This applet simulates generalisations of Conway's Game of Life, running in a wrapped 200 x 200 space, with a random initial population. At each generation, the number of live immediate neighbours (8 at most) are counted and the rule applied to determine the cells survival or death in the next generation. You can design your own rule, generate a random rule or run Conway's rule.
There are a total of a quarter of a million different rules - 2^18. I don't know how Conway found his perhaps uniquely rich rule. The initial density affects the behavior - very high or very low sometimes produces interesting variations.
Click in the image to get the generation number and density, click again to restart.