Waves

Ripples radiate from the center.

Classic Automata · a single painted seed plus one Phlux rule, simulated live · 96×96 grid

The rule that makes it move

This is the whole thing. Phluxel runs it on every cell, every step — the animation is what happens when you repeat it.

R = ((N.R + S.R + E.R + W.R) * 0.5 - G) * 0.98; G = R

Paste it into the Rule Editor, or pick Wave Propagation from the template list and skip the typing.

Make it yourself

1. Open Phluxel and start a new field, or click Waves in the starter gallery to get this exact setup.
2. Turn Wrap edges on — this one is toroidal, so motion that leaves one side comes back on the other.
3. Press play. Change colours or numbers while it runs; you never have to stop and restart.
4. Export a seamless loop as GIF, APNG, MP4, a PNG sequence, or a sprite sheet.