Conway's Game of Life

Life is a zero-player game: its evolution is determined by its initial state, requiring no further input ¹. Each cell counts its eight neighbours. A live cell with two or three live neighbours survives, a dead cell with exactly three is born, and every other cell dies or stays empty ²³. Conway chose the rules after a long period of experimentation ⁴, so that the behaviour of a population would be unpredictable ⁵.

Patterns fall into still lifes, which never change; oscillators, which return to their start after a fixed number of generations; and spaceships, which travel across the grid ¹. The glider rebuilds itself every four generations one cell further along a diagonal ². Conway offered $50 for a proof either way that no pattern grows without limit ³. An MIT team led by Bill Gosper won it in November 1970 ⁴ with a gun that fires a new glider every 30 generations ⁵. Life is as powerful as any computer with unlimited memory: it is Turing complete ⁶.

Life first appeared in the October 1970 Scientific American ¹, in Martin Gardner's column, which was based on personal conversations with Conway ². It became the most widely read of all Gardner's columns and made Conway an instant celebrity ³. Conway later came to dislike how talk about him centred on Life, feeling it overshadowed deeper and more important work, though he stayed proud of it ⁴. The game helped launch a new branch of mathematics, cellular automata ⁵.