Conway's Game of Life
A grid of squares, four simple rules, and no player at all — yet out of it come blinking lights, gliding "spaceships," and machines that build machines. Learn the rules, then try them yourself.
Four rules, one grid
The board is a grid of cells. Each cell is either alive (colored) or dead (empty). Time moves in steps called generations. At each step every cell looks at its neighbors, and all cells update at the same moment.
Every cell has eight neighbors: the cells touching it above, below, left, right and on the four diagonals. The only thing that matters is how many of those eight are alive. Count them, then apply the rules below.
Try it yourself
Click or drag on the grid to bring cells to life, then press Play or Step. New here? Start the guided tour.
Keys: Space play/pause · N step · R rotate stamp · Esc stop stamping
The zoo of patterns
After decades of exploring, Life fans sort patterns by how they behave over time. Every pattern in the library above belongs to one of these families.
Still lifes
Never change. Every live cell has 2 or 3 neighbors, and no empty cell has exactly 3. Example: the block.
Oscillators
Cycle through a fixed set of shapes and return to the start. The number of steps in the cycle is the period. The blinker has period 2.
Spaceships
Repeat their shape but end up somewhere else, so they travel across the grid. The glider moves one cell diagonally every 4 generations.
Guns
Stay in place and keep firing spaceships forever, so the population grows without limit on an endless grid.
Methuselahs
Tiny starting patterns that take a very long time to settle down. The 5-cell R-pentomino churns for 1,103 generations.
History & context
The Game of Life is a cellular automaton, a world made of cells that update by simple local rules. It's called a "zero-player game" because once you set up the starting pattern you only watch. Everything that happens afterward follows from the rules.
- 1940s — John von Neumann, working with Stanisław Ulam, studies cellular automata while asking whether a machine could build a copy of itself. His rules use 29 cell states.
- 1970 — British mathematician John Horton Conway at Cambridge searches for the simplest rules that still behave unpredictably. After trying many variants he settles on two states and the rule now written B3/S23 (Born with 3 neighbors, Survives with 2 or 3).
- October 1970 — Martin Gardner describes the game in his "Mathematical Games" column in Scientific American. Readers everywhere start running it by hand on graph paper and Go boards, and on early computers.
- November 1970 — Conway had offered $50 to whoever could prove a pattern can grow forever. A group at MIT led by Bill Gosper wins with the glider gun.
- 1982 — In Winning Ways for Your Mathematical Plays, Berlekamp, Conway and Guy outline why Life is Turing complete: streams of gliders can act as signals and logic gates, so in principle Life can compute anything a computer can.
- 2000 — Paul Rendell builds a working Turing machine inside Life. Later projects go as far as running Life inside Life.
- 2020 — Conway dies in April at age 82. He had mixed feelings about Life's fame overshadowing his other mathematics, but it remains his best-known creation.
Why it matters
Life is the classic example of emergence, where complicated behavior arises from very simple rules. No rule says "move diagonally," yet gliders move. That idea shows up in biology, physics, artificial life, and the study of complex systems. Life is also a good reminder that knowing the rules of a system is not the same as being able to predict it. For most patterns, the only way to learn what happens is to run them.
Things to try
- Draw a straight line of 10 cells and press Play. Try lines of other lengths too. Small changes give very different results.
- Turn on Show next generation, then predict each step before you press Step.
- Stamp two gliders heading toward each other. Collisions can destroy both, leave debris, or produce something new.
- Load the Gosper glider gun on the Large grid and watch the population graph climb in steps. Then see what happens when its gliders wrap around and hit it.
- Press Random a few times and keep Color by age on. The purple areas are the still lifes and oscillators that survived the chaos.
FAQ
Is it really a game?
Not in the usual sense. Nobody wins and nobody takes turns. "Game" is closer to "simulation" here. Your only move is choosing the starting pattern.
Why do things go off one edge and come back on the other?
The ideal Life board is infinite, but a screen isn't. This board wraps around: the right edge connects to the left and the top to the bottom, like a donut-shaped world. Patterns don't hit a wall, but they can travel around and run into themselves.
Why does the R-pentomino behave differently here than the books say?
Famous figures like "1,103 generations" assume an infinite board. On a small wrapping board, debris and gliders come back around and collide with things, so long-running patterns usually end differently. Try the Large grid for results closer to the real ones.
Does every pattern eventually settle down?
No. Guns grow forever, and there is no general shortcut for predicting what an arbitrary pattern will do, because Life can simulate any computer. On a finite board like this one, though, every pattern must eventually repeat, since there are only so many possible boards. The status badge tells you when the board has settled.
What does "B3/S23" mean?
It's shorthand for the rules: a dead cell is Born with exactly 3 neighbors, and a live cell Survives with 2 or 3. Changing these numbers gives different "Life-like" worlds, such as HighLife (B36/S23), which has a pattern that copies itself.