HPP Lattice Gas Automaton

Proposed by Hardy, Pomeau, and de Pazzis in 1973, the HPP model is a cellular automaton used to simulate fluid dynamics. Particles move on a square grid in four discrete directions. When two particles collide head-on, they scatter perpendicularly, conserving both particle number and momentum.
This simple deterministic rule gives rise to emergent macroscopic fluid-like behaviors such as wave propagation and pressure waves.