Lattice gas automaton

In this model, the lattice is square, and the particles travel independently at a unit speed to the discrete time.

In some models (called FHP-II and FHP-III), a seventh velocity representing particles "at rest" is introduced.

[9] The simple update rule of FHP model proceeds in two stages, chosen to conserve particle number and momentum.

The collision rules in the FHP model are not deterministic, some input situations produce two possible outcomes, and when this happens, one of them is picked at random.

[13] However, calculating density, momentum, and velocity for individual sites is subject to a large amount of noise, and in practice, one would average over a larger region to obtain more reasonable results.

[14] The main assets held by the lattice gas model are that the boolean states mean there will be exact computing without any round-off error due to floating-point precision, and that the cellular automata system makes it possible to run lattice gas automaton simulations with parallel computing.

[15] Disadvantages of the lattice gas method include the lack of Galilean invariance, and statistical noise.

[12] Lattice-gas cellular automata have been adapted and are still widely used for modeling collective migration in biology.

Due to the active nature of biological agents, as well as the viscuous environments cells live in, momentum conservation is not required.

During the collision step, particles reorient stochastically following a Boltzmann distribution, simulating local interaction between individuals.