Phase Transitions in 2D Cellular Automata--A 3D View
When the initial density of occupied cells goes above 0.5, there is a sudden transition from a final state that is eventually vacant to one that is eventually fully occupied.
This Demonstration displays the evolution of a 2D cellular automaton as it runs for the number of steps you specify with the "evolution steps" slider. After enough steps, the CA reaches a state where black or white cells tend to dominate, depending on whether there were more black or white cells in the initial state. The specific configuration of the initial state, which you can vary with the "initial configuration" slider, does not affect the final state very much, except when the initial density of black cells is very close to 0.5.