A cellular automaton is just a lookup table: every cell looks at its neighborhood and the table says what it becomes next tick. The rule string is that table, compressed. Tap any example to run it.

1D — one row evolves, history scrolls down

30

Elementary (0–255). A cell looks at left·self·right. Three cells have exactly 8 possible patterns, so a rule is 8 yes/no answers — one byte. The rule's name is that byte written as an everyday decimal number. Here is rule 30's whole rulebook, one column per pattern:

Top: the pattern a cell sees. Bottom: what it becomes. The answer row is 00011110 as binary, which is the number 30 — hence "rule 30".

r2:2863311530

Radius-2. Same game, wider view: two neighbors per side means 5 cells, 2⁵ = 32 patterns, so a rule needs 32 answers — a 32-bit number (hex works: r2:0xAAAA5555). 4.3 billion rulebooks.

k3:912

Totalistic, k states (2–5). Positions stop mattering — only the sum of the three cells counts. With 3 states the sum runs 0–6, so a rule is 7 answers, each one a state (0, 1 or 2). The code is those answers written in base 3: 912 = 1020210₃.

The sum the cell sees → the state it becomes. Extra states mean extra colors for free.

2D — the whole plane updates at once

B3/S23

Life-like. Each cell counts its 8 surrounding neighbors, so a count is always a single digit 0–8 — and what follows B and S is a set of digits, not a number: B3678 means "born on 3, 6, 7 or 8 live neighbors."

This dead cell touches 3 live cells — under B3 it's born next tick. A dead cell is Born if its count is in the B set; a live cell Survives if its count is in the S set; everything else dies. An empty set is legal: Seeds is B2/S — born on 2, survives never. B3/S23 is Conway's Life; legacy survival-first 23/3 also parses.

B2/S/3

Generations. The same B and S sets, plus a third slash-field that is not neighbor counts: it's the total number of states. Cells that fail to survive fade instead of vanishing — alive → ghost → … → gone, with states − 2 ghost steps. Ghosts hold their square (nothing can be born there) but count as zero neighbors. B2/S/3 is Brian's Brain: born on 2, survives never, 3 states (alive, ghost, dead). B2/S345/4 is Star Wars: born on 2 · survives on 3, 4 or 5 · two ghost steps. Legacy /2/3 also parses.

Grids wrap at the edges (a torus), so gliders that leave come back. The 🎲 button rolls random rules from all these families and quietly re-rolls the duds.