Conway's Game of Life

The Game of Life, also known as Life or Conway's Game of Life, is a zero-player "game" created in 1970 by mathematician John Conway. Given an initial state, a two-dimensional cellular grid of finite automata changes over time in a series of generations. Each cell survives, dies, or reproduces based upon how many adjacent neighbors it has. Conway's game (screenshot shown right) led to the creation of a new field of mathematics called cellular automata. It remains famous as a simple, instructive program for students of computer programming.

Turing Completeness

Conway's game of life represents a Turing-complete or "Universal" machine. It's been proven possible (although difficult and inefficient) to create any other computer using only the rules in Conway's game.

Game of Life's four rules

Isolation: Any living cell with fewer than two live neighbors dies.

Balance: Any living cell with two or three live neighbors survives to the next generation.

Overcrowding: Any living cell with more than three live neighbors dies.

Reproduction: Any dead cell with exactly three living neighbors becomes alive.

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