Fig. 1.
Configurations of a city composed of Q = 36 blocks containing each H = 100 cells, with ρ0 = 1/2. (A) Mixed state. Stationary state of the city for m = 0.5, α = 1, and T → 0. Agents are distributed homogeneously between the blocks, each of them having a density of 0.5. (B) Segregated configuration. Stationary state of the city for m = 0.5, α = 0, and T → 0. Agents are gathered on 22 blocks of mean density 0.82, the other blocks being empty. In the original Schelling model (8), each agent has a distinct neighborhood, defined by its eight nearest neighbors. Here, we only keep the essential ingredient of blocks of distinct densities. Our model shows the same qualitative behavior as Schelling's but can be solved exactly, thanks to the partial reduction of the agents' heterogeneity.