhaustive searches, at perceiving analogies and forming associations between seemingly unrelated items. These aspects of intuition, perception and imagination are the traditional creative engines for architectural ideas. While the model of architectural creativity proposed by this text departs in many ways from the traditional model, it still relies on human skills for the essential first step of forming the concept. The prototyping, modelling, testing, evaluation and evolution all use the formidable power of the computer, but the initial spark comes from human creativity.
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Problems of complexity
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Problems of complexity
The 'sheer imponderable complexity of organisms' overwhelms us now as surely as it did Darwin in his time. The developmental processes of nature inevitably lead to complexity, but they work with simple building blocks and an economy of means to achieve complexity in a hierarchical manner. The coding of all natural forms in DNA is achieved with just four nucleotides, which in turn use just twenty triplets to specify the aminoacids that manufacture protein. The hierarchical structure of living systems is analysed by James Miller on seven levels: cell, organ, organism, group, organization, society and supranational system. These are taken down into nineteen critical subsystems which appear at all levels. This hierarchical and self-similar description applies also to organisms and social systems, which are seen as part of the same continuum.
In the next section I shall examine polyautomata in order to show that even very simple local rules can generate emergent properties and behaviour in a way apparently unpredicated by the rules. Collections of small actions ripple upwards, combining with other small actions, until a recognizable pattern of global behaviour emerges. When a certain critical mass of complexity is reached, objects can self-organize and self-reproduce in an open-ended fashion, not only creating their equals but also parenting more complicated objects than themselves. Von Neumann recognized that life depends upon reaching this critical level of complexity. Life indeed exists on the edge of chaos, and this is the point of departure for our new model of architecture.
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The new model of architecture
Down to page [NCSA Mosaic users only]
The new model of architecture
There is so far no general developed science of morphology, although the generation of form is fundamental to the creation of all natural and all designed artefacts. Science is still searching for a theory of explanation, architecture for a theory of generation - and it is just possible that the latter will be advanced before the former. In other words, form-generating models developed for architectural purposes (or based on unorthodox or incorrect scientific views) may be valuable if they model a phenomenon that scientists are seeking to explain.
In a modest way some contribution has already been made. Many papers relating to this work (particularly on computing and computer graphics) have been enthusiastically received at international conferences and cited in further publications. Many of the resulting graphics techniques are now an integral part of the computer programs used in architectural offices. If taken much further, this could contribute to the understanding of more fundamental form-generating processes, thus repaying some of the debt that architecture owes the scientific field. Perhaps before the turn of the century there will be a new branch of science concerned with creative morphology and intentionality.
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The urge for a unified theory
Down to page [NCSA Mosaic users only]
The urge for a unified theory
In the meantime the approach of the end of the century is signalled by a frantic scramble in all fields to formulate a holistic view of the universe - the great unification theory, or GUT. In the natural sciences this takes the form of two juxtaposed tendencies. One is to embrace everything under the umbrella of evolution (or at least evolution in the form of neo-Darwinism). Evolution of the chemical elements, evolution of physical constants, evolution of information, cultural evolution - evolutionary theory is somehow made to explain all phenomena. The other tendency is to recruit all other developments in science, such as self-organizing systems, to expand the theory of evolution to make a new meta-theory.
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The urge for a unified theory
Down to page [NCSA Mosaic users only]
The urge for a unified theory
Overall there is a tendency to deal with complexity, chaos and catastrophe in the same way; to treat natural and artificial systems equally. The optimistic view is that the current debate about the possibility of a new holistic understanding of nature and science will make a significant contribution to current environmental and social problems. This text hopes to underline the importance of these issues. The pessimistic view is that the urge for this holistic understanding is offset by man's desperately myopic determination to maintain his superiority as a species. As each criterion for uniqueness turns out not to be unique after all, a new twist is applied. First language was considered to be unique, then it was the (more difficult to prove) capacity for abstract thought. The ability to use tools was considered unique until it was demonstrated that other species used tools, and then the criterion became the making of tools ... and so on ad absurdum. What is the problem? Perhaps man's only unique attribute is a self-conscious obsession with uniqueness. And for what is this supposed uniqueness and superiority used? For the mass murder and torture of his own species, for the keeping of other species under atrocious conditions as a living larder, for the deliberate and conscious destruction of the non-renewable resources and fragile ecosystem of our planet. Homo sapiens is arguably the only species to carry out these acts conscious of the fact that it is possible to behave differently.
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As early as 1969 Charles Jencks was predicting that biology would become the major metaphor for the 1990s and the source of the most significant architectural movement this century the Biomorphic School. See C. Jencks, Architecture 2000: Predictions and Methods (Studio Vista).
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A critical overview of biological analogies is given in P. Steadman, The Evolution of Designs: Biological Analogy in Architecture and the Applied Arts (Cambridge University Press 1979).
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D. Barthlemy et al, 'Architectural Concepts for Tropical Trees' in Holm Nielson et al (eds.), Tropical Forests (Academic Press 1989).
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W. Paley, Natural Theology, or Evidences of the Existence and Attributes of the Deity Collected from the Appearance of Nature (Oxford)
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R. Dawkins, The Blind Watchmaker (Longman 1986) and The Selfish Gene (Oxford University Press 1976).
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L. March (ed.), The Architecture of Form (Cambridge University Press 1976)..
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G. Nicolis and I Prigogine, Exploring Complexity (Freeman 1993).
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J. Holland, Adaptation in Natural and Artificial Systems (University of Michigan Press 1975).
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W. J. Mitchell, The Logic of Architecture - Design, Computation and Cognition (MIT Press 1990).
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These difficulties stem largely from the views of Herbert Simon as expressed in The Sciences of the Artificial (MIT Press 1969), an exploration of the problem of complexity with particular reference to artificial (man-made) systems. While Simon's views on the inevitability of a hierarchical strategy in nature have been influential in the formulation of our own theories, his scientific method does not recognize the need for a generating concept when approaching design, and as a consequence design has come to be misunderstood as a problem-solving.
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M Pawley, Theory and Design in the Second Machine Age (Blackwell 1990).
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C.T. Mitchell, Redefining Designing (Van Nostrand 1993).
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J. Thackara, Design After Modernism (Thames and Hudson 1988).
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C. Jencks, The Language of Post-Modern Architecture (Academy Editions 1987).
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In 1972 Alex Pike and I made a presentation to the Royal Institute of British Architects Annual Conference, 'Designing for Survival', which emphasized the need for a responsible approach to energy and materials. Although there was some genuine interest in resource problems, it was clear that it was the survival of the profession, not of the planet, which preoccupied most delegates. It is ironic that if architects had seized the initiative at this time and formulated a comprehensive energy policy, they might have ensured a future role for the profession. Instead the chance was wasted with a 'Long life, loose fit, low energy' campaign motivated more by politics than by a serious attempt to address the issue. See J.H. Frazer and A. Pike, 'Simple Societies and Complex Technologies' in Designing for Survival - RIBA Annual Conference (Lancaster 1972) and RIBA Journal, September 1972, pp. 376-7.
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W. M. Brodey, 'The Design of Intelligent Environments: Soft Architecture', Landscape, autumn 1967, pp. 8-12.
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N. Negroponte, The Architecture Machine (MIT Press 1970). Negroponte now runs the Media Lab at the MIT School of Architecture.
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C. Alexander, 'The Question of Computers in Design', Landscape, autumn 1967, pp. 8-12.
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See J. H. Frzer, 'The Use of Computer-Aided Design to Extend Creativity' in H. Freeman and B. Allison (eds.) National Conference Art and Design in Education, electronic proceedings (NSEAD Brighton 1993).
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I. Aleksander and H. Morton, An Introduction to Neural Computing (Chapman and Hall 1990).
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This discussion is expanded in J. H. Frazer and J. M. Frazer, 'Design Thinking: Creativity in Three Dimensions' in Creative Thinking: A Multifaceted Approach, conference proceedings (Malta University Press 1994) and J. H. Frazer, 'The Architectural Relevance of Cybernetics' Systems Research, vol. 10, no. 3, pp 43-4.
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S. A. Kauffman, The Origins of .Order: Self-Organization and Selection in Evolution (Oxford University Press 1993)
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J. Miller, Living Systems (McGraw-Hill 1978).
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Examples of the holistic view can be found in chemistry: S.F. Mason, Chemical Evolution: Origin of the Elements, Molecules, and Living Systems (Clarendon Press 1991); in physical constants: R. Sheldrake, The Presence of the Past (Collins 1988), in information: S. Goonatilake, The Evolution of Information: Lineages in Gene, Culture and Artefact (??nter Press 1991 ); and in culture R Dawkins, The Selfish Gene (Oxford University Press 1976).
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On complexity, chaos and catastrophe see respectively: G. Nicolis and l. Prigogine, Exploring Complexity(W.H. Freeman 1989); I. Prigogine and l. Stengers, Order Out of Chaos: Lan's New Dialogue with Nature (Bantam 1984); and R. Thom, Structural Stability and Morphogenesis (Benjamin 1972).
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