John Horton Conway · 1970

Conway's Game of Life

A zero-player game on an infinite grid. Four rules. No pieces. No objectives. Pure emergence — and one of the most profound demonstrations of complexity arising from simplicity ever devised.

▶ Open Interactive Demo
4Rules
2States per cell
Possible patterns
1970Year invented
TCTuring complete

Set on an infinite two-dimensional grid of square cells, each cell is either alive or dead. Each generation, every cell applies the same four rules based solely on its eight neighbors. No central controller. No external input. Yet from these rules springs an endless parade of structures — gliders that travel forever, oscillators that pulse, guns that fire streams of spaceships, and configurations so complex they can compute anything a computer can.

The Game of Life is not a game in any traditional sense. Conway called it a "zero-player game". You set up an initial configuration and watch. The rules do the rest.

The four rules
01
Underpopulation
A live cell with fewer than 2 live neighbors dies — as if by loneliness.
02
Survival
A live cell with 2 or 3 live neighbors survives to the next generation.
03
Overpopulation
A live cell with more than 3 live neighbors dies — as if by overcrowding.
04
Reproduction
A dead cell with exactly 3 live neighbors becomes alive — as if by reproduction.
Explore
🖥️
Interactive Demo
Full-screen playground with zoom, pan, draw, erase, presets, speed control, and age-based cell coloring. Load famous patterns or paint your own.
Live
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History
John Horton Conway, the Mathematical Games column in Scientific American, and how a simple cellular automaton captured the world's imagination in 1970.
Deep dive
⚗️
Science
Cellular automata theory, emergence, Turing completeness, the universal constructor, and where GoL sits on Wolfram's classification of complex systems.
Theory
🔬
Patterns
Gallery of famous patterns — still lifes, oscillators, spaceships, glider guns, and long-lived methuselahs. Each with a live demo link.
Gallery
🌐
Impact
How GoL inspired artificial life, complexity science, genetic algorithms, digital physics, and a generation of researchers who saw computation as fundamental to nature.
Legacy