Each cell looks at its eight neighbours and lives, dies or is born by three rules. That is all. Yet out of it come shapes that move, repeat, grow and even compute.
Pick Glider and press Step once four times. The five cells come back to the same shape, one square further along. Nothing in the rules says "move", yet it moves.
Try Diehard: seven cells that churn for a long time and then vanish at generation 130. Then try the R-pentomino, just five cells, which on an endless grid keeps changing for 1,103 generations.
Pick the Gosper glider gun and untick Edges wrap around to watch it fire a glider every 30 generations. Then draw your own pattern and see if you can make something that blinks, or something that travels.
The mathematician John Conway invented the game at Cambridge in 1970. He wanted the simplest rules he could find that still made patterns hard to predict. Martin Gardner shared it with the world in his "Mathematical Games" column in Scientific American in October 1970, and readers everywhere started playing it on graph paper and early computers.
In that column Conway offered a $50 prize to the first person who could prove or disprove that no pattern can grow forever. Before the year was out, a team at MIT led by Bill Gosper won it with the glider gun you can stamp here: it never stops making new gliders, so the pattern grows without limit.
Later it was shown that Life is "Turing complete": with the right starting pattern, the grid can work out anything an ordinary computer can. Three rules about neighbours are enough to build a computer.
