Ecology and the Fractal Mind in the New Architecture: a Conversation.

By: Victor Padrón

B. Sc. (Cum Laude) Universidad Central de Venezuela; Ph. D. University of Minnesota.

Professor of Mathematics at the Universidad de Los Andes, Facultad de Ciencias, Departamento de Matemáticas, Mérida 5101, VENEZUELA.

Visiting Professor of Mathematics at the University of Texas at San Antonio, San Antonio, Texas 78249, USA during 1998-1999.

E-mail: padron@ciens.ula.ve

and Nikos A. Salingaros

B. Sc. (Cum Laude) University of Miami; Ph. D. State University of New York at Stony Brook.

Professor of mathematics at the University of Texas at San Antonio, Division of Mathematics, San Antonio, Texas 78249, USA.

E-mail: salingar@sphere.math.utsa.edu

 

This conversation was published electronically by RUDI -- Resource for Urban Design Information on March 2000.

  1. Fractals
  2. Complexity and fractal boundaries
  3. Creative freedom
  4. Universality
  5. Jungian archetypes
  6. Ecology
  7. The fractal mind
  8. Our vanishing heritage
  9. The collective mind
  10. Bibliography

Keywords

Fractals - Architecture - Mind - Urban Design - Complexity - Evolutionary Psychology - Ecology - Cognitive Rules

 

1. Fractals

Nikos Salingaros (NS): For the past few years, I have been applying the analytic thinking of a scientist to find basic laws for architecture and urbanism, following the lead of my friend, the brilliant architectural theorist Christopher Alexander. The results derived so far show that a building, or city, is subject to the same organizational laws as a biological organism and a complex computer program. The New Architecture depends upon scientific rules rather than stylistic dictates. Using these rules, we can create new buildings that duplicate the intensely positive, nourishing feelings of the greatest historical buildings, without copying neither their form nor their style.

Great buildings of the past, and the vernacular (folk) architectures from all around the world, have essential mathematical similarities. One of them is a fractal structure: there is some observable structure at every level of magnification, and the different levels of scale are very tightly linked by the design. In contradistinction, modernist buildings have no fractal qualities; i.e., not only are there very few scales, but different scales are not linked in any way. Indeed, one can see an unwritten design rule in the avoidance of organized fractal scales.

Victor Padrón (VP): The interest in fractal objects was originally motivated by the study of complex dynamical systems at the beginning of this century; in the work of the French mathematicians Henri Poincaré, Pierre Fatou, and Gaston Julia. But it was not until the 1970's and early 1980's, with the rapid development of techniques in computer graphics, that Benoît Mandelbrot and other mathematicians began to observe and study these fascinating structures, which are full of involuted spaces and surfaces, and in which different self-similar scales are found. This type of structure exists in abundance in nature.

From the distribution of foliage on a tree, to the complex neural network of our nervous system; all of these can be better described with the help of Fractal Geometry. In the human body, the fractal design of its components like the circulatory system, nervous system, the bronchi, and the folds of the brain allow our organism, in a limited space, to greatly extend its contact surfaces in order to carry out the innumerable and complex functions of interchange that make life possible. This optimal structure must surely be motivated by evolutionary reasons.

NS: We also see this type of structure in traditional buildings. All the folk architecture built by people around the world tends to have fractal properties. I believe that our mind is "hard-wired" to construct things in a certain way, so inevitably we build fractal structures. Most great creations of humankind go far beyond strictly necessary structure; we feel a need to generate certain types of forms and geometrical interrelationships. Only when influenced by some style do we depart from what comes naturally to us. Cities -- at least the most pleasant ones -- are fractal. Everything, from the paths and streets, to the shape of façades and the placing of trees, is fractal in the great cities such as Paris, Venice, and London. This has been measured mathematically by people like Michael Batty and Pierre Frankhauser.

 

2. Complexity and fractal boundaries

NS: Fractals have two related characteristics: they show complexity at every magnification; and their edges and interfaces are not smooth, but are either perforated or crinkled. A fractal has some connective structure at different scales. Historical cities are richly structured at every magnification, whereas contemporary cities enhance the largest scale but suppress everything else.

There are no straight lines in fractals. A smooth flat plane has no substructure, and is therefore non-fractal. Colonnades, arcades, rows of narrow buildings with cross-paths all correspond to a permeable membrane with holes to allow interchange -- this is one type of fractal. When an urban interface is not permeable, it is convoluted, like a crinkly meandering river or folded curtain. A building edge couples by interweaving with its adjoining space, creating another type of fractal. This folding arises spontaneously as a natural consequence of urban forces; for example, portions of buildings that grow outwards onto the pavement. Despite the obvious threat to public space, it seems that this process represents a natural evolution of the built boundary into a more stable fractal form.

VP: There is a clear tendency to perceive the complexity of a city as being inversely proportional to its large-scale order. The more legible a city is, with a clear rectangular grid built for car traffic, the less complex it is. Nevertheless, diagonal and shorter paths allow someone to go more directly to their destination, but at the same time can cause disorientation. We are used to the rigid notion of a North-South orientation, but this actually reduces the connectivity possibilities in a city. It makes a city apparently more easy to read, but it also cuts the possible paths of connection. After all, a diagonal path is shorter than a stepped rectangular path. When a city's organized complexity is reduced, it is difficult for a person to connect to it.

NS: I'm sure that that occurs because what we understand as order in a city has to do with the largest scale, whereas human beings connect to the human scales. The most important urban structures exist on much smaller scales, going right down to the detail in the materials.

VP: Also, I think this perception is based on a rigid notion of order inflicted upon modern society by a misinterpretation of natural order. The rigid notion of science that partitions reality into segments has somehow shaped the 20th century mind. While science has evolved to study complex structures, our mind is still stuck with the Cartesian model. There is an underlying order in many of those apparently chaotic systems that we observe in nature. We should seek this type of order for our cities: an order that enhances life by promoting a rich network of interconnected paths at different levels of scale. In a way, this is like a call to go back to nature, and for our mind to be more connected to how nature actually shapes itself and works.

We have been trained -- through our education -- not to want to see the fractal qualities of nature. But they are there, surrounding us. We should expect a city that is closer to nature to share the same type of property; that is, of organized complexity.

NS: One of the stated aims of modernism was to eliminate any architectural interface with fractal dimension. These were replaced by long, straight roads, and reinforced with the strict alignment of buildings. The reason given was to clean up the perceived messiness of older cities; yet that messiness was really the organized complexity that made them alive.

Imagine the range of fractal interfaces as generated by the following mechanical model. Take a wire and compress it longitudinally, fairly evenly along its entire length. It will buckle and crinkle, creating a fractal boundary of dimension greater than one. (The dimension is more than one because the line fills up some area with its undulations, and would have dimension two if it filled in all the area). If you then pull it to straighten it out, again evenly along its length, it will first straighten, and then it will break into aligned pieces so as to be able to extend its length. This creates a fractal line with fractal dimension less than one (i.e., a line with holes in it that is closer to a collection of points having dimension zero than a continuous line of dimension exactly one). Of all possible lines one can create in this way, the perfectly smooth, straight line has a very low probability of occurring; and yet, that is what architects try to enforce all over the world.

Traditional villages show an infinite range of fractal interfaces between their building fronts and street. There, one finds gentle curves that are crinkled on the small scale, and lines that are only approximately straight on the large scale. Even in formal planning, a curved structure such as the Circus and Royal Crescent at Bath arises from compression, and so it is crinkled on the human scale. The opposite is the colonnade and arcade, which comes from tension, and is straight. Even though there exist curved colonnades, such as St. Peter's, I believe that they are far less successful than structures that follow this model.

Another point is the scale on which the fractal dimension is measured: great urban environments use fractals on the human scale, whereas dead environments deliberately remove them. For example, a colonnade is useful when the intercolumn spaces are roughly between 1m and 3m, i.e., comparable to the human scale of movement. Monstrous spaces of more than 5m between columns alienate the user. For this reason, flat, smooth buildings that are aligned and spaced 20m apart may resemble a fractal line on paper, but they so far exceed the human scale as to be totally alienating. They are not fractal on the human scale, which is what is important.

VP: The degree to which a city becomes more alive is measured by how much it is allowed to evolve like a living organism; to reach its natural organized complexity. The spaces and edges are designed by people's activities, and these boundaries and interfaces can evolve in time.

 

3. Creative freedom

VP: It is not difficult to concede that our psyche, which has its assumptions built into the brain, has an essentially fractal structure as well. Nevertheless, with our fractal brains we also have the capability and the freedom to create architectural forms that do not follow a mathematical pattern at all. It seems like the New Architecture might limit artistic freedom, because it requires buildings to conform to a strict set of design laws. How do you justify telling people what they can or cannot do?

NS: Freedom to create should be tempered with the restriction that it does not damage anything. Unfortunately, the creations of some architects damage the world in a number of ways. One cannot go around spreading Plutonium or carcinogens in the environment, but that is analogous to what many post-war architects and urbanists have been doing. Civilization must be protected from such hazards, and it requires a necessary restriction on so-called artistic freedom. People are playing silly games with our environment, and they don't realize the terrible consequences of their actions. They protest violently when their little game is threatened.

Anyway, the idea of architectural creativity in modern architecture is a myth. There is no freedom; every design and building is judged by how closely it follows certain rigid prototypes established in the 1920's. If it doesn't do so, it is attacked by the architectural profession, and is ridiculed in the periodicals and the press. Critics of the strict modernism of stark cubes have not offered anything better; what we see now is a switch to the opposite mode of unpleasantness -- from boring cubes to random, unbalanced, and psychologically alarming forms. In architecture and urbanism today no questioning of dogma is tolerated.

The solution space of the New Architecture -- i.e., an architecture that respects fractal forms -- is infinite, and is vastly larger than the extremely narrow one-dimensional solution space of modernism and post-modernism. It includes all of the greatest buildings of the past, as well as a universe of exciting new buildings we can build in the future. You can hardly call this "restrictive". The negative reaction of most contemporary architects to the New Architecture follows because their solution spaces don't intersect. That condemns the majority of what is being built today, which naturally worries them. Nevertheless, this judgment is in keeping with most ordinary people's feelings.

 

4. Universality

VP: How universal are the laws governing the New Architecture? There could be some topical dependence that does not translate over into other cultures or regions. Art objects are usually shaped by the ideas of the people who make them.

NS: The universality of art is easy to appreciate. When you go to Japan and see what the Japanese people consider beautiful, displayed in their museums, I think you will like at least 85% of the objects. Only a small fraction is going to be culture-specific. In the same way, the Japanese appreciate other people's folk art, even though it has no connection to their own. Note also that certain art forms, like Ikats (a form of weaving), have evolved independently in Indonesia, South America, and Central Asia. This argues for a common root of what is pleasing to human beings.

VP: You are pointing here to the underlying structure of the human mind, and how our physical environment, cities and buildings, interact with this structure in a healthy or otherwise destructive fashion. It seems to me that what is required as a basis for this proposition is the development of what one may call a fractal theory of the human psyche.

 

5. Jungian archetypes

VP: The prominent psychologist Carl Jung, during the development of his theory of the collective unconscious, hypothesized that the aesthetic experience in art consists of the elevation of archetypal images towards the conscious mind, by means of stimuli generated by artistic objects. These archetypal images are deposited in the collective subconscious. Jung proposes that, just as the human body conserves the traces of our mammalian ancestors, the human mind maintains images imprinted in the deepest part of our psyche; structures and models that were captured during our evolutionary process. Our instinctive judgments are directed by universal archetypes, which were configured by the interaction of human beings with their surroundings during the distinct stages of our evolution.

These ideas are supported by current research in evolutionary biology, brain physiology and cognitive science. These disciplines come together in what we may call evolutionary psychology, providing a picture of how the mind evolved over millennia to adapt to the changing world. There is a continuous link from the earlier unconscious action routines of other animals, to the development of language and the conscious mind.

NS: These archetypes must be more like connective templates than overall forms. The mind encodes an image by means of internal relationships, as do computers. It's all in the interconnections, and that's what we have evolved to recognize almost instantly.

I don't necessarily want to analyze Art, even though it suffers from the same malaise, because architecture is a far more pressing problem. Even though most of what is called art nowadays is unworthy of the name, you can in most cases choose to ignore it. You can throw away a painting you don't like, but you are stuck with a building for many years. Ugliness in buildings is more permanent, and transforms society because it influences you throughout your entire life.

Architecture is actually not as important in its total impact as Urbanism. The simplistic modernist ideology has destroyed our cities, by removing urban complexity. That is analogous to trying to simplify an organism by removing pieces of its body that you don't understand -- you will be left only with its skeleton. We can survive in ugly buildings, but our life has been totally changed by the shape of new cities, and for the worse. Society is affected by how people can interact on a daily basis, and that depends on the networks, roads, and city structure.

VP: It seems to me that there has also been some sort of break between art and architecture, since we rarely see murals in and on buildings. In South America, we have a tradition of beautiful murals on important buildings. We observe that now, murals have been replaced by large sculptures, which give a very different effect.

NS: The modernist aesthetic does not allow the blending of paintings such as murals with our built environment. Indeed, representational paintings and decoration of any kind are explicitly forbidden. This reminds me of the Iconoclastic movement in the Byzantine empire, which caused the destruction of all Icons made before the 9th Century. Modernism has neither an artistic nor a scientific basis. It originated as a reaction against class dominance and political oppression in the Austro-Hungarian empire. The world reacted to the horrors of the first world war by rejecting everything that society had valued prior to that catastrophe. That, however, did not solve things, as witnessed by the outbreak of the second world war soon afterwards. People today follow the modernist dictates without ever questioning where they came from.

Most architectural styles of the past were based on something, like materials or use, and then became formalized into a style, usually carried through even when materials and uses changed. Modernism is a political ideology, combining philosophical ideas of the 1920's. It is perhaps the only style in history that ignores the human use of buildings. Buildings should be shaped according to rules that can be justified on a logical and scientific basis, and not by some arbitrary dogma.

VP: You mean, then, that the New Architecture you propose represents a set of design rules that comes from science, and not from political ideas or other similar sources.

 

6. Ecology

VP: I see a gap in your description, since the New Architecture does not explicitly address ecological concerns. Those are, in my opinion, primary in shaping the environment in the 21st century.

NS: While the New Architecture does not address ecology per se, it does lay the groundwork for an ecological approach to planning and building. We have been discussing how scientific laws establish the connectivity of man to his environment, which occurs through fractal qualities of structures. Natural structures are fractal, whereas only traditional buildings are fractal. Modernism teaches us to eliminate fractal structures and to replace them with non-fractal built structures. This philosophy does not respect a tree or an older building. As soon as we realize that we connect only to fractal structures, we will reverse our priorities, and appreciate a tree more than a modernist glass cube. Only then will we think twice about replacing the former with the latter.

Today, there is a split in paradigm between builders, on the one hand, and environmentalists, on the other. In this highly polarized situation, each side thinks the other wrong. There is no common ground for dialogue. After decades of education that conditions us to worship "alien" forms, and destroy natural ones, most of us are taught to side with the developers of dead suburbs and inhuman downtown megatowers. We need to recognize what connects us to our world; after that is accomplished, the ecological message will be far easier to communicate.

Architecture and Urban Design are at an impasse, because the rules that students are taught in schools contradict the structural organization of living forms. The fractality of older cities has been deliberately erased in order to impose certain arbitrary stylistic rules. This has led to the philosophical, psychological, and physical separation of human beings from their environment. Protests from ordinary people that architects and urban planners are deliberately destroying comfortable and emotionally nourishing human environments have had little effect. We are building our cities into places that are hostile to human activities. Look at a contemporary city -- it fails miserably as an environment for children from infants to teenagers. Environmentalists increasingly blame architects for damaging the natural environment, but the damage extends far deeper.

For example, Art Nouveau buildings -- such as the Paris Metro entrances of Hector Guimard -- were ruthlessly destroyed, because they were testaments of a complex and sensual architecture. I tend to think that proponents of dead concrete blocks just couldn't allow people to see how a structure could really make one feel alive.

VP: We human beings are in many ways the synthesis of the universe, being the end result of an evolutionary process that improves structural complexity from inorganic, to organic, to intelligent levels. The ancient idea of the Eastern philosophers on the interconnection between the microcosm and macrocosm is acquiring rigor in our times with the scientific understanding of the universal laws of nature. The discovery of fractal geometry and its role in the description of a great variety of natural phenomena plays an important part in this process.

NS: That is also an idea present in ancient Greek philosophy. The link between macrocosm and microcosm was extremely important in philosophy, and influenced people's daily lives. This was true until very recently. Astrology -- and here I include all the mystical Mandalas of the East as well as the horoscopes of the West -- was the best expression of this connection available to the ancients. Astrology is now known to be unscientific, but it was in fact based on the limited science that those people knew.

Ecology is the study of connections between living beings and their environment. Everything: plants, animals, man, and the chemistry of the earth is connected into a highly complex, interdependent system. We see the system effects, since changing one component can influence the entire biosphere. Contemporary architecture, which strives to deny connections among its components as well as to human beings and natural forms, undoes the basis of ecology. It promotes a separationist mind-set that is inimical to the very concept of an interconnected system. I believe this to be at the root of why our age is so far from an ecological understanding.

 

7. The fractal mind

VP: There should be support from psychology for what defines a good building or city. The fractal structure of nature clearly follows from mechanisms of physical interaction and the evolution of matter. So, we could similarly infer that the structure of our psyche, the collective subconscious of Jung, is essentially fractal. This great reservoir of our ancestral memories have to be structured in the most economical way, not only to allow an almost unlimited capacity, but also with many interconnections to facilitate the free flux of information. What could be more suitable to this than a fractal structure?

It is also interesting to observe that the level of "complexity" of our mental structure is starting to play an important role in mental health. Recent investigations in what is known as "Emotional Intelligence" oppose the monolithic conception of measuring the IQ, and instead intimate at a complex and adaptable mental structure, with many open options. This is now proposed as being responsible for the success and happiness of an individual in our society. We see here a clear tendency towards a fractal conception of the human psyche.

All these ideas were anticipated in some way a long time ago by certain oriental cultures. For example, the Mantras and sounds of some musical instruments like Tibetan metal bowls are used not only in spiritual ceremonies and rituals, but also for curative purposes. They have the property of a great richness of overtones, and thus conform to a fractal scale of sonorities that are extremely agreeable to the ear.

NS: Unfortunately, the crucial experiments that will distinguish between buildings and urban environments that are either healing, or make you ill, have not yet been done. Environmental psychology is only just now starting to become an independent discipline. Also, the people who would fund experiments on the emotional appeal of structures don't want to do so, because it is upsetting to the architects. I have had papers rejected with the excuse that I need to produce experimental data: my response is that everyone feels these effects, so no experiments are necessary, although it would be good to have them for the record.

VP: In any case, I believe that the present state of action in interdisciplinary research between psychology, neurophysiology, evolutionary biology, neural networks, physics, and mathematics (to name only a few of the disciplines that come together in these studies) guide us unfailingly towards a structural conception of the human mind. This work is capable of describing phenomena not only inherent in the human conscience, but also in the subconscious, and should certainly help towards a better understanding of the body-mind relation, as well as the relation between our mind and environment.

Recently I read a very interesting book: "The Evolution of Consciousness" by R. Ornstein, a leading neuro-physiologist, on the subject of evolutionary psychology. The author mentions a study comparing students from Western cities, which contain many horizontal and vertical outlines in their designs, but few oblique ones, to a group of Cree Indians, whose houses contained lines in all orientations. The conclusion of the experiment is that the urban students had less acuity for oblique lines than the Indians did, which shows that the level of complexity of the urban environment has a corresponding impact in the level of complexity of the human mind.

NS: I don't want to use psychology for my arguments, or even philosophy, because they are too easily dismissed. Numerous wise people have condemned modernist architecture and urbanism for damaging the human habitat and psyche, yet they were all ignored. The only argument strong enough to counter the destruction of our environment (both built, and natural) is one that is based on hard science.

 

8. Our vanishing heritage

NS: There exist regions of the world today, which have older, coherent buildings and spaces. These include buildings as well as pieces of walls and architectural ornament that we connect to. They are in danger of becoming lost, because people don't realize their value to our civilization. People with newly-found wealth want to replace their heritage, and anything that looks old, because it reminds them of the past. The situation is entirely analogous to animal species becoming extinct because the last representatives are killed off. We cannot reconstruct a Dodo from a photograph; neither can we build living cities from photographs. The experience is a physical one, not a visual one. Most of us don't have any idea of what it feels like to be in a great building or urban space. As soon as those buildings and spaces are gone, we will have lost the last examples.

VP: I grew up in Caracas, which is a modern city, and had no idea of urban beauty. I still remember getting off the train when I arrived in Paris, and having a profound experience. It was not only visual and psychological -- it was physical, and a shock to my body. It moved me so much that I remember it today; it is one emotional experience that I can recall very vividly. I had no idea that materials and space could have such a positive effect on a person.

Today we have a historical museum in Caracas, in which there is a scale model of the city center as it was in the last century. Nothing is left standing today. Now that I have experienced great buildings and urban spaces, I can imagine what it must have been like to walk past those buildings -- and I feel like crying when I come out into the modern city. Young people, however, don't respond to this model in the same way; they think it is cute, but cannot understand what it represents, because they have never had a truly emotional spatial experience.

NS: My friend Alexander published three important books about twenty years ago. He argued from within the architectural establishment (being a professor of Architecture at Berkeley) for a more humane architecture, which captures those qualities lost in the buildings of our times. He expected to influence both academic and practicing architects, but did neither. Instead, his books became hits with the counter-culture, who were apparently the only ones sensitive enough to appreciate what he was saying.

I once gave a talk in Austin to a group of environmentally-conscious architects. Even though they invited me, and the talk was a success, I felt a certain hostility to me as a scientist coming from some counter-culture types. I am afraid that science has been terribly misused to promote the destruction of the environment. My hosts could not conceive that a scientist could help them, and how scientific analysis could support a holistic, environmental point of view. Today, the worst crimes on the environment are backed by pseudoscientific arguments: the misuse of statistics; rigid grid plans proposed by some planning authority; so-called efficiency studies that ignore all but a single variable; megastructures based on a "scientific" geometry of cubes, etc. All of this is a misapplication of poorly-understood scientific concepts. If one took the trouble to study these cases, then science would give the opposite conclusions.

 

9. The collective mind

VP: I am more optimistic. To me it seems extraordinary that Christopher Alexander's ideas on a more ecological and human architecture have been well received by anyone, and in such a positive way, at least within non-mainstream groups. Generally, innovative ideas that attack the establishment are difficult to communicate, let alone become accepted. I believe that the collective mind, just like the individual mind, is governed by a conservative instinct that protects it from "strange" elements. At the same time it is flexible, and eventually it evolves by incorporating new content. In a certain way, science plays the role of arbitrator. Nevertheless, it is clear that there are two sides to this process. On the one hand, there is a scientific ideal that seeks the truth; on the other hand, science can be manipulated, just as any ideology can, in the abuse of power.

These considerations bring us back to one of the central themes in our conversation. The dynamics of the multiple processes occurring in what we call the collective mind suggest something about its structure. The contents of this great universe of the mind (e.g., ideas and models) are inter-connected. We can envision the collective mind with multiple interconnections on many different levels, similar to the fractal structure of the neural system, as an enormous fractal. In their need to communicate the contents of their mind our ancestors developed spoken language. There succeeded writing, printing, photographs, and finally telecommunications. With each step in this progress, the collective mind becomes more complex and interconnected. Now, in the era of personal computers, the collective mind includes the Internet.

We can now see a possible explanation of why people spontaneously build structures that have fractal properties. Also the other way around, we can connect the fractal structure of the universe with the structure of the mind. We are affected by what we see. Our environment affects us, and this may well be why our mind is fractal; because our environment is fractal. Human beings have been surrounded by fractal structures for millions of years. A great deal of our mind's structure comes from this ancient relationship. It is only recently that we are surrounded by structures that are not fractal.

NS: And what do you think happens when we surround ourselves with a non-fractal environment?

VP: We are then destroying our natural correlation. We begin to lose the support from the environment that we normally use to build our own mental structure. We get confused by non-fractal structures and start losing the natural structure of the mind. As a consequence, we function differently. It is completely unknown what will happen to our mind in such a new, non-fractal environment. Fractal structures in nature do not arise arbitrarily; they usually obey some principle of functionality, like optimizing the interchange of resources through connections and contact surfaces. We need complexity in the mind in order to be healthy. I believe that a healthy mind is one that is presented with multiple options in any given psychosocial situation. It needs to be highly interconnected to be able to survive in our environment, and this is closer to a fractal structure than to a rigid geometry of empty forms.

 

Acknowledgement

NS was supported by a grant from the Alfred E. Sloan Foundation to study the scientific laws of architecture.

 

Bibliography

These conversations occurred during VP's stay in San Antonio, and are left as close as possible to their original, informal style. For this reason, references are not appropriate. Nevertheless, as NS has been strongly influenced by the work of Christopher Alexander, we list some of Alexander's important books:

  1. A Pattern Language (New York: Oxford University Press, 1977), with S. Ishikawa, M. Silverstein, M. Jacobson, I. Fiksdahl-King and S. Angel.
  2. The Timeless Way of Building (New York: Oxford University Press, 1979).
  3. The Linz Café (New York: Oxford University Press, 1981)
  4. A New Theory of Urban Design (New York: Oxford University Press, 1987), with H. Neis, A. Anninou and I. King.
  5. The Nature of Order (New York: Oxford University Press, 2000). (in press).

NS has published a series of supporting papers:

  1. "The Laws of Architecture from a Physicist's Perspective", Physics Essays 8 (1995): 638-643. (http://www.math.utsa.edu/sphere/salingar/Laws.html)
  2. "Life and Complexity in Architecture From a Thermodynamic Analogy", Physics Essays 10 (1997): 165-173. (http://www.math.utsa.edu/sphere/salingar/LifeandComp.html)
  3. "Theory of the Urban Web", Journal of Urban Design 3 (1998): 53-71. (http://rudi.herts.ac.uk/rudiments/urbanweb/urbanweb.htm)
  4. "A Scientific Basis for Creating Architectural Forms", Journal of Architectural and Planning Research 15 (1998): 283-293. (http://www.math.utsa.edu/sphere/salingar/SciBasis.html)
  5. "Urban Space and its Information Field", Journal of Urban Design 4 (1999): 29-49. (http://www.math.utsa.edu/sphere/salingar/UrbanSpace.html)