In 1970, British mathematician John Horton Conway invented a zero-player mathematical game that stunned the world: The Game of Life.

Life takes place on a two-dimensional grid of cells, each of which is either alive or dead. Every cell interacts with its $8$ immediate neighbors (horizontally, vertically, and diagonally).

At each time step, all cells transition simultaneously according to four simple rules:

1. Underpopulation: Any live cell with fewer than $2$ live neighbors dies (as if by underpopulation).
2. Survival: Any live cell with $2$ or $3$ live neighbors lives on to the next generation.
3. Overpopulation: Any live cell with more than $3$ live neighbors dies (as if by overcrowding).
4. Reproduction: Any dead cell with exactly $3$ live neighbors becomes a live cell!

The Wonder of Emergent Complexity

From these elementary rules arises astonishing mathematical behavior:

• Still Lifes: Stable configurations that never change (e.g. Block, Beehive).
• Oscillators: Patterns that repeat in a rhythmic cycle (e.g. Blinker, Beacon, Pulsar).
• Spaceships: Self-propelling entities that travel across the grid forever (e.g. the Glider)!

Mathematicians have even proven that Conway's Game of Life is Turing Complete — you can build logic gates, binary counters, and simulate an entire computer inside it!

Move the mouse over a dotted box for more information.

• Interactive Drawing: You can click and drag with your mouse directly on the grid to create or erase living cells while the simulation is running!
• Toolbar Controls: Use the Play/Pause, Step, and Clear buttons above the canvas to control time.
• Toroidal Universe: The edges of the grid wrap around seamlessly (top connects to bottom, left connects to right).