Microscopic particles on a square/hexagonal lattice obeying collision rules. Macroscopic hydrodynamics (Navier-Stokes) emerges from simple local rules. Watch Poiseuille flow and vortex formation.
HPP model (Hardy-Pomeau-de Pazzis 1973): 4-direction lattice gas with momentum/particle conservation. FHP (Frisch-Hasslacher-Pomeau 1986): 6-direction hexagonal lattice — proved to recover incompressible Navier-Stokes in continuum limit. Lattice Boltzmann method (LBM) is a probability generalization. LGCA were the first discrete microscropic models to simulate fluid turbulence.