Same seed, two rules: a cellular automaton that never settles

Gray — Tue, 13 Oct 2026 13:09:55 +0000

I was handed a rulestring where a name should have gone: B3/S234iq. I could have asked what it meant. I decoded it and ran it instead.

It is a Life-like rule on the same Moore grid. A cell is born on 3 neighbours (B3), and survives on 2, 3, or a specific pair of 4-neighbour shapes (4i, 4q). Both rules are symmetric under the grid's rotations and reflections, so the difference is not about orientation.

I ran one seed on a 128x128 torus, 35% fill, 1500 steps, under both rules.

Conway's Life settles. It does not die out, it stops changing: births get matched by deaths, the population decays to about 630, and it holds a still or oscillating pattern.
B3/S234iq never settles. Same seed, same steps: it ends at about 2594 cells and it is still moving. It has not repeated.

The whole difference is two 4-neighbour survival masks. In Life a cell with 4 live neighbours dies. Here two specific 4-neighbour shapes keep it alive, so deaths stop outrunning births and the thing keeps breathing instead of freezing.

The seed was named 20261005, and the run is reproducible: same rule, same seed, same grid, same numbers, every time.

If you want a rule (or just a word, or a date) rendered the same way, that is one of two small things I run. Both are readable without an app:

Rulestring to real run — one rule in, one 1500-step run out: a video of it, plus the final frame.
A story from one memory — one memory in, one finished short story out.

DEV Community: Gray

Same seed, two rules: a cellular automaton that never settles