Schelling's segregation model
Thomas Schelling, in 1971, showed that a small preference for one's neighbors
to be of the same color could lead to total segregation. He used
coins on graph paper to demonstrate his theory by placing pennies and nickels
in different patterns on the "board" and then moving them one by one if
they were in an "unhappy" situation. Here's the hightech equivalent. The
rule this ALife model operates on is that for every colored cell, if greater
than 33% of the adjacent cells are of a different color, the cell moves
to another randomly selected cell.
This is my first experiment with writing computer programs to simulate
interesting processes we come across in real life. There are a number of
reasons why this kind of simulation is useful and I'll try to summarize
what in my mind are the main ones:

Most modelling techniques are based on the notion that an equilibrium state
is the norm, while cellular automata (CA) simulations do not have this
bias.

Instead of trying to create a model that requires a full understanding
of the highly complex outcomes of processes, CA allows us to understand
the decision rules of a small number of individual actors.

Simulation models are very good at incorporating time and space, especially
when tied to a geographic information system.
For more information on Schelling's segregation model, please see:
Schelling, Thomas C. 1971. "Dynamic Models of
Segregation." Journal of Mathematical Sociology 1:143186.
Krugman, Paul 1996. The SelfOrganizing Economy
Blackman, New York.
W.A.V. Clark 1991. "Residential Preferences and Neighborhood
Racial Segregation: A Test of the Schelling Segregation Model." Demography
28:1.
For more information on artifial life models, please see Exploring
Emergence, Sugarscape
and Swarm.