With Cellular Automata for a World of Self-Organization

This weeks post at the Archdruid Report by John Michael Greer, “An Old Kind of Science“, is actually about a new kind of science called cellular automata by Stephen Wolfram. Here’s an introduction from the essay:

I’m not sure how many of my readers were paying attention when archetypal computer geek Stephen Wolfram published his 1,264-page opus A New Kind of Science back in 2002. In the 1980s, Wolfram published a series of papers about the behavior of cellular automata—computer programs that produce visual patterns based on a set of very simple rules. Then the papers stopped appearing, but  rumors spread through odd corners of the computer science world that he was working on some vast project along the same lines. The rumors proved to be true; the vast project, the book just named, appeared on bookstore shelves all over the country; reviews covered the entire spectrum from rapturous praise to condemnation, though most of them also gave the distinct impression that their authors really didn’t quite understand what Wolfram was talking about.  Shortly thereafter, the entire affair was elbowed out of the headlines by something else, and Wolfram’s book sank back out of public view—though I understand that it’s still much read in those rarefied academic circles in which cellular automata are objects of high importance.

Although this is a new science it’s more aligned with how humanity has worked traditionally, and Greer sees it as an opportunity to reconnect humanity with the way nature works.

The sort of science that Wolfram has proposed offers one way out of that overfamiliar trap. Ironically, his “new kind of science” is in one sense a very old kind of science. Long before Sir Francis Bacon set pen to paper and began to sketch out a vision of scientific progress centered on the attempt to subject the entire universe to the human will and intellect, many of the activities we now call science were already being practiced in a range of formal and informal ways, and both of the characteristics I’ve highlighted above—a recognition that scientific models are simply human mental approximations of nature, and a focus on systematic observation of what actually happens—were far more often than not central to the way these activities were done in earlier ages.

Michael Mehaffy has written a longer essay on how to apply cellular automata to design, using very simple rules going stepwise toward a society of huge complexity:

– The New Modernity: The Architecture of Complexity and The Technology of Life

Today we are doing many things basically wrong, setting up hindrances for cellular automata to unfold. Here are a few outlined by Christopher Alexander:

“In order to see the contrast, here is the order in which these things were usually done in conventional 20th-century development work, many of them specified in existing city codes. In current practice, there are many conventions of sequence, which have become part of the accepted wisdom, in planning, architecture, and development.

The following examples are all harmful:

  • Conventionally: Roads are built before the buildings they serve.
  • Conventionally: In a tract development, street sewers are laid long before the houses are built.
  • Conventionally: Houses are placed, and the garden is whatever is left on the lot, comes second.
  • Conventionally: Windows are designed and positioned at the time the building’s plans are submitted for plan check.
  • Conventionally: Drawings are completed before any construction work is done.
  • Conventionally: Neighborhood plans are completed, before any construction work is done.
  • Conventionally: Public spaces are designed after individual buildings.
  • Conventionally: Changes are done by change orders, and therefore become very expensive.

These practices do not support the creation of living neighborhoods.

Read more here.

I’ll end with republishing a smaller essay by Mehaffy & Salingaros.

Frontiers of Design Science: Self-Organization

by Michael Mehaffy, Nikos A. Salingaros, originally published by MetropolisMag.com

Frontiers of Design Science: Self-Organization

Informal settlements show classic signs of self-organization into distinct components analogous to the organs of a body, like this settlement in Colombia. Similar patterns can be seen in the much-loved villages of Tuscany or Provence.

Image: NASA

A remarkable revolution is under way in the design sciences today — fueled by powerful new insights into the workings of nature, and articulated by the burgeoning science of complexity. New terms tantalize us with their suggestion of innovative directions and new possibilities: self-organization, biophilia, generative design, and much more.

But what’s visible on the surface is still mostly froth: old ways of doing things gussied up in fancy clothing of the new. To see what’s really going on we have to dig a lot deeper, and we need to understand the science a bit more fully.

Within this promising field, no topic is likely more promising than “self-organization” — the ability of complex adaptive systems to grow, order, and organize all by themselves, without any master controller. We observe this phenomenon at work in complex termite colonies that lack architects and blueprints, in biological cells organizing and differentiating into organs without any additional controls, and as we now see, in the very processes that gave rise to life itself.

The complexity scientist Stuart Kauffman described this phenomenon as “order for free” — a kind of spontaneous order that is able to solve problems and adapt successfully to environments. Clearly this is a powerful and very important natural mechanism that might hold important clues for human use.

As a matter of fact, we do see characteristics of self-organization in many human settlements — for example, the remarkably well-ordered villages of traditional societies that did not use architects with blueprints, but instead, relied upon fairly simple rules for generating form, and adapting it to the form that existed. These processes turn out to be efficient at solving human problems — much as the termite mounds manage to achieve very sophisticated self-regulating cooling systems, or species develop very successful solutions to problems of swimming or flight. And they can accommodate powerful forms of art too — a point we’ll come back to.

What turns out to be key is the idea of fairly simple adaptive rules, operating at a fine grain. In the case of life, the grain is the molecular level of DNA, and going up from there, the cell, the organ, and the organism. In the case of human settlements, the grain is the scale of a person, and going up from there, a family, neighborhood, and city. (A big problem comes when we misunderstand the scale of these systems, and try to impose rules at a too-large scale.)

Another crucial and related point is that the “rules” are not usually the bureaucratic kind we’re used to, but rather, rules of self-interest and self-governance, within an evolving system of ethical standards. An obvious example of this peer-to-peer rule is: move your store close to your customers. Another is: build your house conveniently near stores, schools, your church, etc. But with this freedom from top-down government directives (such as: no apartments on top of stores; no stores in the middle of a neighborhood) come small-scale regulations that allow adjustments without compromising any one of the urban actors.

As these small-scale actions interact, they form patterns that become adaptive, and coalesce around certain key features. These kinds of pattern-generating systems are called “cellular automata” — units or “cells” that follow simple local rules yet generate complex global patterns. We can see these patterns in the swirling formations of bird flocks and many other spontaneous processes in nature. For us as designers, the very interesting thing is that these processes are actually capable of generating a sophisticated, organized, problem-solving structure.

In the case of an animal’s body, the cells form organs. In the case of a self-organizing town, the people form neighborhoods, retail centers, and even streets. This is a kind of “bottom-up” order — coming from the scale of people acting in their own world, on their own initiative. It is not that there isn’t some top-down order too — say, a government that builds a water system — but the top-down order is ideally complementary: it empowers the bottom-up system, and doesn’t smother it.

So how would we take advantage of such a strategy today — in say, the field of urban design? In a sense, we already do, when we provide “capacity-building” resources to a neighborhood or a community. Don’t just wish people good luck, and let them build their own favela from scrap materials. We give them specific generative tools, such as financial backing, plan types, and related resources. Moreover, the resident/builders themselves will formulate small-scale adaptive rules to work out the problems they have, and over time these rules will grow in complexity. They will self-organize into a “culture of building,” just as cultures have done for millennia before them.


The informal settlement of Rosetown, Jamaica, shows surprising self-organization, including retail functions, groupings of semi-private spaces like porches, and even small-scale delights like planters.

Image: Steven Mouzon

In natural systems, this kind of bottom-up evolution turns out to be essential for the creation of sustainability. There is reason to think this is no less essential in urban systems. In fact, our work persuades us that any urban configuration that has not evolved — has not been computed step-by-step using adaptive adjustments — is probably dysfunctional and unsustainable. It will have to be propped up by enormous and unsustainable energy and resource expenditures. Examples include regularly-spaced high-rise buildings in a Le Corbusier type of pattern (i.e. “towers in the park”) as well as suburban sprawl of cookie-cutter houses. These are both template-based models imposed from above, and they do not manifest an efficiently optimized self-organized pattern of the kind we are describing.

A strategy of adaptive design for self-organization, then, will utilize local rules acting on the small scale to generate large-scale complex order. The configuration must evolve, with each step a “computation” that depends upon interactions with all local and global elements. The final result embodies such advanced complexity that it could never have been designed all at once, or even drawn in an office.

Let’s consider a simple schematic example to demonstrate the point. We will use an elementary one-dimensional cellular automaton. The figures are from our book Algorithmic Sustainable Design. Take the “Rule 90 Cellular Automaton” defined by Physicist and Computer Scientist Stephen Wolfram, which is a string of white cells with one black cell in the middle (for further reading, see his book A New Kind of Science). Then evolve this string of cells by following the rule: “Turn black if either neighbor is black; turn white if both neighbors are either black or white.” By listing the string of cells as it evolves in time — with the evolution going down for convenience — and putting all copies together we can generate the Sierpinski fractal triangle, one of the most interesting complex fractal structures.


Time evolution of the cellular automaton generates global order from local rules.


The evolution of the string of cells depends upon the previous state, beginning with the initial state. If we let it evolve long enough, the pattern will grow to infinite length.


A complex fractal structure emerges when we adjoin all evolved states of the string of cells.

A higher-order complexity emerges from this simple one-dimensional cellular automaton. It begins to show regularity and symmetry — but none of those properties were put in initially! Also note that the symmetries are best seen in a higher-dimensional space than the original string of cells: the cellular automaton is one-dimensional, whereas the patterns show best in two dimensions. The lesson, by analogy, is that living cities exist in hyperspace extending beyond the two-dimensional ground plan into dimensions of movement, network flux, information-exchange, fractal loading, shared common realm, sacred space, etc.


Continuing to evolve, the cellular automaton generates the Sierpinski fractal triangle. The longer we let the automaton run, the more levels of coherent structure we get.


A crucial result follows when we vary the initial conditions. Instead of beginning from just one black cell in the middle of the string, let’s start with the simple pattern: B-B-W-W-B. The same cellular automaton with different initial condition generates an entirely distinct complex configuration.

This is visual proof that the same algorithm will generate totally distinct configurations (and patterns) when it begins from different initial conditions. Its global complexity is of the same order. The implications for architectural and urban design are staggering: we can use the same general adaptive computation to design human environments, and every single one will turn out different because it starts from distinct initial (local) conditions.

The corollary to this result is equally important: any design that seeks to impose a “standard”, “formal”, pre-conceived, or self-referential architectural or urban typology is fundamentally flawed, because it has not computed an adaptive configuration starting from the local conditions. Much of post World-War II urban planning has to be rejected on the basis of this result! We can begin to see that for all its power — fueled largely by cheap energy, and especially oil — the current model for city building is actually a primitive form of template-based order-creation. It makes no difference that artists have draped a kind of razzle-dazzle visual excitement over this rigid underlying structure. This includes such technological fantasies as are now being built in the Arabian Desert and in China (destined eventually to be abandoned as so much scrap metal and shattered plate glass).

But let us not discount the vital importance of design creativity and freedom. Art plays an essential role in illuminating the rich complexities of this generated urban structure, as Jane Jacobs famously pointed out. What matters is not the particular “style” or form language that we use, but the degree to which it is adapted through the kind of process we are describing. As the process of adaptive computation proceeds (unconcerned with a pretty pattern on the ground, but really generating an intricate socio-geometrical configuration), it produces aesthetic results that are rich and complex. The aesthetics are not applied as a veneer of self-conscious abstract compositions, but emerge much more powerfully from the deep structure of the process (just like the Sierpinski triangle above).

Hopefully, we’ve lain to rest the common error that traditional form languages restrict architectural creativity and aesthetic sophistication. As the logic of this process should suggest, that statement is mathematically false. We can certainly use an adaptive design algorithm with a traditional form language to design very different buildings depending upon different initial conditions. The best classical and traditional architects have always known this, and have exploited it in the past to build the world’s most-loved and sustainable cities by re-using much older form languages in their own day: Paris, London, Rome, and many others.

By adapting to local conditions, these cities and their buildings became unique while using essentially the same algorithm. And there exist many distinct adaptive design algorithms that have evolved over the millennia of human existence. Using these algorithms with different local conditions makes possible an infinity of innovative results — as we see in the world’s vast diversity of architecture built before 1900. By contrast, the more contemporary architecture tries desperately to be novel, the more it takes on a disquieting global sameness — like the average sameness of white noise.

So we ask, which computational algorithm do we use to design adaptive buildings and cities? By following nature’s own algorithms, sustainable design algorithms have been selected over long periods of time. Those that were unsustainable simply never repeated, leaving the surviving ones that generated sustainable results. A Darwinian selection of algorithms therefore has led to some of our traditional building typologies, and those algorithms are constantly evolving to incorporate new developments and the exigencies of today’s modern world.

The big mistake of the Modernist era — the era of industrial production of the built environment, with artists providing exciting product design themes — was not only to throw out all evolved sustainable design algorithms, but also to fatally damage the very system that allowed them to evolve. Today we’re beginning to tease out Nature’s secrets, and learn how to regenerate this vital process of self-organization.

Michael Mehaffy is an urbanist and critical thinker in complexity and the built environment. He is a practicing planner and builder, and is known for his many projects as well as his writings. He has been a close associate of the architect and software pioneer Christopher Alexander. Currently he is a Sir David Anderson Fellow at the University of Strathclyde in Glasgow, a Visiting Faculty Associate at Arizona State University; a Research Associate with the Center for Environmental Structure, Chris Alexander’s research center founded in 1967; and a strategic consultant on international projects, currently in Europe, North America and South America.

Nikos A. Salingaros is a mathematician and polymath known for his work on urban theory, architectural theory, complexity theory, and design philosophy. He has been a close collaborator of the architect and computer software pioneer Christopher Alexander. Salingaros published substantive research on Algebras, Mathematical Physics, Electromagnetic Fields, and Thermonuclear Fusion before turning his attention to Architecture and Urbanism. He still is Professor of Mathematics at the University of Texas at San Antonio and is also on the Architecture faculties of universities in ItalyMexico, and The Netherlands.

Read more posts from Michael and Nikos here.

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