Conway's Game of Life
Run Conway's Game of Life in your browser. Draw cells, load classic patterns like the Gosper glider gun and pulsar, control speed, and watch how four simple rules produce gliders, oscillators, and self-replicating structures.
Click or drag on the grid to draw and erase cells.
The four rules
The Game of Life, devised by mathematician John Conway in 1970, is a zero-player game: you set an initial state and the grid evolves on its own. Every cell is either alive or dead, and each step (a “generation”) every cell updates simultaneously based only on its eight neighbors.
- Underpopulation: a live cell with fewer than 2 live neighbors dies.
- Survival: a live cell with 2 or 3 live neighbors stays alive.
- Overpopulation: a live cell with more than 3 live neighbors dies.
- Reproduction: a dead cell with exactly 3 live neighbors becomes alive.
That is the entire ruleset — often written as B3/S23 (born on 3, survives on 2 or 3). Despite its simplicity, the system is Turing complete: anything a computer can compute can, in principle, be built inside it.
Pattern types
| Class | Behavior | Examples |
|---|---|---|
| Still life | Never changes | Block, beehive, loaf |
| Oscillator | Repeats with a fixed period | Blinker (2), beacon (2), pulsar (3) |
| Spaceship | Translates across the grid | Glider, lightweight ship (LWSS) |
| Gun | Emits spaceships forever | Gosper glider gun |
| Methuselah | Tiny start, long chaotic evolution | R-pentomino, acorn |
Things to try
Load the Gosper glider gun and press Play — it produces a stream of gliders indefinitely, the discovery that proved patterns could grow without bound. Try the R-pentomino: just five cells that churn for 1,103 generations before stabilizing, scattering gliders along the way.
Toggle Wrap edges off to see patterns die at the boundary instead of re-entering from the opposite side. Draw your own shapes by clicking and dragging — symmetric starting blobs often collapse into a mix of still lifes and blinkers.
Why it matters
The Game of Life is the canonical example of emergence — complex, lifelike behavior arising from trivial local rules with no central control. It is widely used to teach cellular automata, parallel computation, and self-organization, and remains an active area of recreational mathematics where new patterns are still being discovered.