Science for Designers: Complex Adaptive Systems

 

By: Nikos A. Salingaros  & Michael Mehaffy

Today the world of design is in a position to benefit enormously from advances in sciences, mathematics and particularly, geometry—probably not in a way that many designers think. As humans we are remarkably good at conceiving the world as a collection of objects, their geometric attributes, and the ways they can be taken apart and re-assembled to do spectacular things (either perform marvelous tasks for us, or provide an aesthetic spectacle, or both). This way of designing underlies much of our powerful technology—yet as modern science reminds us, it’s an incomplete way. Critical systemic effects have to be integrated into the process of design, without which we are likely to trigger operational failures and even disasters.

Today we are experiencing just these kinds of failures in large-scale systems like ecology. As designers (of any kind) we must learn to manage environments not just as collections of objects, but also as connected fields with essential features of geometric organization, extending dynamically through time as well as space. This is a key lesson from the relatively recent understanding of the dynamics of “complex adaptive systems,” and from applications in fields like biology and ecology. At issue is not just avoiding failures. Though our designs can certainly be impressive, nature’s “designs” routinely put us humans to shame. No aircraft can maneuver as nimbly as an eagle (or a fruit fly, for that matter), and no supercomputer can do what an ordinary human brain does. The sophistication and power of these designs lies in their complex geometric structures, and more particularly, in the processes by which those structures are evolved and transformed within groupings or systems.


The ecosystem of a coral reef requires continuous mutual adaptation of individuals and species, like Yolanda Reef in Ras Muhammad nature park, Sinai, Egypt. Photo: Mikhail Rogov, Wikimedia Commons. We can readily see that in the natural world forms arise as adaptive evolutions that solve specific kinds of problems—an eye gathers information about predators and prey, a wing or leg allows rapid movement, and so on. Anatomical forms do not arise within one large undifferentiated collection; they develop as specific groupings of systems and sub-systems. These systems in turn relate to and comprise other, larger systems. The structural dynamics of systems are consequences of interactions between parts and wholes. This is a new science built upon a previous generation of biologists recognizing the adaptive processes of form generation, and their characteristic geometries—what is now known as “morphogenesis”. Pioneers like D’Arcy Thompson saw that living structures had characteristic groupings that were intimately connected to the processes by which they grew. Crucially, these pioneers came to see that formal and aesthetic characteristics were not separate, but were systems-specific geometric attributes. Over evolutionary history, organisms had learned to identify such attributes, the better to respond effectively to their environments. Our own capacity to experience beauty is, from an evolutionary point of view, just such a biological recognition of what is most likely to promote our wellbeing.



Soap bubbles form a complex pattern as a result of their mutual adaptation. It was not put in. Photo: Timothy Pilgrim, Wikimedia Commons.

What does this mean for designers, in concrete terms? It means that all the parts have to be mutually adapted to each other to an adequate degree, through a process of some kind. So let’s consider a general procedure for adaptive design, one that uses these new insights from systems theory. First, we will need to decompose a design problem so that it actually represents fundamentally distinct yet overlapping subsystems. Second, we will employ several alternative decompositions of the system into more tractable subunits or components. As is known since the work of complexity theorist Herbert Simon, a hierarchical complex system has several inequivalent decompositions. Connectivity dictates how to perform each of the problem decompositions based upon one different aspect of the entire system: the designer has to discover and give equal weight to connective components as well as to the structural components. Relations among objects are just as important as the objects themselves, and system decomposition in terms of relations makes that clear.



Six distinct ways (among an infinite number of possibilities) of partitioning a disk to implement radial sectors, or concentric rings, or linear strips, etc. In an analogous manner, we can decompose a system according to distinct conceptualizations, for example to emphasize the distribution of interior spaces, or the path structure, or exterior urban spaces, etc. Drawing by Nikos Salingaros. For example, designing a building involves at least five distinct system decompositions. These could be concerned with: (i) harmonizing the building’s exterior with its environment and avoidance of geometrical conflict, which of course includes adaptation to climate, orientation to the local solar and weather patterns, etc., (ii) connecting the site to the circulation present in its environment, (iii) shaping public spaces, from a sidewalk to one or more open plazas, (iv) planning interior paths, (v) identifying the interior spaces in relationship to each other. There could be other systems as well, based upon individual needs, conditions, and uses. Each of these problems requires a system decomposition that defines a distinct type of subsystem of the entire design. And each has to be addressed separately, at least initially. Of course, eventually everything will have to be recombined, and a professional with experience will in practice handle all of the subsystems simultaneously. But since this method is unusual for today’s designers, we offer this artificial separation to make the point of alternative decompositions. Our task as designers is to optimize the functions of each subsystem so that those functions support the whole system in which they are embedded, but do not impede any alternative system decompositions.

We require adaptive selection criteria that guide the design to converge to an overall coherence (which we help along but do not dictate). The final configuration converges neither to an “approved” image, nor to some fixed initial abstraction, but rather towards an emergent quality of the system itself as it adapts to generate strong internal and external coherence. The operational secret for achieving a tight connection of a design to its environment is to make as many design decisions as possible on the site itself. In this initial conception, no overall form has yet been decided! The procedure described here was developed by Christopher Alexander, following a method used by humankind throughout the ages for vernacular building. Such a procedure simply cannot be performed in the office, because it is fundamentally contextual. The design method relies upon on-the-ground experience. Only after key decisions about the dimensions, positioning, and geometry of the various subsystems have been taken in the actual setting using one’s imagination aided by physical props, then, this information can be transferred to a scale model, sketch, and computer screen.

Adaptive design’s principal aim is to facilitate the different components of a particular subsystem so they assemble themselves into a coherent subsystem. For example, the conditions and uses require specific internal paths, but there is freedom in connecting them into a network — this must be done in a way consistent with all the other system decompositions. Here is where the real novelty lies: we let each distinct subsystem develop according to rules for adaptation, and our role as designers is merely that of facilitator. Namely, we are not going to dictate its design using any preconceived ideas or images (a shocking suggestion for contemporary practitioners), only search for the possibilities that satisfy the constraints of use, site, environment, etc. In this way, the components we have to work with will, in a real sense, “assemble themselves”. This phenomenon is called self-organization — a very important topic that we discuss extensively in our essay “Frontiers of Design Science: Self-Organization”.

The result should still have a degree of roughness, for reasons that will become clear later. This procedure is repeated for each distinct subsystem to give us several subsystems that are more-or-less coherent within themselves. In the end, we superimpose and combine all the different subsystems into a coherent whole. Crucially, the distinct subsystems will engage in a way that makes functional sense. Again, we don’t impose our will, but simply facilitate an intimate union of all the subsystems. In the case of a building as discussed above, there will be at least five subsystems, and these will need to merge together.



Non-adaptive versus adaptive plans for a group of buildings: Left, the plan is only a formal geometrical idea; right, the plan reflects typical adaptations to several distinct systems of human needs, such as complex spatial volumes, movement, definition of usable urban space, connectivity on a human scale, etc. Drawing by Nikos Salingaros.

The final design will be a structural compromise among all the alternative system decompositions, which compete with each other in design space. It is important to accept and handle this “conflictual” component of design, which arises from the need to accommodate several distinct systems, each one of which has its own optimum, but which could very easily degrade another subsystem’s functionality. Thus, the intertwining of the distinct subsystems can only be achieved through each of the subsystems compromising to some extent. This is how the larger whole achieves an optimum configuration. This description might sound exotic—but something like this goes on all the time in natural systems. It’s the process by which the mitochondria adapt to the cell nucleus and vice versa, or the organisms within a reef’s ecology mutually adapt to one another. At our best, we do the same thing—or we let the natural processes around us do this for us. We “copy nature,” or we go through an “optimization cycle,” for example. But as we noted earlier, too often, we humans tend to treat the products around us as separated things of very limited function that we can choose to isolate or recombine at our whim, with little consequence. This is, functionally speaking, a mistake.

According to a key principle from systems theory, we can only treat systems as closed up to a point. Ultimately we have to see the ways in which all systems are partly open and inter-connected. Biological and ecological systems—of which we humans are ultimately an inseparable part—are open systems. A key lesson for designers of all kinds follows: Product design can’t really be separated from environmental design. We are all, in some sense, environmental designers, working in the human environment. Since every system is only partially closed, we have to find ways to work on these systems as open systems — that is, as parts of larger, optimizing wholes. Routine failure to do so has led to our ecological misfortunes.



Human places are systems of room-like structures that span many scales — literal rooms indoors, and then more room-like outdoor spaces. These systems are made to adapt well to our activities and needs (especially our need for privacy) and to be adaptable by users — we can close doors and windows, draw curtains, etc. On the right, a composite example of a typical mixed-use London street, photos by Michael Mehaffy.

This means we must come to see (and work on) these systems of spaces where we live as a fabric of connections between partially open sub-systems of spaces with geometric characteristics. As designers, our job is to weave together parts of this fabric into more life-supportive, continuous structures. We discuss the details of this structure elsewhere (in what is known as “place network theory”); but for now, we can think of this structure as a network of room-like structures, each with a membrane-like connection to the other spaces around it. (Think of rooms with doors and windows, gardens with gates and hedges, etc.) An important aspect of adaptive evolution is afforded to users in such environments. They give us the capacity to control the degree of stimulation and variety, to explore intricate and varying layers of space, to locate rich geometrical structures that users might find interesting and beautiful. We might elaborate on these structures as a way of clarifying them and making them more legible—or even more beautiful.

It is the freedom to evolve our environment (in part), thereby vastly broadening its functionality, which is missing from the deterministic approach of most contemporary architecture. As we alluded to earlier, research in environmental psychology reveals that such aesthetic characteristics are essential attributes of human wellbeing—they are not separate from this cellular, systemic structure of the human environment. The boundaries of different spaces become identifiable borders. And the geometrical centers become identifiable points around which local temporal symmetries might regularly appear. We might see regular patterns of repetition or alternation, or other characteristic patterns of human use and movement that arise from the particular geometry. It seems we are hard-wired to find geometries that generate these patterns aesthetically interesting, and often very beautiful. (Elsewhere, we have discussed the fascinating and promising topic of biophilia in more detail.)



Two places in London, not far from one another, with opposite system characteristics: Left, a “place network” that is a well-articulated system of geometric spaces. Right, a place without a network — a jumble of poorly-articulated abstract parts, with little relation to human experience or need, photos by Michael Mehaffy.

This, then, is a key role of environmental designers: to facilitate such adaptive evolutions in both short and long (more permanent) time scales. It is essential to understand and apply the geometric properties of human space, particularly its patterns of connections. We, as urban designers, or as architects—as designers of any kind—have to take this problem seriously. The art of our work lies in the way we elaborate and elucidate these deeper realities of life. Understanding geometric systems within environments gives us a remarkably coherent way of approaching the problems of the human environment. The question at stake is whether we can actually design, in the deepest spatial sense—that is, harness the organizational power of evolutionary systems, to generate richer, more connected, more adapted, more alive human environments. We must contrast this approach with today’s dominant “business as usual” approach—a holdover from an earlier pre-modern industrial mode of design (indeed, of science).

Instead of creating and transforming mutually adapted systems, disconnected objects are created and assembled, and then aesthetic “packaging” is layered onto them. Someone creates the “guts” of the car, and then somebody else places a sleekly “styled” body on top. Or we create filing-cabinet-like buildings around prosaic “programs” and then we create razzle-dazzle aesthetic veneers, outside and perhaps inside—all package, no substance. Or we create filing-cabinet cities of superblocks and segregated zones, and then we “shrub them up” with various forms of landscaping and ecological gizmos. This last example often comes with a phony “sustainable” label. In the process, we leave a toxic planetary wreckage, the consequences of which, it is clear, we simply will not survive. This, too, is a necessary adaptation we must make—one that will challenge our orthodox thinking, about the very methods and aims of design.

http://www.metropolismag.com/Point-of-View/August-2012/Science-for-Designers-Complex-Adaptive-Systems/

Science for Designers: The Meaning of Complexity

By Michael Mehaffy and Nikos Salingaros

Today’s designers seem to love using new ideas coming from science. They embrace them as analogies, metaphors, and in a few cases, tools to generate startling new designs. (Computer algorithms and spline shapes are a good recent example of the latter.) But metaphors about the complexity of the city and its adaptive structures are not the same thing as the actual complexity of the city. The trouble is, this confusion can produce disastrous results. It can even contribute to the slow collapse of an entire civilization. We might think that the difference between metaphor and reality is so obvious that it’s hardly worth mentioning. And yet, such confusion pervades the design world today, and spreads from there into the general culture. It plays a key role in the delusional expectation that metaphors will create reality.

Psychiatrists speak of this as an actual disorder known as “magical thinking”: if our symbols are good enough, then reality will follow. In the hands of designers, this is very dangerous stuff. We see it at work in the failed iconic buildings that were sure to create economic development, or urban vitality, or greater quality of life purely because of a futuristic image. We see it also in the many “tokenistic” sustainability features (wind turbines, etc.) of other iconic new buildings whose actual performance in post-evaluation studies is woefully poor. From the perspective of design methodology, this phenomenon is an interesting and important design problem in its own right. We recognize it as a fundamental weakness of human thought, and need to adjust our design methodologies accordingly. In this process, the methodologies and insights of a humane science, applied by literate designers, can be invaluable.

Distinguishing physical from metaphorical complexity clarifies a presently confused and unsustainable situation, and can help us out of it (the ultimate aim of any science, and any philosophy). The topics of urbanism, architecture, product design, environmental design, sustainability, and complexity in science are all tightly interrelated. Humans “design” with much the same aim toward which nature “designs” — both aim to increase the complexity of a system so that it works “better”. “Better” in this sense means more stable, more diverse, and more capable of maintaining an organized state — like the health of an organism. We learn from the structures and processes by which nature designs, so that we can also create and sustain these more organized states. Some scientists shy away from the notion that nature “aims” for anything. But this begs the question: are we not part of nature, and do we not “aim” for something in our own designs, and in the other parts of our life (e.g. seeking our own health and wellbeing)? Then we must accept “aim” as a characteristic of at least some part of nature. Otherwise, we severely hobble the usefulness of the scientific tradition as a relevant tool for designers. (Indeed, we would set ourselves on a very dangerous philosophical path: in effect, rendering the very idea of intelligence — human or otherwise — as meaningless!)

Traditional city fabric evolved over generations as an extension of our own biology, thus representing an application of a kind of “collective intelligence” due to the system, not of any individual. Traditional Islamic urbanism, by Mustapha Ben Hamouche.

Let’s start instead from the premise that we are here, and need to make sense of our own situation and determine our aims. Then we can begin to ask, given this intentionality, what is the most intelligent approach we can take? How can we learn from the intelligence — the “intentionality” in that sense — of natural systems? This is now an urgent question because much of human production — especially since modern industrialization enabled us to do things with really big footprints — is intentional in the wrong sense. Instead of building up complex systems that work better within the natural systems that support them, they acquire a fragile, non-resilient complexity that works against nature. In this way, human systems of life, movement, production, and economies depend on ever more energy consumption just to keep running at the same pace, setting us up for an inevitable catastrophic scenario. At the same time, the design of our environment seems to be driven not so much by any intelligent intentionality as by images that are stubbornly, even religiously, adhered to, even as mounting evidence shows that those typologies are inappropriate for complex adaptive systems. How can we fix this extremely precarious situation?

What’s required is a paradigm shift in the way we perceive and act upon the systems that make our world function. Those systems are complex and adaptive — that is, their elements are mutually co-adapting and co-evolving, thereby forming an exceedingly complex pattern. Even so, such a pattern can be understood scientifically, and exploited by designers, following a new understanding of the phenomenon of complexity. This effort is part of the burgeoning, but historically recent, discipline of “complexity science” — the set of astonishing findings into topics like fractals, strange attractors, emergence, and algorithmic patterns. What these fields of investigation all have in common is the curious property of systems when a lot of elements are interacting. Complex systems take on entirely new characteristics that are very different from those with only a few elements — and usually impossible to predict. They have properties that are remarkably similar to living systems (which is no coincidence). For environmental designers and planners, knowing this phenomenon of “emergence” is the key to getting things right.

Cities, for example, are certainly complex adaptive systems, and so are most other kinds of human environments. If we are trying to solve the problems of cities, then we need to know the kind of problem we are dealing with. If we treat this as a search for simplicity, or perhaps, an artistic challenge of visual design, when it is really a problem of organized complexity obeying its own rules of evolutionary intelligence, then we are likely to make a mess of things. And yet, that is exactly what architects and planners have done in the past several decades. Complexity science was at its dawn when, in the middle 20th Century, the adaptive living fabric of our cities was gutted and replaced by a much more elementary, mechanical model of design. The result is a simplistic machine, intentionally far from natural complexity. This drastically reductive process was draped with more complex poetic analogies, which convinced society to implement crude models that substituted for a richly complex reality. Since then, the scientific discipline has advanced farther than anyone hoped, and has begun to tease out formerly inscrutable secrets of nature — the marvels of evolution, the behavior of Earth systems, even the workings of genetic processes. For geographers and planners, the phenomena of cities became more comprehensible too.

Self-generated city — disrespected by those designers who wish to impose their own will on cities, and by governments who want total control — yet representing a natural phenomenon as basic as life itself. Dharavi, India, by YGLvoices.

Many designers are still unaware of these developments. For them, design is essentially about conveying expressive meaning, symbolism, and metaphor. Others pretend to keep up with the times but don’t bother with generating adaptive structural complexity — they continue to use fashionable metaphors to build non-adaptive, dysfunctional architectural and urban forms. This is a distorted artistic heritage of design, not at all about understanding systems and their emergent properties, which has come to a frontal collision with its scientific heritage. Artists at some point became specialized cogs in the same commodified industrial machine. Their job was now to sprinkle “meaning” (metaphor, analogy, expressive character) onto top-down industrial structures, and give them an acceptable, or better yet marketably desirable, aesthetic character. Things really took off when this project came to be associated with the allure of fine art. You may want to protest here, and ask: isn’t it our job to symbolize the scientific spirit of our age, and the new cosmological view of nature? Yes, but not as a mere sugar coating, a razzle-dazzle product “theming” — the meaning should be embodied in the objectives we achieve with our designs, and the way they accommodate and improve human life.

The best architecture does not confuse these two aspects of life and art in a mutually destructive manner, but uses them to serve one another. When we paste a metaphoric “theme” over the design, after a few years, it begins to look ridiculous. That’s because the thing on the outside has no inherent relation to the thing on the inside — it’s little more than a veneer. And it works rather poorly. So the once-futuristic cases for old personal computers, the expression of another age’s romance with technology, now look absurd. The futuristic skins of famous art museums and concert halls are already stale and dated, so that now the only remaining customers for such a style are third-world countries playing catch up with Western architectural fashions. If, instead, we let the expression of the object grow from its complex relationship to its environment, and to the job it has to do for human beings, something remarkable happens: it takes on a kind of “classic” quality. The design seems almost to have “grown” that way, or to be inevitable — and then we say: “it’s a classic”. It is timeless. It will be valued by future generations just as we value (or ought to value) the greatest design achievements of previous generations. Alas, most design firms today don’t work towards this goal at all. Instead, they seek to attract attention through novelty and “theming”. They may give lip service to the approaches we discuss here, but without understanding the deeper methodological change those require. Though they are experts at glossy marketing in competing for major new projects and the practice of smooth talking to impress clients, they continue to do business as usual. A good designer is responsible for both implementation and adaptation. Do not confuse “intentionality” in a system changing itself so as to adapt — a sign of intelligence — with the intentions of a designer who ignores adaptation. The latter is a sign of unintelligent action. We see this over and over in products based strictly upon visual images. Dysfunctional satellite cities and suburbs were built in this manner.

Design “intentionality” increases complexity so as to make the system work in the best way possible, not only for its explicit function, but especially as it is embedded both within its context and its environment. The job weaves together many things — like a city does — thus the design has to embrace and encourage connectivity within diversity. The chore of design, in such a complex environment, is not to impose an overly simple order from above, but to help to orchestrate the diversity, using its own latent dynamics, into a more spontaneous kind of patterned order. When it succeeds, we recognize it as a beloved city that nourishes us in more ways than one. A model of organized complexity proposed by one of us in 1997 (and reprinted as Chapter 5 of our book A Theory of Architecture) finds a striking parallel in the “Integrated Information Model for Consciousness” later developed by neuroscientist Giulio Tononi. Its essence is that complex systems evolve an integrated connectivity among their components so their information output is high, yet coherent. This coherence is often mistaken for simplicity, and this is the source of much of the confusion we address in this essay.

Human life on earth is creating signs of informational intelligence: an earth that is conscious because it is intimately interconnected. We can save civilization from self-destruction by understanding the underlying mechanisms. Egypt at night, by NASA.

Note that “complexity” is very different from “complicatedness”. Some postmodernist urbanists seem eager to conflate these two very different ideas. You don’t get a system when you pile up disjointed fragments, because there is no integration. Instead, a complex system arises through a process working to organize different and often conflicting elements in some way, in spite of their differences. Intentionality in building complexity sheds all “complicatedness” that is irrelevant and unconnected, just like in natural systems. It does not “streamline” processes to a single aim, but simply evolves the system to include those multiple connected cycles, however large or small, that interact in some essential way. That process is often a subtle dynamic, such as a set of apparently simple adaptive rules that each element follows. Why do people walking through a park all move along one line and not others? Why does one store get lots of pedestrian customers and another, just as good, fail? We can discover and document the socio-geometric patterns that people are following, as they make the simple human calculations that we all do: head in the direction of your destination, avoid obstructions, stop only if you see something interesting, and so on.

If we understand these patterns, we can place our pavement more effectively, or place our store in a more successful location. Other patterns of complex organization can be documented and put to work for us in our designs. The human inhabitants of even the most diverse city are, and remain, part of a complex emergent whole. Their complex behaviors and interactions must not be reduced for the city to work like some crude yet giant machine, for that would (and does) severely damage living systems. So, too, the elements of an ecosystem have a history, as do other natural systems. This is the nature of complexity — it has an inherent wholeness or whole-systems quality to it. The elements we are considering possess what the physicist David Bohm called an “implicate order” — they have a much deeper relationship within a whole system that predates our observation. We face a perceptual problem, however. The reason most people think of complexity as being more like “complicatedness” — a messy collection of unrelated parts — is that we are very good at seeing particular fragments of the world.

This view has its evolutionary benefits — we can see just a snapshot of what happens at a certain point and at a particular time, and omit all the interactions that brought those parts together in the first place. While this ability gave early humans an advantage in quick decision-making, it handicaps us when confronting the complex systems that we are now capable of building. We tend to forget that this way of looking at the world and its complex interactions is merely an abstraction, helpful for some purposes, but not for design. This is because in design, we are working with complex, implicate-ordered systems. Earth and life systems manifest design intentionality (in the sense of organizing their complexity) and intrinsic intelligence. When we treat these systems as problems of simplicity, we fail to understand the actual complex systems that we are creating, disturbing, and often destroying — a neighborhood, a city, an ecology, a human economy, or a living planet. And so, today, we find ourselves in a great deal of trouble.

Science for Designers: Scaling and Fractals

By Michael Mehaffy and Nikos Salingaros

With apologies to real estate agents, we’d like to say that the three most important factors in design are scale, scale, and scale. One reason is that many of the worst environmental design blunders of the 20th century have been mistakes of scale — especially our failures to come to terms with the linked nature of scales, ranging from small to large. The cumulative consequence of these failures is that the scales of the built environment have become highly fragmented, and (for reasons we detail here) this is not a good thing. Can we correct this shortcoming?

Most designers know something about “fractals,” those beautiful patterns that mathematicians like Benoît Mandelbrot have described in precise structural detail. In essence, fractals are patterns of elements that are “self-similar” at different scales. They repeat a similar geometric pattern in many different sizes. We see fractal patterns almost everywhere in nature: in the graceful repetition at different scales of the fronds of ferns, or the branching patterns of veins, or the more random-appearing (but repetitive at different scales) patterns of clouds or coastlines.

Figure 1. The beautiful structure of fractals, patterns that are repeated and sometimes rotated or otherwise transformed at different scales. Left, a natural example of ice crystals (Photo: Schnobby@wikimediacommons). Right, a computer-generated fractal coral reef that, helped by color and shading effects, could be mistaken for a natural scene (Photo: Prokofiev@wikimediacommons).

We can also reproduce fractal patterns in a computer, often with strangely beautiful results. Some graphic designers use fractal methods to reproduce very realistic-looking landscapes and other natural phenomena. These, too, seem to trigger something in our perception. We somehow recognize them as being “natural” and connect with them emotionally.

We seem to be wired to “read” fractals in our environment, probably for two key reasons. One is that biological structures are largely fractal in their patterning, and we are innately interested in other biological structures because they might be food, or predators, or other people, or just a key component of the biologically supportive environment.

The other reason goes deeper into geometry. When we look at a long vista, structures that repeat (trees for example), repeat at smaller apparent scales when they are farther away. This fractal information helps us read distances and depth in the environment. Doing so gives us an effortless understanding of the geometrical order of our environment. We’re aware of this only as a pleasurable sense and not, coincidentally, as an important survival need, from an evolutionary point of view.

Fractal structures also give us other kinds of useful information, like complex relationships among environmental elements. The order of an essential but non-graspable structure, like an ecosystem, is more intelligible to us because we can detect the symmetrical fractal patterns of its plants and animals — another important evolutionary need. In modern times we have a greater need for urban environments to be legible to us, and there is evidence that we do this by reading fractal relationships in buildings and details (after all, we have evolved with this sense).

From an evolutionary point of view, it’s evident that we perceive these relationships because they are supremely useful to us. They help us understand the structure of choices that our environments present, and how the different alternatives might offer us different benefits. It is an innate skill.

Importantly, fractal urban structures typically provide multiple combinations of benefits that work in synergy. And our pleasurable perception of fractals is probably related to this too. For example, the branching, layered, fractal-like paths we can take within a city help us carry out many different tasks simultaneously. People moving along such paths for the purpose of higher-level information exchange (going to a business meeting) can thus carry out lower-level information exchange (having informal “spillover” exchanges with other people, or perceiving pleasurable scenes). The time required for higher-level exchange is therefore used more effectively, and the net effect is a synergy of activities that often translate into economic, social, and other benefits.

Figure 2. The fractal pattern of self-organizing urbanism. On the left is a simple fractal pattern called a “Cantor Gasket” (Drawing by Nikos Salingaros). On the right is a much more complex and irregular pattern with recognizably similar fractal properties, a traditional urban neighborhood in Baghdad, Iraq. Notice the similar patterning at different scales of bordering spaces and alternating patterns of indoor-outdoor space (Photo: G. Eric and Edith Matson Photograph Collection, Library of Congress).

This “fractal loading” means that each high-level exchange carries with it simultaneous exchanges on many smaller levels. An ensemble of exchanges on different scales is supported by a physical infrastructure that permits mixed information exchanges, but does not let other competing exchanges squeeze out the weaker or lower-level exchanges.

Fractal loading is important at all scales. But it becomes especially important at the scale of a human being. For instance at the scale of a region there are not that many structural choices that are relevant to an individual going about his daily activities. But as we approach the scale of a human being (in fact, a group of scales ranging from 1mm to 10m), more and more structural choices begin to crowd into the picture, so that by the time we are at that scale, the environment often presents a rich set of structural choices that a person might make on a daily, hourly, and even instantaneous basis.

At this scale, the fractal loading of our environment vastly expands the structural options, and builds synergies between them. If I am in a well-connected, fractal-loaded spot at this human scale, I can read the newspaper, I can talk to a friend, I can say hello to a passerby, or I can run one errand or more. And I can easily connect these activities into a web of choices.

This is very likely a key reason that, within urban systems, well-structured pedestrian networks are so important. As our work has shown, there is reason to believe that there are important synergies of economics, resource conservation, psychological health, and other benefits, which are only provided by pedestrian networks that have this key property of fractal loading.

Figure 3. The pedestrian networks of medieval Rome have a fractal structure, extending into the buildings and even the rich ornamental details of the buildings themselves. These “place networks” offer pedestrians a dense and overlapping set of choices of movement, views, and other enriching experiences (Drawings/Photos: Michael Mehaffy).

Fractal loading is one example of a “scaling phenomenon” in complex network structures like cities, and an active area of urban research. Another related phenomenon is that as the scale of a structure like a network increases, the phenomena that happen at a smaller scale often do not increase at a linear (proportional) rate. Often they are “super-linear” (they increase more than proportionally) or “sub-linear” (they increase less than proportionally).

These phenomena, such as economic growth and resource use per person, are very important to us. If we get more economic growth per person at a larger scale, or less resource use per person, then our quality of life can improve. This may be one important reason why people are attracted to large cities. Dense settlements really do offer more quality of life for proportionally less cost than sprawl does. And by understanding scaling, we can deal better with challenges like resource depletion and climate change.

But notice that this phenomenon occurs as a result of the specific network structure of the city, and its “metabolic” interactions and synergies (such as fractal loading). A collection of entirely separate individuals all “doing their own thing” would likely not benefit from such scaling phenomena. It is in the multi-scale interactions that these phenomena, and the synergetic benefits they bring, come about.

Interestingly, this characteristic of fractal loading tends to emerge spontaneously within urban systems that are allowed to self-organize within the natural processes of human culture — that is, within traditional urban environments. We all recognize this intuitively in the fractal-rich environments of popular tourist destinations like Bruges or Edinburgh. (And we recognize its absence in engineered environments that are decidedly not tourist destinations, like London’s Docklands, or Paris’ La Defense.)

Figure 4. On the left is the highly fractal structure of urbanism in Bruges, Belgium. On the right, a much more sparse, fractal-free environment in the modern suburbs of Bruges — which is also far less walkable, and has other negative impacts (Photos: Michael Mehaffy).

What does this tell us? Are fractal urban structures just nostalgic remnants of an obsolete pre-modern era? Or do they offer crucial lessons for designers today?

While there are certainly ideologically dogmatic theories of style and history that support the nostalgic remnant proposition, they are unsupported by real scientific evidence. And, critically, there is important evidence for the crucial lessons for today’s designers proposition. To see what these lessons might be, we will discuss how fractal structures are formed in nature — and, it appears, in human nature — and why they might be such important attributes of a well-functioning environment.

Fractals have two related characteristics: They show complexity at every magnification. Their edges and interfaces are not smooth, but are either crinkled or perforated.

Figure 5. Some essential properties of fractals. (a) Fractal loading uses a basic scale as a carrier for other successively smaller mechanisms and structures. Far from being monofunctional and simplistic, every structure becomes richly complex and carries information on several distinct scales. (b) Longitudinal compression forms a “folded” fractal, creating a crinkled line that then generates crinkles on its crinkles. This interface can catalyze urban interactions, mimicking the non-smooth surface of a chemical catalyst. (c) Longitudinal tension and breaking along the entire line form a “perforated” fractal, here shown at its first stage. This is a natural mechanism for defining an urban colonnade and any semi-permeable urban boundary, such as a row of bollards that protect pedestrian from vehicular traffic (Drawings by Nikos Salingaros).

Fractal patterns tend to form naturally for one simple reason: there is a “generative process” that creates the geometric pattern, and it does so at more than one scale. For example, in a blooming flower, the genetic code that creates the pattern does so in a time sequence, while the previously generated patterns grow larger.

In a computer-generated fractal, the generative process is called an “algorithm,” a bit of code that generates the pattern from a complex interaction with what has been generated previously. In a city the generative processes are carried out by people doing what people do in making cities. They articulate spaces with boundaries that are shared to varying degrees. They create spaces that have degrees of publicness, somewhere along the spectrum ranging from public to private, from the most public streets and squares to the most private bedrooms and baths.

The boundaries of living spaces are not simple structures either, but complex membrane-like structures offering their own set of structural choices, either to maximize privacy (by closing a curtain) or publicness (by opening a door). These boundaries are wonderfully complex structures in themselves and self-organize into larger patterns (doors or windows that become shared types over time, and neighborhoods that develop characteristic interface patterns of porches or colonnades).

How are the different scales linked? Just as biological structures and computer algorithms spontaneously repeat their geometric patterns at different scales, so do we, unless we’re forced to do otherwise either by legislation or by ideology. Individuals might make small repetitions of a pattern (a rectangular room shape) while groups might make larger versions of the same pattern (a courtyard) and larger groups might make a still larger one (an urban plaza).

But as with biological and computer structures, the story does not end at any particular scale. The boundary of a room is perforated with smaller structures like rectangular doors and windows. The boundary of larger spaces might be perforated with colonnades (we are talking about living spaces and not the dead spaces characteristic of post-war architecture and urbanism).

These repetitive perforations at smaller scales — the fractal loading that results from the characteristic “generative algorithm” of fractal structure — will often continue on down to the scales of detail and ornament. Why is this? It seems likely that we, the users, making our way through these places find such complex environments (complex in a very precisely ordered sense) easier to comprehend, more intelligible, more usefully organized, and more beautiful. We are very good at reading the multiple scales of these “place networks”.

But there is a serious problem. If we are not users, but designers educated in our industrial/artistic culture, we might have another agenda: to impose another kind of order on the built environment. And that agenda might come from a very different set of criteria than the environmental experience of humans.

Such is indeed the case. To put it simply, our current methods of making cities are over-reliant on economies of repetition and scale, which do offer narrow advantages but are also extremely limited, and from a human perspective, very crude and destructive. Natural systems never use those strategies in isolation, but are always combined with economies of differentiation and adaptation. Surprisingly, we haven’t really figured out how to employ these in our current strategies (though many people are working on this problem, and our own work takes up this challenge).

Choosing to work with a severe technological limitation, modernist designers argued that a more sophisticated approach was to strip down buildings into “minimalist” compositions, much easier and cheaper to produce under the crude industrial processes of the early 20th century. It was the compositions of these elementary “Platonic” solids that were most beautiful, postulated architects like Le Corbusier, because they were “pure” expressions of form. The old Gothic cathedrals, with their fractal tracery, were “not very beautiful,” he said infamously. Nor were the lively streets that he despised! Indeed, Corb and other designers made a strong ideological case (still persuasive today) that the old ornamented designs were bourgeois, contemptible, even (in the famous words of Adolf Loos) “a crime”.

In this ideologically driven design movement, we have come to accept the incorrect idea that fractals are somehow primitive, whereas smooth, undifferentiated “Platonic” forms are “modern” and sophisticated. Ironically, the opposite is the case: The most advanced theories of today’s science are all about complexity, differentiation, networks, and fractals — a dramatic contrast with the straight, smooth industrial geometries of early modernism.

Recognizing this, many architects and urban designers are speaking in terms of fractals, scaling laws, and “morphogenetic design.” But the question remains: Are these individuals really engaging such principles to create human-adaptive structure? Or are they only using them to create attention-getting aesthetic schemes, tacked onto what is essentially the same failing industrial model of design? These questions are at the heart of the debate on the future of the built environment.

What, then, are the lessons to be drawn? Fractal structure is not just an aesthetic gimmick. It is an important characteristic of sustainable human environments. And this structure does not arise from the well-meaning top-down schemes of old-mode art-designers, but from those with a skilled application of processes of self-organization, as part of a new way of thinking about what it is to design.

And yet, we designers have been exceedingly stubborn in taking on this lesson. Under a misguided theory of environmental structure that confuses simplicity with order, we have been stripping away the critical connected scales and fractal relationships within our environment. We have replaced a world of richly connected urbanism with a disordered geography of artfully packaged, catastrophically failing art-products.

http://www.metropolismag.com/Point-of-View/May-2012/Science-for-Designers-Scaling-and-Fractals/