Conway’s Game of Life
Conway's cellular automaton — draw your own cells or load a glider, blinker or R-pentomino and watch what four simple rules produce.
Click or drag on the grid to toggle cells, even while it is running.
Four rules, and really two
A live cell survives on two or three neighbours and dies otherwise. A dead cell comes alive on exactly three. That is the entire specification — everything else you see here is a consequence of those two sentences applied to every cell at once.
Try the R-pentomino. Five cells, and it refuses to settle for over a thousand generations. It is the standard demonstration that simple rules are not the same thing as simple behaviour, and it is why this stopped being a curiosity and became a field.
Things worth knowing
- Four rules, and really two: a live cell survives on two or three neighbours, and a dead cell is born on exactly three. Everything else in Life is a consequence.
- A block never changes and a blinker flips forever with period two. If those two do not behave, the rules are wrong — they are the fastest check there is.
- A glider returns to its own shape every four generations, moved one square diagonally. That is why it travels, and it is the pattern that made people take Life seriously.
- The R-pentomino is five cells that do not settle for over a thousand generations. Simple rules are not the same thing as simple behaviour, and that is the entire point of the exercise.
- On a wrapping grid a glider eventually comes back and collides with its own debris. On a bounded one it sails off the edge and vanishes, which is why the wrap setting changes what you see.
How to use
- Draw cells by clicking, or load a preset pattern.
- Start the simulation and watch it evolve.
- Adjust the speed to follow what is happening.
- Try the R-pentomino for a long, unpredictable run.
Frequently asked questions
What are the rules?
Four, and that is all. A live cell with two or three live neighbours survives; one with fewer dies as if from isolation, and one with more dies as if from overcrowding; a dead cell with exactly three live neighbours becomes alive. Everything the system does emerges from these.
Who invented it and why?
John Conway, in 1970, while looking for the simplest possible rules that could produce unbounded complexity. He tuned the thresholds by hand over months of experiment on a Go board. He later had mixed feelings about it, since it overshadowed mathematics he considered far more important.
What is a glider?
A five-cell pattern that moves diagonally across the grid, returning to its original shape every four generations one square further along. It was the first moving pattern found, and its existence is what makes the system capable of transmitting information.
What is the R-pentomino?
A five-cell pattern that runs for 1,103 generations before settling, producing gliders and debris along the way. It is the classic demonstration that a tiny, simple starting configuration can behave in a way nobody can predict without simply running it.
Is the Game of Life Turing complete?
Yes, which is the deepest fact about it. Gliders can be arranged into logic gates, and from gates into a general-purpose computer — people have built working computers, and even the Game of Life running inside itself. Four rules on a grid are enough to compute anything computable.
Can you predict the outcome without running it?
In general, no — and this is provable rather than merely difficult. Because the system is Turing complete, asking whether a pattern eventually dies out is equivalent to the halting problem, which has no general solution. Some patterns can only be understood by watching them.
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