The image above shows the evolution, per iteration, for a run of the Schelling simulation.
The upper left grid shows the initial condition, which is a randomly arranged state. The seven remaining grids show the state of the board after each iteration, 8 of them in this case, before the simulation has found an end state, in this case, where no agent is dissatisfied. (The other possible end state is where there have been no moves in an iteration, indicating that an optimal but not satisfactory state has been reached).
Below some stat’s on this particular run:
- average number of foes at start: 3.15
- stopped at iteration 8 due to no more unhappy agents
- average number of foes after 8 iterations: 0.31
- moves per iteration:
[774 188 78 35 18 8 3 2]
It’s interesting to note that already after the first iteration of moves, the main divided clusters have been formed. The remaining iterations just provide the finishing touches to reach perfect segregation.