This discussion originally appeared on the Wired New York forums.
Allow me to point to a great example of contemporary emergence in New York City, and perhaps clarify the principles involved.
This, as most of you probably know, is Times Square.
There is a geometry to Times Square that makes it different from the rest of the city, that is to say there is some pattern in Times Square that is shared by every single building and not shared by buildings in the rest of the city. This pattern is the shape of the advertisements.
Those advertisements are not random. There is a complex order to them. The Times Square zoning regulations require that advertisements be placed, in relative (to building floors) proportions, on each facade. This was the result of an intervention by Robert A. M. Stern in the early 90's. This building code is a localized instruction given to each individual building, that constrains what the owners can do at one scale but gives them total freedom to personalize within that scale and beyond that scale.
The resulting pattern, no matter what advertisements are swapped in for other advertisements, is a place that is immediately recognizable. The code has created an organic symmetry. Should the same code be applied somewhere else in the world, it might be mistaken for Times Square.
Times Square is a system where different individuals, applying the same rule to their own individualized problems, work together without consciously being aware of it to create a large-scale geometric order.
Didn't Times Square have advertisements beforehand? From the point of view of complexity science, it is irrelevant where the rules that generate complexity came from. It can be from culture. It can be tradition. It can be imposed by government. It can be a multilateral protocol like the Internet. It can be just the physical nature of the thing, like cells that follow their DNA to generate organisms, or it can asserted as abstract logical constructs, like the Wolfram elementary cellular automatons, in which cases there is no will involved in following the rules.
What makes something emergent is this feature: localized decisions unconsciously create large-scale form by following a set of rules shared by other local decisions while solving local problems.
All cities, without exception, are emergent. Even Brasilia has favelas. There is just no way for one single human mind to design at that scale. Even if you were to build a plan for millions of apartments in neat rows of housing complexes, if someone so much as built a shack outside of your sphere of control, the experience of moving from that shack to the housing estate would be emergent. There was never a mortal power, from master builder to god-emperor, capable of avoiding that.
However not all cities are complex, and this is what we generally term an organic city. Complexity means that the city is solving multiple problems at multiple scales concurrently (it is fractal), which means that not only my house and my neighbor's office are fitted to their task, they are also fitted to their street, their neighborhood, their borough, and the metropolis as a whole. And the street is fitted to its space and the neighborhood, and the neighborhood is fitted to borough, and so on.
As we've seen in the past century, a lot of emergent processes are first of all completely accidental, and second complexity-destroying. But even the most boring of suburbia looks "organic" when you zoom out the scale far enough, because at that point it escaped the control of any single individual.