Conway's Game of Life
Four rules, a grid, and generations of emergent behavior—still lifes that never change, oscillators that repeat, and spaceships that travel across the board forever.
By Austin Archuleta, Founder & AI Solutions Architect
Quick Answer
What Are the Rules of Conway's Game of Life?
Every cell on the grid is either alive or dead. Each generation, a live cell with fewer than two live neighbours dies (underpopulation), a live cell with two or three live neighbours survives, a live cell with more than three live neighbours dies (overpopulation), and a dead cell with exactly three live neighbours becomes alive (reproduction). Written in standard notation, that ruleset is B3/S23. From those four lines, every pattern below emerges.
Last updated: August 18, 2026
Still Lifes
A still life satisfies the rules exactly as it is, generation after generation—no cell has the wrong neighbour count to change state. These are the patterns you find at the edge of almost any random configuration once it settles down.
Block
2×2 square. The smallest and most common still life.
Beehive
6-cell hexagonal ring, the second most common still life found in random soups.
Loaf
A 7-cell asymmetric still life, common in ash from larger explosions.
Boat
5-cell still life resembling a block with one corner cut.
Tub
4-cell diamond, the smallest still life with 4-fold symmetry after the block.
Oscillators
An oscillator returns to its starting shape after a fixed number of generations—its period—and then repeats forever. A 2024 proof established that Conway's Game of Life is omniperiodic: an oscillator exists for every period from 1 upward, a question that had been open since the 1970s.
Blinker
Period 2Three cells in a row, flipping between horizontal and vertical.
Toad
Period 2Six cells, one of the first oscillators discovered after the blinker.
Beacon
Period 2Two diagonally touching blocks that flicker their inner corners.
Pulsar
Period 348 cells with 4-fold symmetry; one of the most recognizable Life patterns.
Pentadecathlon
Period 15A 10-cell-long oscillator, among the first found with a large period.
Spaceships
A spaceship is an oscillator that also translates—it returns to its original shape, but shifted to a new position, so it appears to travel across the grid indefinitely.
Glider
5 cells, moves one cell diagonally every 4 generations. The smallest known spaceship.
Lightweight Spaceship (LWSS)
9 cells, moves 2 cells horizontally every 4 generations.
Middleweight Spaceship (MWSS)
Larger orthogonal spaceship, one size class up from the LWSS.
Heavyweight Spaceship (HWSS)
The largest of the three classic orthogonal spaceships Conway found by hand.
How New Patterns Get Classified
Most interesting patterns weren't designed by hand—they were found by throwing random starting configurations (“soups”) at the rules and seeing what stabilizes. A soup-search engine runs each soup forward and then classifies whatever is left: still lifes and oscillators by their exact period, spaceships by their measured velocity, and long-running methuselahs by their final population and the generation count at which they stabilize.
Confirmed finds are typically encoded as an apgcode—a compact, standardized notation for Game of Life objects—and cross-referenced against Catagolue, the community-run census database, to check whether the discovery is already known or genuinely new.
We built exactly this kind of engine for LIFE, a free simulator running 13 soup-search strategies plus an Evolution Mode where the birth and survival rules themselves mutate under fitness pressure. The engineering write-up is in the case study.
Play Conway's Game of Life Online, Free
LIFE is a dependency-free simulator with a custom rules editor, an Evolution Mode that mutates the ruleset itself, and a Pattern Discovery Engine that classifies what it finds. Installable as a PWA, runs entirely in your browser.