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Gray
Gray

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

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:

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