Introduced by Frisch, Hasslacher and Pomeau in 1986, the FHP model shows that a fluid's macroscopic behaviour — including vortices, wakes and something close to the Navier–Stokes equations — can emerge from an extremely simple microscopic rule: identical particles hopping between the nodes of a triangular lattice and colliding when they meet, with nothing more sophisticated than exact momentum conservation at each site.
Despite using only boolean occupation numbers and integer arithmetic, the FHP automaton reproduces real fluid phenomena such as the von Kármán vortex street behind a cylinder — a striking demonstration that complex continuum behaviour can emerge from a discrete, deterministic-plus-a-coin-flip microscopic rule.
A hexagonal lattice of particles streams and collides under a handful of local rules, and out of that simple bookkeeping a recognisable fluid flow — including a wake behind an obstacle — emerges.
Particles hop between triangular-lattice sites along six directions and redirect on collision while conserving particle number and momentum exactly, showing how continuum-like fluid behaviour emerges from discrete microscopic rules.
Set the inflow density and bias to drive flow from the left, adjust the obstacle size to see a wake form behind it, and change simulation speed to watch the lattice evolve tick by tick.
The FHP model, published in 1986, was one of the first cellular automata shown to reproduce genuine fluid dynamics — including something close to the von Kármán vortex street — from purely local, reversible-in-spirit rules.