The Game of Life
An infinite grid, two states, a four-line rule: run the most famous constructions, from the glider to giant computers, and watch them live.
Variables
- The pattern: more than 80 constructions sorted by family, from still lifes to guns, puffers, methuselahs and reflectors, plus the giant structures, each loaded in one click
- The cells: draw, erase, select, copy, cut, paste, rotate, flip, fill at random, import or export an RLE file
- The rule: Conway (B3/S23), HighLife, Seeds, Day & Night… or any B/S rule you type
- Time: generation by generation, up to 60 steps per second, in jumps of 2^k generations, or straight to the generation of your choice
- The view: from a single cell to millions of them, follow a spaceship, highlight births and deaths
Key figures
- B3/S23
- Conway’s rule: birth with 3 neighbours, survival with 2 or 3
- c/4
- the glider’s speed: one cell diagonally every 4 generations
- 30 gen.
- between two gliders of the Gosper gun
- 1,103
- generations before the 5-cell R-pentomino settles down
- 81
- catalogue patterns checked by the engine (period, speed, growth or lifespan)
What happens, step by step.
- 01
Four rules
Every cell is alive or dead and looks at its 8 neighbours. A dead cell with exactly 3 live neighbours is born. A live cell with 2 or 3 neighbours survives; with fewer it dies of loneliness, with more of overcrowding. All cells change at once, generation after generation. John Conway picked these rules in 1970 so that nothing could be predicted in advance.
- 02
A zoo of objects
Still lifes stop moving, oscillators return to their shape after a period, spaceships come back shifted: the glider moves one cell diagonally every 4 generations. Nothing really moves: cells die on one side and are born on the other. A ship’s speed is written as a fraction of c, one cell per generation, the speed limit of the game.
- 03
Machines that build machines
The Gosper glider gun (1970) fires a glider every 30 generations: it proved that a population can grow without bound. Puffers leave trails, rakes sow spaceships, and breeders build guns: their population grows like the square of time.
- 04
Unpredictable, yet deterministic
The R-pentomino has only 5 cells and churns for 1,103 generations before settling down; the acorn, 7 cells, for 5,206. Nothing is random: the same start always gives the same sequence. But in general there is no shortcut: to know what becomes of a configuration, you have to run it.
- 05
A universal computer
With gliders as signals and collisions as logic gates, the Game of Life can compute anything a computer can: it is Turing complete. Complete Turing machines, prime number calculators and even a cell, the OTCA metapixel, that simulates the Game of Life itself have been built in it. As a consequence, whether a configuration will eventually die out is, in general, undecidable.
- 06
HashLife: computing the future piece by piece
To run millions of cells over millions of generations, the lab uses Bill Gosper’s HashLife algorithm (1984). The universe is cut into nested squares; identical squares are stored only once, and the future of each square’s centre is remembered. A construction made of repeated parts then jumps 2^k generations in a single computation, even for a huge k.
What the scene simplifies
- The universe has no edge, but your device’s memory does: HashLife keeps at most a few million squares in memory and cleans up when it overflows. On the least repetitive constructions, a step of 2^k generations can then take several seconds.
- There is no colour by cell age: HashLife only keeps whether a cell is alive or dead, not each cell’s history. Instead, cells born or dead since the previous generation are highlighted, and only between two consecutive generations.
- From afar, one pixel stands for a 2^m × 2^m square of cells; its brightness shows the share of live cells, not how they are arranged. Zoom in to see the cells one by one.
- When the step is more than one generation, or the simulation runs faster than the screen, the display skips generations; the computation does them all.
- Period detection compares a fingerprint of every generation, up to translation: it only works one generation at a time, up to 40,000 cells and 20,000 generations. Two different states could in theory share a fingerprint; it is extremely unlikely.
- Only two-state rules of the B/S form are possible, without B0 (birth with no neighbours would light up the whole infinite universe).
- A methuselah’s “lifespan” follows the LifeWiki definition: the generation from which what remains is stable or periodic, ignoring gliders flying away.
Further reading
- Gardner, Scientific American 223 (4), 120 (1970)
The column that made John Conway’s game famous.
- Berlekamp, Conway & Guy, Winning Ways, vol. 2 (1982)
Chapter “What is Life?”: the Game of Life can simulate a computer.
- Gosper, Physica D 10, 75 (1984)
“Exploiting regularities in large cellular spaces”: the HashLife algorithm.
- Rendell, Turing Universality of the Game of Life (2002)
A Turing machine built in the Game of Life.
- Johnston & Greene, Conway’s Game of Life: Mathematics and Construction (2022)
The reference textbook on constructions: spaceships, guns, circuits, universal machines.
- LifeWiki, conwaylife.com
Discoverers, years, periods, speeds and lifespans of the patterns; official RLE files (conwaylife.com/patterns, December 2025 snapshot), kept as they are with their credits.
- Collection de motifs de Golly
A few files (ruler, ticker, HighLife, Day & Night and Replicator patterns), credits in each file.