Conway's Game of Life
B3/S23 — the rule that started the field
The 1970 original. Cells die of loneliness or crowding, and a dead cell with exactly three neighbours comes to life.
How it works
In plain English, before the notation
Every square on the grid is either on or off, and it looks at the eight squares around it to decide what to do next. Too few neighbours and it switches off; too many and it switches off; a dead square with exactly three live neighbours switches on. That is the entire rule. Run it on a random field and you get patterns that hold still, patterns that blink, patterns that walk across the screen, and — if you build them deliberately — patterns that compute.
Three things to try
- Open Presets and load "Gosper Glider Gun". It emits one glider every 30 steps and never stops.
- Press Clear (C), pick the Pencil, and draw three cells in a row. Press Play — it flips between horizontal and vertical forever.
- Open the Stamp picker, choose "Eater (Fishhook)", and place it in the path of the gun’s gliders. It swallows each one and repairs itself.
Starting configurations
Loads straight into the simulatorTry any rule
The catalogue covers a few dozen rules. Here you can run any of the 262,144 two-state grid rules, or any of the 256 one-dimensional rules, including ones nobody has written up.
Well-known rules
Where it came from
John Horton Conway devised the rule at Cambridge in 1969, working on a question posed by John von Neumann: what is the simplest set of rules under which a machine can reproduce itself? Conway tried many variants on a Go board before settling on B3/S23 as the one that was neither obviously doomed to die out nor obviously destined to fill the plane.
Martin Gardner described it in his Mathematical Games column in the October 1970 issue of Scientific American. The response was large enough that Life became the standard example of emergence, and the community that formed around it has been cataloguing patterns continuously ever since.
The rule, precisely
What each cell looks at
The 8 cells touching it, including diagonals (the Moore neighbourhood)
What a cell can be
Two states per cell — 0 (dead) and 1 (alive) — on a square grid
The update
next = 1 if (state = 0 and n = 3) or (state = 1 and n in {2, 3}); otherwise 0
B3/S23 reads as: Birth on 3 neighbours, Survival on 2 or 3. Everything not listed results in a dead cell. The same notation describes every rule in this family.
The standard vocabulary of patterns
Almost everything that appears in Life falls into one of four categories, and each has an accepted name:
- Still lifes never change: the block, beehive, loaf and boat account for most of the debris a random start leaves behind.
- Oscillators return to their starting shape after a fixed number of steps — the blinker after 2, the pulsar after 3, the pentadecathlon after 15.
- Spaceships return to their shape at a new position. The glider moves one square diagonally every 4 steps; the lightweight spaceship moves two squares sideways in the same time.
- Guns and other growing patterns increase in population without limit. The Gosper glider gun was the first found, in 1970.
Life can compute anything
Streams of gliders can carry bits, and colliding two streams at the right angle implements a logic gate. Everything a computer needs — gates, wires, memory, a clock — can be built from Life patterns.
What it is and is not a model of
Life is not a model of any particular physical system, and it was never meant to be. Its value is as an existence proof: it shows that a rule with no notion of a glider can nevertheless produce gliders, and that local rules with no central controller can produce coordinated large-scale structure. That argument is what gets borrowed by biology, economics and physics — not the rule itself.
Things to try
- Draw obstacles in a glider stream: place a single cell in the path of a glider and watch what the collision leaves behind. Most collisions produce debris; a few produce something useful.
- Set Cell Scale to 2px in Settings to simulate a much larger grid, then press Soup (R). At that size you can watch the population crash and then level off.
- Use Step (.) rather than Play when a collision is about to happen — the interesting part usually lasts four or five steps.
Frequently Asked Questions
References
The community reference, including the pattern catalogue and the history of each discovery.
A careful account of what cellular automata do and do not tell us about emergence and computation.
Good summary of the 1970 Scientific American column and the results that followed it.