What is the Game of Life?

Conway’s Game of Life is a cellular automaton invented by British mathematician John Horton Conway in 1970. It is a zero-player game: you set up an initial configuration of living cells on a grid and then observe how the population evolves over time according to four simple rules. Despite those simple rules, the Game of Life produces strikingly complex and unpredictable behavior - a vivid illustration of how emergent complexity can arise from simple local interactions.

The four rules

At each generation (time step), every cell on the infinite grid is evaluated simultaneously:

Underpopulation: A live cell with fewer than 2 live neighbors dies.
Survival: A live cell with 2 or 3 live neighbors survives to the next generation.
Overpopulation: A live cell with more than 3 live neighbors dies.
Reproduction: A dead cell with exactly 3 live neighbors becomes alive.

“Neighbors” means the 8 cells surrounding a cell horizontally, vertically, and diagonally (Moore neighborhood).

Controls

Click a cell to toggle it alive or dead.
Play / Pause: start or stop the simulation.
Step: advance exactly one generation while paused.
Speed slider: control how fast generations advance.
Clear: reset the grid to all dead cells.
Random: seed the grid with a random live/dead pattern.

Classic patterns

Three broad categories of pattern emerge from the rules: still lifes (stable), oscillators (periodic), and spaceships (translate across the grid).

Category	Name	Description
Still life	Block	2×2 square; the simplest stable pattern.
Still life	Beehive	6-cell hexagonal cluster; very stable.
Still life	Loaf	7-cell pattern; common in random soups.
Oscillator	Blinker	3 cells in a row; alternates horizontal/vertical. Period 2.
Oscillator	Toad	6 cells; shifts one cell each generation. Period 2.
Oscillator	Pulsar	48-cell symmetric oscillator. Period 3.
Spaceship	Glider	5 cells; moves diagonally across the grid. Period 4.
Spaceship	LWSS	Lightweight spaceship; 9 cells; moves horizontally. Period 4.
Gun	Gosper Glider Gun	Emits a new glider every 30 generations - the first known pattern with unbounded population growth.

Why it matters

The Game of Life is Turing complete: given a large enough grid, you can construct patterns that simulate any computation a computer can perform, including logic gates, memory, and even a full computer. It has influenced computer science theory, artificial life research, and biology, where similar rule-based models are used to understand cell division, tumor growth, and population dynamics. Conway’s work demonstrated that immense complexity - including self-replication - can arise from the simplest possible rules.

Pattern resources

LifeWiki (conwaylife.com/wiki) is the canonical reference for Game of Life patterns, containing thousands of named patterns with their properties, discovery history, and RLE (run-length encoded) format for importing into simulators. The Golly simulator supports patterns with populations in the billions through the Hashlife algorithm, enabling exploration of patterns that run for millions of generations.