During the 1940s, British mathematician John H. Conway was studying John von Neumann's complex research into self-replicating systems. He created a set of rules that greatly simplified von Neumann's work and introduced them in 1970 as the Game of Life.
The rules are simply this: Given a grid, each cell in the grid can be "alive" or "dead". A cell becomes alive when exactly three of its neighbors are alive, and dies when it has fewer than two living neighbors (loneliness) or more than three living neighbors (overcrowding). The grid starts with a random number and placement of living cells and is updated at regular intervals until an unchanging, stable community is reached.
The Wikipedia entry on Conway's Game of Life is a great place to learn more about this facinating puzzle.