How a city splits up when nobody wants it to

Schelling's model: mild preferences, a very segregated city.

In 1971 the economist Thomas Schelling scattered coins on a grid and moved them by one rule. A coin is content if enough of its neighbors match it. Otherwise it moves to an empty square. There's no history, no institutions and no hate in the model.

Set how many same-color neighbors a household wants, then press Run or Step. Start at 30%, where every household is happy being outnumbered two to one.

They asked for 30%. They got 75%.

The city settles where the average household's neighbors are three-quarters its own color, two and a half times what anyone wanted. One unhappy household leaves, which changes the mix for the neighbors left behind, and some of them leave too. A mixed city is possible here but unstable, like a pencil on its tip.

At 20% almost nothing happens, so the tipping point is between one in five and one in three. At 60% the city ends 98% separated. At 70% it takes thousands of moves to separate completely. At 80% the demands can't all be met at once, so households keep moving forever.

What the model proves

Schelling never said segregation is innocent. American cities had redlining, racial covenants and steering, which this model leaves out. His point was that you can't read individual intent from an overall pattern. A segregated map fits a city of bigots and a city of people happy to be minorities.

The reverse holds too. If segregation doesn't need bigots, removing bigotry won't automatically undo it. Everyone is already content, so nobody has a reason to move. Good intentions at the bottom don't add up to the outcome you wanted at the top.