Emergence

Conway's Game of Life

Conway's Game of Life is a discrete mathematical model on a two-dimensional grid. Each cell is either alive or dead, and time advances in fixed ticks. On each tick, a dead cell is born with exactly 3 live neighbours, and a live cell survives with 2 or 3 live neighbours. This is the classic B3/S23 rule.

Try the simulation below ↓

Scientific interest

The update rule is deterministic: the next state of each cell depends only on its current state and the count of its eight live neighbours. There is no randomness in the rule itself. Given the same initial state, each run produces the same trajectory. But deterministic does not mean easy to predict; to know what happens, you still need to run the system forward — try R-pentomino ↓.

That is why the model is scientifically useful. Simple local rules create rich global behaviour: stable structures, oscillators, moving patterns, long transients, and sensitivity to initial conditions — see canonical patterns ↓. Complexity emerges from interaction, not from central control.

Press play to start. Selecting a seed stops and resets the simulation. The simulation is deterministic.