Let's start with the most famous cellular automaton: the life-likes. A life-like automaton lives on a 2D grid where every cell is either dead or alive, and its next state depends only on how many of its eight neighbors are currently alive. A ruleset has two parts: how many neighbors a dead cell needs to be born (B), and how many an alive cell needs to survive (S). Everything else dies or stays dead.
The example below is EightLife, written as the rulestring B3/S2,3,8:
a dead cell is born with exactly three living neighbors, an alive cell survives with two,
three, or eight.
Try other rulestrings:
e.g. B3/S4,5, B3,4/S8, Conway's Game of Life: B3/S0,2,3.
Things get more interesting when the neighborhood is widened: instead of only the eight adjacent cells, count every cell within a radius r.
| Radius | Rulestring | Behaviour |
|---|---|---|
| 2 | B6,7/S5 | |
| 2 | B6,7/S7,8,9 | |
| 3 | B9,7/S9 | |
| 4 | B15,10/S11,10,5 | |
| 7 | B18,22,21/S23,43,49 | slowly degenerative |
| 10 | B38,50,70,45,61,91,90/S43,49,61 | degenerative |
| 10 | B60,38,50,70,45,61,91,90/S43,49,61 | degenerative |
| 10 | B60,38,46,50,70,61,91,90/S40,49,61,65,78,81,99 | very slowly degenerative |
| 20 | B60,38/S81,99 | stable |
Rulestring: Radius:
The same idea extends to three dimensions, where richer structures can appear. The grid wraps around on every axis, so opposite faces of the cube are identified with each other, giving the topology of a 3-torus. Patterns drifting off one side reappear on the opposite one.
Click inside the canvas to capture input. Look around with the mouse, use W/A/S/D to move along the surface, E to rise and Q to descend.
Rulestring: