Lattice Gas

The HPP model of Hardy, Pomeau, and de Pazzis (1973) was the first lattice gas automaton: particles live on a square grid, move in four discrete directions, and conserve mass and momentum exactly. Head-on pairs collide and scatter at right angles; everything else passes through untouched. From these reversible micro-rules, recognizably fluid-like pressure waves emerge.

Here each patch holds four boolean channels, one per direction, so a patch can host at most one particle per heading. Every tick runs two staged phases: a collision phase that rotates head-on pairs ninety degrees, and a streaming phase where each patch pulls incoming particles from its neighbors via directed lookup. A dense central blob relaxes into an expanding density wave that wraps the torus and interferes with itself.