Tag Archives: Fractal Urbanism

Don’t demolish Detroit

The following story about a presidential program to demolish whole neighborhoods of inner city fabric in the United States and turn them back into wilderness has been making the rounds around news blogs.

Having outlined his strategy to Barack Obama during the election campaign, Mr Kildee has now been approached by the US government and a group of charities who want him to apply what he has learnt to the rest of the country.

Mr Kildee said he will concentrate on 50 cities, identified in a recent study by the Brookings Institution, an influential Washington think-tank, as potentially needing to shrink substantially to cope with their declining fortunes.

Most are former industrial cities in the “rust belt” of America’s Mid-West and North East. They include Detroit, Philadelphia, Pittsburgh, Baltimore and Memphis.

In Detroit, shattered by the woes of the US car industry, there are already plans to split it into a collection of small urban centres separated from each other by countryside.

“The real question is not whether these cities shrink – we’re all shrinking – but whether we let it happen in a destructive or sustainable way,” said Mr Kildee. “Decline is a fact of life in Flint. Resisting it is like resisting gravity.”

This is the type of neighborhood that the government wants to disurbanize. It is located in central Detroit.

Detroit Demolished

To someone trapped in the mindset of development and control that we have practiced in the 20th century, a place like this is a nightmare. It is not possible to consolidate properties in order to bring in a large developer and a large bank that will finance “re-development” of the place. Worse yet, properties have been abandoned randomly, turning what were neat row houses with identical lots into a pockmarked landscape of randomly-sized public land chaos. Better to demolish everything and start over.

There is another mindset through which to interpret such a neighborhood, that of complexity. If we embrace complexity, then the randomly sized pockets of open land are an exceptional opportunity to renew the city of Detroit. They form a fractal solution set to new construction that many different people can participate in and contribute to. It can accomodate small, medium-size and eventually large-size businesses in close proximity with diverse housing and convenient transportation structures.

But why has this not worked for Detroit? Because its process of growth has not been focused on fractal scales but only on big projects and big businesses. Now that the big businesses are dying the city is threatened with disappearing and has to beg even bigger governments to prevent their death. That cannot go on forever. Death is a normal, natural process, and big businesses disappearing should never be a threat to a large city. The economic fabric of a city must always be renewed by new businesses. It is this renewal that creates a sustainable business ecology. At some point Detroit stopped the process of new business creation, and from then on its decline was assured.

Instead of demolishing its remaining neighborhoods and surrendering to the decline and death that will surely follow in its reduced form, Detroit should instead adopt the process of a special economic zone in those neighborhoods it wants to return to “nature”. Tolerate people build as they wish and let a slum happen, and from the slum will emerge the businesses that will renew Detroit’s economy. It can’t be worse than the bulldozer.

The Fundamentals of Urban Complexity

This is part II in an ongoing series of excerpts of an article set to be published this summer in The International Journal of Architectural Research, tentatively titled The Principles of Emergent Urbanism. Click here for part I, The Journey to Emergence.

The qualities of an emergent city

The adoption of mass-production processes, or development, in substitution for spontaneous urban growth in the mid-20th century created for the first time a phenomenon of alienation between the inhabitants and their environment. While the physical features of spontaneous cities could be traced to complex histories of families, businesses, and organizations, the physical features of planned cities owe their origin only to the act of planning and speculation. This has severe consequences towards the sustainability of place as there will not grow any particular attachment by the residents, their presence there being only a temporary economic necessity and not the outcome of their life’s growth. Mass-production of the environment left people as nothing more than consumers of cities where they used to be their creators. A building culture was replaced with a development industry, leaving the landscape culture-less and with no particular sense of identity. This took place despite the evidence that a building which has a unique history and has been fitted to someone’s life, as opposed to speculatively produced, generates market value for that property. (Alexander, 1975) This is why, although the demolition of so-called “slums” to replace them with modern housing projects created a great deal of opposition against urban renewal programs, the demolition of the housing projects later on did not lead to a popular preservationist opposition. They were not the physical expression of any culture.

In additional to cultural patterns, spontaneous settlements also have a peculiar morphology that has not successfully been imitated by modern growth processes. Spontaneous settlement processes give individuals full freedom to determine the boundaries of their properties. Spontaneous settlement is one where total randomness in building configuration is allowed, with no pre-determined property lines acting as artificial boundaries. Buildings and building lots as such acquire general configurations comparable to cell structure in living tissues, unique sizes and boundaries that are purely adapted to the context in which they were defined. In the absence of abstract property boundaries, property rights are bounded by real physical limits such as a neighbor’s wall. (Hakim, 2007)

Very attractive spontaneous cities have a specific pattern of the urban tissue. It consists of similar vernacular buildings that appear very simple when considered individually, but produce a visually fascinating landscape when considered as a whole. This is a form of fractal geometry. In mathematics a fractal is a geometric object of infinite scale that is defined recursively, as an equation or computation that feeds back on itself. For example the Sierpinski triangle is defined by three triangles taking the place of one triangle as in figure 4.


Figure 4. A triangle triggers a feedback function that produces three triangles, which themselves trigger the feedback function to produce nine triangles, and so on. This process can unfold as long as computational resources can be invested to increase the complexity of the object.

The Mandelbrot Set is a much more interesting fractal that is defined as a simple recursive mathematical equation, yet requires a computation to visualize in its full complexity. When computing how many cycles of feedback it takes for the equation to escape to infinity for specific coordinates, figure 5 is the outcome.


Figure 5. The image on the right is a deeper magnification of the image on the left, produced with a narrower range of coordinates as the input of the Mandelbrot set’s feedback function.

In addition to its remarkable similarity to natural phenomena, this form of geometric order informs us of a very important law in geometry: a feedback loop that is fed through the same function will produce an ordered but unpredictable geometric pattern out of any random input.

This tells us why cities of vernacular buildings have such appealing geometric properties at the large scale, despite being often shabby and improvised at the scale of individual buildings. Shanties made of scrap metal and tarp look rough at the scale of the material, but because multiple shanties share the construction process and originate from similar feedback conditions they form an ordered geometric pattern with its specific “texture”. The same process takes place at other scales of feedback, for example the production of a door. Whether the input for one door is larger, taller, wider than another door, if the same production process is employed the two doors will contribute to the overall fractal order of the urban space. This law has been employed not only in traditional and spontaneous cities, but also for modern urban planning initiatives. In the New York City neighborhood of Times Square the structure of billboard advertisements is defined by a building code that determines their configuration in relation to the configuration of the building. The outcome is a unique tissue of advertisement billboards that has become more characteristic of the neighborhood than the buildings themselves, which are not produced by a shared feedback function.

Fundamentals of urban complexity

Christopher Alexander showed in A City is not a Tree (Alexander, 1965) that social and economic networks formed complex semi-lattice patterns, but that people who observed them limited their descriptions to a simple mathematical tree of segregated parts and sub-parts, eliminating connections in the process. (Figure 6 compares the structure of a tree and semi-lattice.) In attempting to plan for urban structure, a single human mind, without a supporting computational process, falls back on tree structures to maintain conceptual control of the plan, thus computing below spontaneous urban complexity, a phenomenon that is consistent with Wolfram’s theory of computational irreducibility of complex systems. (Computational irreducibility states that the only accurate description of a complex system is the system itself and that no abstraction or reduction to a simpler process is possible.) Nikos A. Salingaros later detailed the laws of urban networks in Theory of the Urban Web. (Salingaros, 1998) Network connections form between nodes that are complementary, and therefore the complexity of networks depends on an increasing diversity of nodes. Salingaros describes the urban web as a system that is perpetually moving and growing, and in order to do this the urban tissue has to grow and move with it. Consider for example the smallest social network, the family. Debate over accessory units or “granny flats” has intensified as normal aging has forced the elderly out of their neighborhoods and into retirement complexes, while at the other end of the network young adults entering higher education or the labor market vanish from a subdivision, leaving a large homogeneous group of empty-nesters occupying what was once an area full of children, and often forcing school closures (a clear expression of unsustainability).


Figure 6. A comparison of a tree pattern on the left and a semi-lattice pattern on the right. The tree structure is made of groups and sub-groups that can be manipulated separately from others. The semi-lattice pattern is purely random without distinct sub-parts.

These social networks grow more complex with increasing building density, but a forced increased in density does not force social networks to grow more complex. For instance the spontaneous settlements of slums in the developing world show remarkable resilience that authorities have had difficulty acknowledging. Because of squalid living conditions authorities have conducted campaigns to trade property in the slum for modern apartments with adequate sanitary conditions. To the authorities’ befuddlement some of the residents later returned to live in the slum in order to once again enjoy the rich social networks that had not factored in the design of the modern apartments and neighborhoods, demonstrating that the modern neighborhoods were less socially sustainable than the slums.

In commercial networks, space syntax research (Hillier, 1996), using a method for ranking nodes of semi-lattice networks, has shown that shops spontaneously organize around the multiple scales of centrality of the urban grid at its whole, creating not only commercial centers but a hierarchy of commercial centers that starts with sporadic local shops along neighborhood centers and goes all the way to a central business district located in the global center of the spatial network. The distribution of shops is therefore a probabilistic function of centrality in the urban grid. Because the information necessary to know one’s place in the hierarchy of large urban grids exceeds what is available at the design stage, and because any act of extension or transformation of the grid changes the optimal paths between any two random points of the city, it is only possible to create a distribution of use through a feedback process that begins with the grid’s real traffic and unfolds in time.

The built equilibrium

Although they may appear to be random, new buildings and developments do not arise randomly. They are programmed when the individuals who inhabit a particular place determine that the current building set no longer provides an acceptable solution to environmental conditions, some resulting from external events but some being the outcome of the process of urban growth itself. It is these contextual conditions that fluctuate randomly and throw the equilibrium of the building set out of balance. In order to restore this equilibrium there will be movement of the urban tissue by the addition or subtraction of a building or other structure. In this way an urban tissue is a system that fluctuates chaotically, but it does so in response to random events in order to restore its equilibrium.

This explains why spontaneous cities achieve a natural, “organic” morphology that art historians have had so much difficulty to describe. Every step in the movement of a spontaneous city is a local adaptation in space and time that is proportional to the length of the feedback loops and the scale of the disequilibrium. For spontaneous cities in societies that experience little change the feedback loops are short and the scale of disequilibrium small, and so the urban tissue will grow by adding sometimes as little as one room at a time to a building. Societies experiencing rapid change will produce very large additions to the urban tissue. For example, the skyscraper index correlates the construction of very tall buildings with economic boom-times, and their completion with economic busts. The physical presence of a skyscraper is thus the representation of a major disequilibrium that had to be resolved. (Thornton, 2005) The morphology of this change is fractal in a similar way that the movement of a stock market is, a pattern that Mandelbrot has studied. In general we can describe the property of a city to adapt to change as a form of time-complexity, where the problems to be solved by the system at one point in time are different from those to be solved at a later point in time. The shorter the time-span between urban tissue transformations, meaning the shorter the feedback loops of urban growth, the closer to equilibrium the urban tissue will be at any particular point in time.

Modern urban plans do not include a dimension of time, and so cannot enable the creation of new networks either internally or externally. They determine an end-state whose objective is to restore a built equilibrium through a large, often highly speculative single effort. They accomplish this by creating a large-scale node on existing networks. In order for such a plan to be attempted the state of disequilibrium in the built environment must have grown large enough to justify the immense expense of the new plan. This is why development will concentrate very large numbers of the same building program in one place, whether it is a cluster of 1000 identical single-family homes or a regional shopping mall, just like the skyscraper concentrates multiple identical floors in one place. Demand for these buildings has become so urgent that they can find a buyer despite the absence of local networks, the standardized building plan, or the monotonous setting. This is not as problematic for large cities for which a single subdivision is only a small share of the total urban fabric, but for smaller towns the same project can double the size of the urban fabric and overshoot the built equilibrium into an opposite and severe disequilibrium.

The mixed-used real estate development has attempted to recreate the sustainable features of the spontaneous city by imitating the morphology of sustainable local economic networks. It has not reintroduced the time dimension in economic network growth. Often this has resulted in a commercial sector that serves not the local neighborhood but the larger region first, consistent with the commercial sector being a product of large-scale economic network disequilibrium. In other developments the commercial sectors have struggled and been kept alive through subsidies from residential development, which is evidence of its unsustainability as part of the system.


Alexander, Christopher (1965). ‘A City is not a Tree’, Architectural Forum, vol. 122 no. 2
Alexander, Christopher (1975). The Oregon Experiment, Oxford University Press, USA
Hakim, Besim (2007). ‘Revitalizing Historic Towns and Heritage Districts,’ International Journal of Architectural Research, vol. 1 issue 3
Hillier, Bill (1996). Space is the Machine, Cambridge University Press, UK
Salingaros, Nikos (1998). ‘Theory of the Urban Web’, Journal of Urban Design, vol. 3
Thornton, Mark (2005). ‘Skyscrapers and Business Cycles,’ Quarterly Journal of Austrian Economics, vol. 8 no. 1
Wolfram, Stephen (2002). A New Kind of Science, Wolfram Media, USA

The complex grid

In a medieval-era city the pace of urban growth is slow to a point where the growth of the city is not consciously noticed. Buildings are added sporadically, in random shape and order, as the extremely scarce economic situation makes no other pattern possible. Typically this means that the shape of streets will match the existing natural paths of movement, giving the street network an organic structure that is preserved through successive transformations in the urban fabric.

This works until the street network becomes large enough to become a functional problem. Because it is random, the medieval street network becomes complicated to move around in once the structure exceeds a certain scale. Some people see this as an obstacle to commerce and project to restructure the emergent medieval grid into something more rational. These projects fail for the same economic reasons that shaped the emergence of the medieval streets.

As the pace of urban growth increases and as the cartesian paradigm expands in the 17th and 18th centuries, deliberate city planning through the pre-emptive definition of an urban grid becomes fashionable. The practice of baroque planning remains the privilege of ultra-rich landlords considering the scale of construction involved. (Louis XIV’s Versailles is still the case study.) In the Americas such concentrations of capital do not yet exist. Grids are not truly part of a city plan, they are the outcome of regulations meant to avoid the pitfalls of medieval urban growth. Although the idea of a block is defined, the limiting shape of the grid itself is undefined. This allows cities to grow out, in theory, infinitely.

This works until the grid encounters and existing structure in the landscape. While Europe’s land is already very complex, in America the land is mostly empty. One exception is New York, which has multiple grids expanding towards the center of Manhattan, all with their own alignment with the waterfront. Compounding the medieval streets below Wall Street, the city’s network is getting messy. The solution conceived is the first city plan of New York, the Commissioners’ Plan of 1811, which grids Manhattan in the pattern it is famous for to this day with the help of a concentrated political power. In Europe this much centralization is not available, cities being ringed by a large number of villages that already structure the land. One notable exception is Barcelona, which under conservative military domination had reserved a large non aedificandi zone outside of its defensive walls. With the military out of the picture, and the industrial revolution putting enormous pressure on the city’s growth, the next most famous cartesian grid plan is imposed: the eixample. Adepts of the medieval city such as Camillo Sitte praise its artistic value and quality of life, but fail to truly describe how to reproduce it in the context of accelerating urbanization.

The 19th century is the triumph of the cartesian plan. It is not only employed to plan cities but to plan the entire American landscape. West of the original colonies the map becomes rectilinear. The flexibility and fluidity of New York’s grid plan promotes very rapid land development and the city achieves growth rates never before seen. European city planners are facing the same growth pressure but are trapped by the land’s existing structure, both physical and political. One simple solution is discovered: demolishing city walls and building a high capacity road that encircles the city, the boulevard. If it is to be complicated to get inside a city, it will at least be simple to get around it. Paris builds two on its two successive walls, and Vienna builds the famous Ringstrasse. An interesting phenomenon emerges from subsequent growth. While the boulevards were meant to be restful promenades, they emerge to become important centers on their own due to their attractiveness for traffic. In space syntax terms, they are integrators.

Manhattan’s grid extends to over a hundred streets but starts to suffer from severe scale problems. The medieval street system drives traffic away to boulevards, but in an endless grid traffic goes everywhere, and there is no place that is free of the increasing congestion. With the introduction of the car the endless grid is in crisis. Since no better idea is found, the grid system is replaced with the high-capacity collector road to concentrate all the congestion, from which huge, isolated developments  access each other. This is the suburban sprawl system that remains the norm. It has the advantages of being simple to plan and giving enormous clout to land developers. However people are dissatisfied with the enormous scale of their environment. That they enjoy a single-family home does not sufficiently conceal the fact that they are clustered with thousands of similar homes, and next to those are huge strip malls, office parks and shopping malls that require long vehicle trips to access. The disconnect between their homes and their activities means they live in a form of crowded isolation. The suburbanites escaped congestion only to arrive at emptiness. There is more life in the less populated countryside. Adepts of the metropolitan grid such as Rem Koolhaas praise the culture of congestion as a lifestyle that the collector road fails to create.

This was as briefly stated as I could the modern history of the urban network: one system failing to adapt to the scale of the city, being replaced by a larger system that erases the small scale complexity of the previous only to itself fail at a much larger scale, and then another larger system crushing all complexity to resolve a problem of modernity.

Is there a way that we could have the benefits of all systems balanced as a whole urban network? To describe such a system, we can first define some proscriptions.

  • Any size of urban growth is allowed as long as the new growth extends the boundary of the network. This ensures that the city has the economic flexibility of the medieval city and allows anyone, no matter their economic importance, to contribute to the city’s growth.
  • The network must not become so complicated that it becomes impossible to move around in order to participate in large-scale activities and a culture of congestion.
  • Streets must not grow too long without interruption in such a way that speeding and traffic accidents are encouraged.

How does this work out in terms of prescriptions? It turns out to be very simple. If we assume that we start with a hamlet of a single block, or a regional road that is undeveloped, we need only two rules: one for private development and one for the community.

  • For private development: you may build on any available part of the network so long as you replace the part you used up by extending the network around your new block.
  • For community development: any time a part of the network becomes too complicated (for example it takes more than 4 steps to get out of a sector), extend the boundary of that part with a higher capacity road (a boulevard).

How do we tell if these two rules really do meet the proscriptions we defined? Since we’re talking about an emergent design, the only way to see how it works is to do an explicit simulation of the computations involved. For this I employed a Fibonacci sequence to stand for a random growth process. With each new block that the sequence generated, I placed it in the section of the network that minimized the private cost of extending the boundary. I also used square blocks to simplify the computations involved, and also to demonstrate how such a process would work in a structure of land that has been made square, for better of worse, through cartesian planning. The process would work just as well in a more fluid, rounder land structure such as exists in Europe and the American East.

Stage 1: The village


The village is a cluster of houses and small businesses, whose only real challenge is maintaining a facade with the outside by ensuring that every new block also fronts the countryside. This provides the village with a path that everyone can walk around on whenever they want to get some fresh air and open space.

Stage 2: The town


The town starts to support development at larger scales with bigger block sizes. The first boulevards are built around the original village, preserving its traditional atmosphere from the growing businesses on the new boulevards.

Stage 3: The city


Now a significant regional center, the city’s economic complexity is heralded by the construction of the ring road enclosing the town’s neighborhoods. Large developments such as a regional shopping mall, an airport and a TND line the ring road alongside other smaller blocks of more traditional housing and business that take advantage of the high centrality of the ring and its new culture of congestion, eventually forming whole neighborhoods of their own. The ring road also encloses available green spaces for recreation, making it a parkway in some segments.

Emergent properties of the process

The most interesting outcome is that the structure of the network makes a very nice chaotic fractal, showing the balance between scales in the city’s growth. It is simultaneously simple to grasp and complex, living geometry.


The spatial integration created by the boulevards and ring roads also promotes the creation of a hierarchy of different centers that are evenly distributed between neighborhoods. Tightly knit residential quarters provide security for children and the elderly, with neighborhood centers within walking distance and no threat of heavy traffic until the edge of the city, liberating citizens from automobile dependency.

Adopting a complex grid is going to benefit small towns and villages most, as their economy is typically not large enough to support the collector road system. It might even result in the emergence of new villages in rural regions that have experienced large-scale urbanization and thus make them more resilient to economic shocks.

For existing cities, history provides a precedent for increasing the grid’s complexity when the problem is scaling up the grid. The urban renovations of Haussmann in Paris or Robert Moses in New York showed how to compose a larger scale within an existing city. (In Moses’ case, how not to do so as well.) However there is no precedent for scaling down a network that is too big, which is what modern cities suffer from. I suspect that contrary to scaling up which requires a strong centralization of power, scaling down involves a decentralization and a multiplicity of new powers transforming neighborhoods, breaking up regional, municipal and even neighborhood authorities such as homeowners’ associations to create local economies.

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