In 1971, Thomas Schelling published “Dynamic Models of Segregation,” which proposes a simple model of racial segregation. The Schelling model of the world is a grid; each cell represents a house. The houses are occupied by two kinds of “agents,” labeled red and blue, in roughly equal numbers. About 10% of the houses are empty.

At any point in time, an agent might be happy or unhappy, depending on the other agents in the neighborhood. The neighborhood of each house is the set of eight adjacent cells. In one version of the model, agents are happy if they have at least two neighbors like themselves and unhappy if they have one or zero.

The simulation proceeds by choosing an agent at random and checking to see whether it is happy. If so, then nothing happens; if not, the agent chooses one of the unoccupied cells at random and moves.

You might not be surprised to hear that this model leads to some segregation, but you might be surprised by the degree. Fairly quickly, clusters of similar agents appear. The clusters grow and coalesce over time until there are a small number of large clusters and most agents live in homogeneous neighborhoods.

If you did not know the process and only saw the result, you might assume that the agents were racist, but in fact all of them would be perfectly happy in a mixed neighborhood. Since they prefer not to be greatly outnumbered, they might be considered xenophobic at worst. Of course, these agents are a wild ...

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