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.