Underpopulation
A live cell with fewer than two live neighbors dies.
Interactive Life research lab
Conway's Game of Life, explained through live patterns
Explore still lifes, oscillators, spaceships, methuselahs, and glider guns with a simulator that connects every structure to a concrete observation. Load a pattern, step through the rules, then read what changed and why it matters.
Simulation status
Generations0
Live cells5
Period4
Choose a starting pattern
Load a structure, then press play
Study path
From four local rules to engineered behavior
The Game of Life is simple enough to explain in one minute and deep enough to support a research community. This guide turns the canonical pattern families into a practical sequence: stability, periodic motion, travel, long transients, and signal generation.
Survival
A live cell with two or three live neighbors survives.
Overpopulation
A live cell with more than three live neighbors dies.
Birth
An empty cell with exactly three live neighbors becomes alive.
Pattern taxonomy
Every structure has a role in the larger system
Stable
Still lifes
Stable objects that never change after the first generation. They are the anchors and catalysts used to contain more active reactions.
Browse examplesPeriodic
Oscillators
Patterns that return to their starting phase after a fixed number of generations. They make periods, phases, and symmetry visible.
Browse examplesMoving
Spaceships
Self-contained patterns that reappear translated across the grid. They are the basic signal carriers of Life engineering.
Browse examplesChaotic
Methuselahs
Small seeds with unexpectedly long lifetimes. They are useful for studying growth, stabilization, and emergent debris fields.
Browse examplesEmitter
Guns
Periodic factories that emit spaceships. They connect local reactions to larger signal circuits and computing constructions.
Browse examplesGrowth
Growth patterns
Patterns that keep leaving debris, signals, or repeated output behind. They are a natural bridge from small examples to the advanced infinite board.
Browse examplesFeatured experiments
Load a pattern, then inspect the explanation
These examples cover the core ways people learn Conway's Game of Life: rules, classic patterns, moving spaceships, unpredictable seeds, and the first finite pattern with unbounded growth.
Oscillators
Pulsar
A large period-3 oscillator with strong fourfold symmetry.
Methuselahs
R-pentomino
A five-cell seed that takes over one thousand generations to stabilize.
Guns
Gosper glider gun
The first known finite pattern with unbounded growth.
Guns
Simkin glider gun
A compact true glider gun discovered by Michael Simkin in 2015.
Spaceships
Loafer
A small orthogonal spaceship with an unusually slow c/7 speed.
Learning toolkit
Keep exploring after the first pattern
Life becomes easier to understand when each object is tied to an action. The simulator lets you test a claim immediately, while the notes explain what to watch for in each family of structures.
Dedicated notes
Each entry has a focused page with a preview, behavior summary, observations, and a direct link back to the simulator.
Concept families
Still lifes, oscillators, spaceships, methuselahs, and guns are grouped by how they behave, so learners can move from stable shapes to moving signals and long-running reactions.
Source-backed reading
Articles turn LifeWiki, Golly, and classic cellular automata references into focused explanations that link back to playable patterns.
Further study
Read the research notes behind the lab
Continue with source-backed articles written for this lab. Each article explains one idea and links back to the pattern you can run.
5 min read
Conway's Game of Life rules: B3/S23 with examples
Learn the B3/S23 rule: births on exactly 3 neighbors, survival on 2 or 3, and simultaneous updates across the whole board.
Read article6 min readStill lifes are the quiet objects that make Life engineering possible
A block or beehive looks inert, but stable objects become anchors, eaters, and cleanup tools in larger reactions.
Read article6 min readOscillators turn Life into a clock
Blinkers, pulsars, and pentadecathlons explain period, phase, rotor, stator, and why bounded motion matters.
Read article5 min readSpaceships are how Life learns to send signals
The glider and the lightweight spaceship show that a finite pattern can move without leaving itself behind.
Read article7 min read3x3 methuselah in Conway's Game of Life: the R-pentomino
A 3x3 methuselah is best understood through the R-pentomino: five cells, 1,103 generations, 116 final cells, and 6 escaping gliders.
Read article8 min readMethuselah patterns in Conway's Game of Life, compared
Compare R-pentomino, Acorn, Diehard, Edna, B-heptomino, and Herschel by bounding box, lifespan, final ash, and board-size needs.
Read article6 min readGosper glider gun in Conway's Game of Life: period 30
Run the period-30 Gosper glider gun, watch the core repeat, and see why one finite pattern proved unbounded growth in Life.
Read article7 min readCommon objects in Conway's Game of Life: the patterns you see first
Blocks, blinkers, tubs, boats, beehives, loaves, and pulsars make a practical first map of Life ash and repeated behavior.
Read article7 min readSpaceships in Conway's Game of Life: gliders, LWSS, and Loafer
The glider, lightweight spaceship, and Loafer explain translation, period, speed notation, and why moving objects became Life signals.
Read article6 min readGosper vs Simkin glider guns: two ways to explain infinite growth
The Gosper glider gun is the historical first gun. The Simkin glider gun gives modern users a compact period-120 comparison.
Read article7 min readPuffers, rakes, and breeders in Conway's Game of Life
Pufferfish, switch engines, rakes, and breeders are the growth patterns that make the infinite board useful.
Read article7 min readLife engineering starts with eaters, Herschels, and reflectors
Eater 1, B-heptomino, Herschel, and Snark-style reflectors explain how Life patterns become controlled signal circuitry.
Read article6 min readWhich Life patterns belong on an infinite board?
Large guns, growth patterns, Turing machines, breeders, and hotels are better served by an isolated Hashlife-powered viewer than by a fixed teaching grid.
Read article