Emergent Urbanism

Rediscovering Urban Complexity

A demonstration of complexity in London

The immensely productive Physicist-Mathematician-Entrepreneur Stephen Wolfram theorized, based on his studies of cellular automatons in the 1980's, that there exists four classes of physical processes in the universe. Class I is simple continuous behavior (line). Class II is repetitive behavior (checkerboard). Class III is nested, hierarchical-fractal behavior (basic fractals like the Sierpinski triangle). Class IV, the most fascinating, is chaotic behavior (random fractals such as the Mandelbrot Set). Wolfram believes that Class IV behavior, exemplified by the Rule 30 automaton, is behind the complexity we see in the universe, and that very simple generative rules produce it.

The way we as humans are used to doing engineering and to building things, we tend to operate under the constraint that we have to foresee what the things we're building are going to do. And that means that we've ended up being forced to use only a very special set of programs--from a very special corner of the computational universe--that happen always to have simple foreseeable behavior. But the point is that nature is presumably under no such constraint. So that means that there's nothing wrong with it using something like rule 30--and that way inevitably producing all sorts of complexity.

Wolfram gave this speech on his new science to big shot architecture schools at Yale, Princeton and MIT. He believes that his new science has profound implications for the generation of form in architecture. I agree with him, but not for the reasons he provided. In fact his classification of the geometric properties of different physical phenomenons provides extremely profound insight into the history of architecture, and its future.

A visit to London was what really made me appreciate this insight. London, as an architectural artifact, is quite unique in that its greatest period of growth, the period 1750-1850, coincides with the beginning of modernism in architecture, a time when architecture became in a sense aware of itself and in search of its meaning. Neoclassicism was followed by Gothic Revival, Romanesque Revival, Neo-Venetian, all of it got mixed up in eclecticism, and the invention of new materials and building processes came to confuse things even more. Regardless of stylistic debates, what may be most important about that period is that, for the first time in history, large capital funds for speculative real estate development became available. Where architecture had once been a piecemeal business occurring quite randomly, in London, for the first time ever, housing subdivisions were possible. The result was the terrace housing.

Chelsea South Kensington

The big housing developments in London were initiated by aristocratic landowners who hired architects to plan and control the form their estates would take. Walking through Chelsea and South Kensington, one is faced with sometimes overwhelming repetition of identical houses. Class II behavior, that Wolfram claims is fundamental to engineering, is obviously visible. The architects of the estates, not really knowing the specific constraints of the future residents of the place, opted for endless repetitions of the same building. The fact that each building is a copy of the next, inadapted to the particular wants of its occupants, makes it standard behavior, far from complex.

The human mind is by nature fractal and is repulsed by Class II geometry, which is why traditionally architects have built Class III, hierarchical fractal geometry. This was employed by some terrace builders, such as the architect of the Regent's Park estate, John Nash. Here the monotony of the model is interrupted by nesting houses in flourishes like arches, or bigger houses with large porticoes.

Cumberland Terrace, Regent’s Park, London

You can see a 19th century panorama of this terrace here.

Classical architectural education, based on the teaching of the classical orders, trained architects in the art of doing such hierarchical decompositions of their buildings. As such most of the high western classical architecture, starting from the renaissance architecture of Alberti (the first modern architect in the sense that his name is more important than any of his buildings, not true of the medieval architects of cathedrals), is rigidly symmetrical. Classically-trained architects only expanded the scales of decomposition as the size of buildings increased, up to the neoclassical skyscrapers that modernists considered to be ridiculous. The classicals were right about the need to create fractal geometry by decomposition of what were rigid engineering plans, what the modernists claimed was ornamental crime, philosophically dishonest and replaced with elementary repetition in their designs (regression to type II geometry). People have hated architects ever since.

Whenever I read through architectural history books, even those of honest traditionalists like David Watkin, I am struck by what is clearly missing from the record. That is to say the towns built up over centuries, the accretion of simple building acts into complex symmetries. The topic is touched by some thinkers of urban morphology, typically under the label of "organic" growth, such as in The City Shaped by Spiro Kostof, but everyone appears dumbfounded by the means through which such symmetry was accomplished. And largely the whole career of Christopher Alexander has been dedicated to decoding this mystery.


But even in the 19th century, when large-scale development was sweeping London, some complex geometry was achieved. These are four distinct buildings on Lincoln's Inn Fields.

Lincoln’s Inn Fields

We immediately notice that each building is different from the other, having been built for a unique purpose and therefore being a unique solution to a unique problem. Despite that, the buildings form a harmonious geometric composition because they share many transformations to which randomness is applied. Even within one building, Lincoln's Inn on the left, randomness is visible. The tower is unique, but symmetric with the rest through shared transformations. What we are seeing here is, I believe, a genuine Class IV pattern.

How could this be possible? If Wolfram's theory on the origins of complexity is correct, then there must be a very simple rule to produce this kind of street scape. This rule can be applied to any random architectural demand and provide a perfectly appropriate solution to an individual problem while remaining completely harmonious with other such random solutions in its neighborhood! Since such organic complexity appears in all human civilizations, then we must conclude that every single building culture in the world has known, at some point, such a rule, and has applied it to solve building problems of all forms. Without understanding how these rules created complexity, they simply repeated them after each successful building.

What to do with new technology? New technology necessarily creates a new scale into the rule, but the remaining rules are still valid. This is visible in the glass structure appended to the Royal Opera House.

Royal Opera House

We can see many shared patterns between the central structure and rightward structure, but not with the new addition on the left. Typical of modernist architecture, the left building is only made of elementary geometry, barely even qualifying it as a Class II structure. It doesn't feel as though it belongs there at all. There is an important lesson here, one that architects I fear do not want to learn.

Wolfram claims that complexity science is about finding simple rules that can generate complexity. We can decode simple rules from traditional architecture that, even with the modest means of poor villagers, will generate complexity when applied repeatedly to random events, creating random fractals while simultaneously solving a vast diversity of unique problems. This is exactly the kind of work that good urbanists should be doing today, and from there we could allow maximum diversity in our cities without breaking symmetry and harmony at costs as low as the meanest buildings currently cost. If Wolfram is correct, then the rules may be so simple that they may be easily codified into building regulation even by the dullest bureaucrats. Then again the behavior may be so complex (that is to say there is emergence) that no a posteriori codification is even impossible, and the processes by which cities are governed may have to be completely reconsidered. Either way this is not good news for architects. If architecture is so easy, then their idiosyncratic designs are not necessary nor valuable. The big shot schools of architecture that Wolfram visited will be made irrelevant by Wolfram.

Mathieu Helie - Complex geometry and structured chaos
Stephen Wolfram - The Generation of Form in A New Kind of Science
Christopher Alexander - The Process of Creating Life


I agree: the obsession of modern architects with elementary geometric forms - minimalism, glass structures and grey colour is terrible, and is creating placelessness, even in architecturally rich cities like London. There are numerous old buildings here which have been appended using glass structures looking awfully out of place.


I enjoy this, the houses on the South Kensington Street

But I hAVE A QUESTION /Which is the name of the street?

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