Conway's Game of Life
The background of this site is a living Game of Life simulation. Three rules. Infinite complexity. Turing-complete computation emerging from a grid of cells that are either alive or dead.
"It's known that the Game of Life is, in theory, universal — my conjecture is that it's universal in practice, that it can be made to do anything that any computer can do."
— John Horton Conway
The rules
An infinite two-dimensional grid. Each cell is alive or dead. At every tick, each cell counts its eight neighbors and applies three rules:
- Birth. A dead cell with exactly three live neighbors becomes alive.
- Survival. A live cell with two or three live neighbors stays alive.
- Death. Everything else dies — from loneliness or overcrowding.
That's it. No randomness, no special cases. Every future state is determined entirely by the initial configuration. Yet from this determinism emerges staggering complexity.
Origin
John Horton Conway, a mathematician at Cambridge and later Princeton, devised the Game of Life in 1970. He was searching for a cellular automaton that was unpredictable — a system where simple rules could produce behavior so complex that no shortcut could predict the outcome without actually running the simulation. He spent years adjusting rules by hand, playing out generations on a Go board with colleagues, before arriving at these three.
The game was first introduced to the world through Martin Gardner's Mathematical Games column in the October 1970 issue of Scientific American. It became an overnight sensation. Readers across the world began discovering patterns, building increasingly complex structures, and pushing the boundaries of what a handful of rules could produce.
Emergence
The Game of Life is the canonical example of emergence — complex behavior arising from simple components with no central control. From the three rules come stable structures (still lifes), repeating patterns (oscillators), and structures that move across the grid (spaceships). The most famous spaceship is the glider, a five-cell pattern that drifts diagonally forever.
In 1982, Conway proved the game is Turing-complete: it can simulate any computation that any computer can perform. People have built logic gates, adders, clocks, and even entire processors within the Game of Life. A universal Turing machine was eventually constructed — a pattern of cells that can compute anything, given enough space and time.
Conway
John Conway (1937–2020) was one of the most inventive mathematicians of the 20th century. His contributions span group theory, number theory, combinatorics, and geometry — the surreal numbers, the Doomsday algorithm, monstrous moonshine, and far more. He was famously ambivalent about the Game of Life's fame, sometimes frustrated that it overshadowed his deeper mathematical work. But the game's enduring influence on computer science, complexity theory, and artificial life is undeniable.