Fig. 1.

Transition from a finite difference model into a continuous model. The Schelling model (Left) can be considered as a finite difference version of a more general continuous model (Right). Instead of counting neighboring individual grid cells, we can use angular coverage around a point where one neighboring grid cell on a rectangular grid corresponds to 45° angular coverage. In this way the cell configuration (a) is transformed into c and b into d. White represents empty space. Utility is the mirror of energy: high utility means low energy and vice versa. Energy is a function of the angle covered by unlike neighbors, and utility depends on the number, or proportion, of unlike neighboring cells. Now we have a complete description of the transformation from the Schelling model into its physics analogue.