Introduction

Abstract

Invented in 1948 by von Neumann and Ulam, cellular automata (CA) are fully discrete dynamical systems with their dynamical variables defined at the nodes of a lattice and taking their values in a finite set. The dynamics results from the synchronous application of a local transition rule at each lattice site, the new value of a cell variable being a function of current values of the variables in cells belonging to a small neighborhood around the site. From the point of view of physics, it is straightforward to interpret the lattice as a discretized version of the physical space, the variables as occupation numbers of particles with a discrete repartition of internal states, and the evolution rules as propagation and collision rules for these particles. Lattice gases defined in this way evolve according to some fully discrete dynamics which may seem more accessible to analysis than the realistic fully continuous molecular dynamics. These systems therefore present themselves as ideal testing grounds for the explicit derivation of macroscopic equations describing continuous media but also, at a more practical level, as promising alternative tools for simulating fluid flows in nearly realistic conditions.