This page illlustrates Conway's Game of Life, a cellular automaton. The world comprises discrete squares which are occupied or not. Whether a square is occupied next time is determined by the eight squares adjacent to it following the simple rule:
An occupied cell remains occupied if it has 2 or 3 neighbours
An unoccupied cell becomes occupied if it has 3 neighbours
You can select different start patterns: some move, some oscillate, some reach a steady state, some die out.
The Press Next to update once or Run to continually update until you press Pause: you can also Speed Up / Slow Down the updates.