There are two methods for producing fractal geometry. The first method, the decomposition, is the most easily understood. In a decomposition we apply an algorithm that breaks up the geometry of some starting point into several parts. We then re-apply this algorithm to the smaller parts created, obtain many more, even smaller parts, and continue this reiteration until we have reached the complexity limit at the smallest scale of object we can possibly make. This is how an architectural design proceeds because it reflects the way that building proceeds. A building has a hierarchy of dependencies that begins with the largest structure, the frame. The building is then built with smaller and smaller components until we reach the smallest, for example door handles and light fixtures.
The other method is the composition. In a composition we also apply an iterative algorithm, but instead of breaking down the initial geometry, we expand it. The fractal grows out instead of growing in. This is how urbanisation proceeds, by composing new streets and buildings onto an already existing web of streets and buildings, until we have reached the complexity limit of the largest city we can support.
If we look at this compositional fractal we see that the scale of the structure composed to the initial geometry increases exponentially. The largest structure comes last.
Many of the elementary cellular automatons discovered by Stephen Wolfram produce this fractal using only one dimension of instructions. Each cell, depending on its state (black or white) and the state of its left and right neighbors, applies the rule to determine its new state. A new line is written for every iteration of the algorithm on the previous line. The complexity of the structure only becomes visible when the time dimension is displayed. At their local scale, the cells are not able to "see" how their actions create the system, but their actions do in fact make something bigger than themselves. They are creating a structure by emergence, and this emergence is visible only in a dimension larger than their actions: the emergent dimension.
I believe that the distinction between building and urbanisation, that is to say the distinction between action by decomposition and composition, also defines the distinction between architecture and urbanism. Architecture intervenes on a rigid structure defined at the beginning of the process, the building, and so runs into very strict economic limits of the scale of this large structure. Urbanism has to deal with the problem of creating large structures out of all of the small scale urbanisations that are undertaken by large numbers of individuals, all seeking to build something to suit their own personal problems. It is in that sense the inverse of architecture. Urbanism takes place in the emergent dimension.
The field of urban design has gained a lot of popularity since efforts to plan whole cities were abandoned. The focus of the urbanists has shifted to the scales considered controllable: the development, greenfield, brownfield and other. The most successful of the urban designers are the New Urbanists. They have managed to produce their name-brand Traditional Neighborhood Developments in practically every city in North America. It starts off inevitably with one developer and centralized ownership of the land that will be urbanised. This land is then decomposed into streets and squares along the principles proclaimed by the New Urbanist charter, the negative of which is decomposed into lots that will be further decomposed into buildings. In terms of production processes, New Urbanist TNDs are no different than the regular, economically-unsustainable subdivisions. They belong in the realm of architecture, and what is worse, they provide no connection to the larger urban context within which they are being inserted, suburbia.
Here is the Mackenzie Towne TND at the limits of Calgary Alberta, in mid-decomposition.
And here we see the development within the larger context of southern Calgary.
What were to happen to the people who have moved into the first part of the development if the developer declared bankruptcy, as has been the case in many developments these recent times? The construction site would remain in perpetuity, and their town would be incomplete. That is the very opposite of what a city is supposed to do, to provide a complete system regardless of the chaotic course of events.
Will the people of Mackenzie Towne live a New Urbanist lifestyle? One look at the bigger scale of the City of Calgary is sufficient to say no. The development is not the relevant scale of the urban life of its inhabitants. This follows from the fact that it is only a small part of the city as a whole, but is also what makes urban design economically possible in the first place. In order to be able to undertake a decomposition at that scale, we must be composing it to a much bigger system of urban relations.
I fear that no matter how intense the efforts the New Urbanists undertake to convert local authorities to their system, they will never be able to transform cities in their emergent dimension. We will continue to see appear, alongside TNDs, gigantic commercial strips, industrial zones and office parks, which will continue to form the emergent dimension of North American cities. At their center will be the caracteristic integrator of all of these urbanisations, the one space that every inhabitant of any modern city shares, the highways.
What then is urbanism? It is the glue that sticks different urbanisations, different architectural projects, together. North America has known only two general types. For all of the 19th century, and the first part of the 20th, the urbanism of North America was The Grid: unending checkerboard patterns of streets between which were blocks that were more or less developable into anything not bigger than the block. As cities grew with more urbanisations, new streets and blocks were composed onto existing streets and blocks, and this went on until the urban chaos became intolerable and people fled to the suburbs, a flight that was enabled by the new urbanism: the highway strip. The highway strip continues to be the compositional rule that integrates all North American cities. If you look again at Mackenzie Towne, the highway that borders it seems to have no relation at all to the development. This amounts to no urbanism. The emergent dimension is empty of any structure.
The New Urbanists have launched a parralel effort, alongside the TND, to reform municipal authorities' urbanism by inventing a building code, the SmartCode, that is supposed to fit into any city. Building codes have been the primary tool of urbanism for centuries. The reason they worked so well is that they made it possible for the smallest possible urbanisations to create large-scale structures, balancing local adaptation with large-scale solutions in order to create what we today call organic cities. Such a building code can do much to enable complexity, but it must be combined with the creation of the integrator spaces, streets, avenues and highways, that must also grow organically.
Looking over the fact that it doesn't appear to provide any indication of what to do with highways, the SmartCode ran into the objection that it was rules, and therefore anti-market. Ironically, the market is one of the first rules-based complex systems fully investigated. Adam Smith even christened its emergent dimension with a metaphor that continues to mystify people today: the invisible hand. The invisibility of the market results in many hotly-debated political issues, for example the incomprehension with surging gas prices during hurricanes. The reasons why gas prices should rise so rapidly escape the individual perspective, and angry commuters everywhere demand from politicians that something be done to control things. That attempt at control of the market would have unexpected consequences, just as it does in the emergent dimension of urbanism. Brasilia was the most famous realisation of fully-controlled town planning ever built, but today it is ringed with favelas and functions as one city with them. The emergent dimension of Brasilia escaped the strict control of its planners.
Urbanists must, by the nature of their work, be experts at seeing things in the emergent dimension. The tools to achieve that have yet to be invented. Economic treatises crudely made the case for the economy as an emergent system, but the 200 years of economic history that followed them showed that people would not believe what they could not see. They will not believe in the SmartCode until they can see it either. The invention of the microscope made it possible to see what was too small to see. We must invent the tool that makes it possible to see what is too large to see. Only then can we truly begin to create the cities that we want, as individuals and as communities, without taking a blind leap of faith.
Sustainable algorithmic design lecture series by Nikos Salingaros.