Interactive simulator
Field guide
Preset patterns
Load a known pattern into the center of the grid. Each one clears the board first.
Background
What is Conway's Game of Life?
The Game of Life is a cellular automaton devised in 1970 by British mathematician John Horton Conway. It isn't a game in the traditional sense — there are no players, no moves, and no way to win. Instead, you set an initial pattern of living cells on a grid, and the simulation evolves it forward one generation at a time according to four fixed rules.
Every cell on the board looks at its eight neighbors and decides whether to live, die, or be born. Applied over and over, these simple local rules give rise to gliders that crawl across the grid, oscillators that pulse in place, and "guns" that fire off new patterns indefinitely — behavior nobody explicitly programmed in.
- 01Underpopulation — a living cell with fewer than two live neighbors dies.
- 02Survival — a living cell with two or three live neighbors keeps living.
- 03Overpopulation — a living cell with more than three live neighbors dies.
- 04Reproduction — a dead cell with exactly three live neighbors becomes alive.
Why mathematicians still care
Conway originally searched for a rule set where patterns were unpredictable enough to be interesting, but not so chaotic that everything died out or exploded instantly. The Game of Life sits right at that edge — a balance point often called "the edge of chaos." Researchers have since built working logic gates, memory registers, and even self-replicating structures entirely out of Life cells — all from the same four rules above. It's a favorite example in discussions of emergence, and it's Turing complete: in principle, patterns built from these rules can perform any computation a computer can.