Consider an n x n grid. 30% of the cells are colored green and another 30% are colored blue at random. The remaining cells are empty. It is preferred that each colored cell has 3 neighbors (of the 8 neighbors) of the same color. Colored cells which do not have 3 same color neighbors are called "wrong". The following process occurs: At each time step, a wrong cell will choose to relocate to an empty cell such that after the move it has at least 3 neighbors of the same color. What's interesting to note is that this process results in clustering of the cells, with green cells in 1 cluster and blue cells in another. This goes to illustrate that small group preferences within a community can lead to large segregation. A demonstration is shown in understandingprejudice.org.
Now if you see the racial dot map of the united states, can you explain why there is so much segregation?
Alright, if you want a puzzle (or rather a research problem), calculate the expected number of clusters when the process terminates. A cluster is a contiguous region of colored cells of the same color. Also calculate the probability that there are 2 clusters (one for blue and one for green). Again, it's a research problem, I don't know if an elegant solution exists.