The Critter

a self-relaxing organism · two geometries, one rule

A living organism that runs our engine on itself. Each cell relaxation-labels toward its neighbours (the E-step); then the body reshapes (the M-step) — it grows where it's coherent, grooms away cells that can't decide, tunes its own temperature to the critical edge, and buds a child when it's whole. It feels, grooms, grows, and reproduces itself. Shown two ways — the simplicial body (a mesh of cells & triangles that flexes like a 3-D form) and the grid body (the same organism on a 2-D lattice). Same rule, same three cell-types. Click to poke it.

The loop. E-step — every cell relaxes its label toward its neighbours through a Potts compatibility at temperature T (relaxation labeling). M-step (morphogenesis)grow: a coherent boundary sprouts a new cell (the "can"); groom: an undecided cell is pruned (the "cannot"); reproduce: a whole, coherent body buds off a peripheral patch as a free child. Self-organized criticalityT auto-tunes (simulated annealing with a homeostatic set-point): it heats when the body freezes, cools when it churns, hovering at the critical edge between order and chaos.

Two bodies, one organism. The simplicial body flexes in continuous space — cells are nodes held by springs, filled in as 2-simplices (triangles), so the mesh reads like a 3-D creature. The grid body lives on a lattice — the same three cell-types as coloured squares. Switch between them above: it is the same relaxation-plus-morphogenesis loop on two geometries.

Honest framing. This is a toy of autopoiesis (Maturana & Varela) — a network that produces what produces it — not a claim of life or mind. But the loop is real: label relaxation feeding structural growth feeding label relaxation, "relax applied to relax," poised at criticality.

🎮 Play it: Roblox · Minecraft · Python →

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