Conway's Game of Life in Minecraft

Check this out. This is a massive simulation of Conway's Game of Life in Minecraft using logic circuits built out of redstone wire and redstone torches. Each cell in the video calculates how many neighbour cells are on and decides whether to stay active (or "alive") or turn off ("die"). Each cell can have 0-8 active neighbour cells. Every cell is 13 blocks wide, 16 blocks long and 35 blocks high. It takes 2 to 6 seconds for the cells to calculate the next stage in the game.

The game works like this:
If a cell is active and has 2 or 3 neighbours it stays alive.
If a cell is dead and has 3 active neighbours, it will turn on.
Otherwise, the cell dies.

To learn more about redstone circuits, this is an awesome resource: Minecraft crafting recipes.