Emergent Urbanism

Rediscovering Urban Complexity

The mathematical definition of a city

20th century professional urbanism is the story of a war on complexity in order to control urbanization.

The modernists rebelled against the "mess" of the city. They put everything in their place. In this square shall be the houses. In that square the offices. In that square the stores. In some form of another, this system, called zoning, is in force over 99% of the American continent. Its main advantage is that it is incredibly lazy.

For more than half a century, the in-between, what is not really a house, a shop or an office, has had no place. The "boomtowns" of today are endless grids of single-purpose zones.

They call this urban planning. They took control of the city's future by destroying it. But they didn't really know what they were destroying.

A city is not reducible to parts. A city is a mesh of relationships between spaces. It begins once a space is built to provide a specialized function that is not fulfilled by another existing space, and the two spaces are linked together by a communication system. Let's call this first space a and the new space b. Once a and b form relationship a-b, the city X is born. X is a set which contains relationships.

When a and b are deficient in some manner, a third space, c, is added to the set. X then becomes (a-b, c-b). Then space d may be added to form the set (a-b, c-b, c-d). This process continues as more spaces are created and new relationships are formed. The city becomes a very complex mesh, or semi-lattice. You cannot isolate any part of this mesh from the rest.

Sim City 4 pictures the shape of these relationships when you click on the commutes for any building. Each building has a web extending out through the city, and these webs overlap and interweave each other as a single system.

The relationships do not split up into group. You cannot define "sub-cities," groups of relationships independent from each other. You cannot say that city A is made up of building set B and C. Inevitably some buildings in either group will need to form relationships to each other. But this is exactly what zoning is meant to prevent! In doing so, zoning destroys many forms of exchange and holds back the complexity of the city.

What exactly are such relationships? Any reason you might have to get out of the house. It could be going to the bakery. Your house d would form a relationship with bakery f, d-f. The bakery would have many customers in the neighborhood, and they would form relationships f-g, f-h, f-i and so on, even though you may never meet any of them. These people will have jobs that will form relationships g-m, h-n, i-n. All of you, together, create the life of the city, though you may never run into each other. Without business m, bakery f may not have enough customers to continue, and then you would no longer have access to a bakery.

Sometimes a space will lose all of its relationships and will be destroyed, but all the other relationships will remain part of the set. The continuous mesh of relationships is itself fully permanent. This is why cities have names that last through millennia, such as London and Paris, even though every building that made them up at their beginning has long since been removed and forgotten. The set of relationships is still exactly where it has always been. It has been transformed and developed, but never destroyed. At every point in time the set exists even though spaces flow in and out of it, much like a river is not defined as a lump of water molecules but the flow of them.

It is only relationships and not the individual spaces that form a city. A block of identical row houses will not form relationships. Relationships will only form between spaces that are complementary, that is to say spaces that are differently adapted to their own specific functions. It thus makes no sense to create zoning codes for identical houses as there is no reason for these houses to be near each other. However, it does make sense to create multiple houses around a playground, as these houses will form a relationship with the playground.

Defining a city as relationships allows us to differentiate cities which are alive and growing from cities which are dead or dying. When the number of relationships in a city is increasing or stable, the city is alive. When the number of relationships in a city is shrinking or zero, the city is dead, despite the fact that there may still be buildings there! A ghost town does not have relationships.

Good urbanism is the creation of support systems for building relationships. Streets, public spaces, transportation networks and building codes achieve this. Zoning kills them.

The best support systems, the best urbanism, will permit the greatest density of relationships (not density of people), implying the greatest spacial complexity and diversity achievable.


Alexander, Christopher. A City is not a Tree.


Thanks for the site full of inspirational toughts and articles.

the best urbanism, will permit the greatest density of relationships (not density of people)

I couldn't agree more on this point. I believe that density of people is reasonably good proxy for the density of relationships when the later is harder to measure empirically. Denser urban areas (shorter distances between people and places) as well as better urban accessibility (less travel time also in the case of greater physical distances) make it easier and more propable to create relationships, but what else contributes to the creation of relationships? Is it possible to have really dense and busy streets that are actually poor in relationships?

My interest is to think (and eventually do) how for example the connectivity or density of relationships could be observed empirically in different scales in the data rich world where we live in.

To generate exuberant diversity in a city’s streets and districts […] There must be a sufficiently dense concentration of people, for whatever purposes they may be there.

― Jane Jacobs, The Death and Life of Great American Cities

Jacobs made a strong argument that a lively neighbourhood needs to have more than one primary and secondary usage so that there is a sufficiently dense concentration of people at all times of the day. The office blocks or sleeping suburbs can not support lively action, because people move and use the places all for the same purposes and at the same time. This causes traffic congestion and other types of infrastructure overuse at peak hours, but still can not guarantee steady flow of customers to support different services. For example a restaurant succeeds better in a place where there are both working places (lunchtime customers) and residential buildings (evening customers).

What data should be analyzed: Analysing the location data of mobile devices in city level has been used already to determine better public transport networks (see the video below ) based on the real movements of masses of people . The mobile data could be used also to measure the real time-varying concentration of people in different areas or neighborhoods (metrics for the Jane Jacobs idea) and the interconnectivity of the neighbourhoods (a person that moves from one place to another creates a connection between those places - more connections between two places the more interconnected those places are)

Insights in Motion: Improving Public Transit in Istanbul (IBM + Vodafone)

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