Thermodynamics and Hydrodynamics of Cellular Automata

Cellular automata (CA) are discrete dynamical systems which give simple models for many complex physical processes [1]. This paper considers CA which can be viewed as discrete approximations to molecular dynamics. In the simplest case, each link in a regular spatial lattice carries at most one "particle" with unit velocity in each direction. At each time step, each particle moves one link; those arriving at a particular site then "scatter" according to a fixed set of rules. This discrete system is well-suited to simulation on digital computers. The state of each site is represented by a few bits, and follows simple logical rules. The rules are local, so that many sites can be Updated in parallel. The simulations in this paper were performed on a Connection Machine Computer [2] which updates sites concurrently in each of 65536 Boolean processors [3].