Cellular Automata Lab
Simple rules on a grid can produce chaotic waves, self-replicating crystals, power-law avalanches, and universal computers. Below is an overview of the six families in this simulator, how their rules work, and why they behave the way they do.
The six families
Pick one to read how it works, then launch it. Each rule also has its own page.
Conway's Game of Life and its relatives
How the rule works
Every cell is either alive or dead. It counts how many of the eight cells touching it are alive — that single number decides what it becomes next. All cells update simultaneously, using the state of the grid before the step.
B<birth counts> / S<survival counts>
Conway's rule is B3/S23: a dead cell with exactly three live neighbours comes alive, and a live cell with
two or three neighbours stays alive. Everything else ends up dead. Changing those two
lists gives you the other 262,143 rules in the family.
Why this one rule got famous
Conway settled on B3/S23 in 1969 because it was the only variant he tried that did neither of the two boring things — die out immediately, or fill the plane. That balance is what makes room for gliders, oscillators and, eventually, logic gates built out of colliding gliders. Life is Turing complete.
- HighLife (
B36/S23): one extra birth condition, and a twelve-cell pattern that copies itself every twelve steps. - Seeds (
B2/S): nothing survives its own turn, so everything on screen is a chain reaction. - Life Without Death (
B3/S012345678): cells are born normally and never die, growing a permanent maze.
Try 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
Controls
| Action | Key | Where | What it does |
|---|---|---|---|
| Play / pause | Space | Bottom dock | Starts and stops the simulation. |
| Single step | . | Bottom dock | Advances one step. Worth using whenever something interesting is about to happen. |
| Draw | 1 | Pencil | Paint cells directly on the canvas. Multi-state rules add a colour picker beside it. |
| Erase | 2 | Eraser | Clears cells under the brush. Removes ants in the turmite rules. |
| Stamp a pattern | 3 | Stamp icon | Places a known pattern with a live preview. Life-like and Generations rules only. |
| Grid lines | G | Grid icon | Shows cell boundaries. Needs a cell scale of 3px or more. |
| Randomise | R | Soup | Fills the grid at random. For the sandpile it drops several piles instead; for turmites it randomises the paint and leaves the ants alone. |
| Clear | C | Trash icon | Empties the grid. Turmite ants are kept where they are. |
| Speed, scale, boundaries | — | Settings (sliders icon) | Steps per second, pixels per cell, brush size, and whether the grid edges wrap or act as walls. |
Common questions
What is a cellular automaton?
A grid of cells where each cell has a state (alive/dead, a colour, or a count). At every tick, every cell computes its next state simultaneously from what its neighbours are doing. There is no central coordinator — everything on the canvas is the result of that local conversation.
Are turmites cellular automata?
Strictly, no. Turmites (like Langton’s ant) are Turing machines on a two-dimensional tape: a single active head moves over a passive grid of colours, rather than every cell updating simultaneously. They are included here because their history and dynamics (order → chaos → highway) are studied in the same breath.
What makes Conway’s Game of Life so famous?
John Conway tested dozens of candidate rules in 1969 to find one where populations neither died out immediately nor exploded to fill the plane. That narrow balance lets structures collide, bounce, shoot gliders, and simulate logic gates — making Life Turing complete.
Why does Rule 110 matter?
Rule 110 is the simplest known Turing-complete system. Matthew Cook proved in the late 1990s that its interacting gliders can simulate a cyclic tag system, meaning an elementary 1D rule with an 8-bit lookup table can compute anything any modern computer can compute.
Can I design my own rules?
Yes. Use the Try any rule explorer below to type custom birth/survival counts (e.g. B35/S236) or enter any 1D rule number from 0 to 255. You can also import standard RLE format strings from the Presets modal in the top bar.