9. Modelling macroscopic phenomena

It has been discovered through experimentation that cellular automata can be constructed to be­have in ways similar to higher-order physical sys­tems; in other words, they are useful for simulat­ing physical phenomena including hydrodynamics [18], percolation, nucleation, Ising dynamics [19], the movement of sand on the beach, and other phenomena [1]. We distinguish such systems from DM, which is intended only as a direct model of the most microscopic physics. We do not antici­pate that direct DM models will be useful for any­thing other than such microscopic models, but the principles of DM may be more widely applicable.

We will discuss many properties of DM in the context of models of physics. Rather than cover­ing the spectrum of possible RUCA and DM sys­tems, we will describe a hypothetical yet plausible DM that combines properties that we have seen in various other DM systems; we will match up those properties with corresponding properties of physics.

[1]  T. Toffoli and N. Margolus, Cellular Automata Machines - A New Environment for modelling (MIT Press, Cambridge, MA, 1987).

[18]  U. Irisch, B. Hasslacher and Y. Pomeau, Lattice-gas automata for the Navier-Stokes equation, Phys. Rev~ Lett. 56 (1986) 1505-1508.

[19]  M. Creutz, Deterministic Ising dynamics, Ann. Phys. 167 (1986) 62-76.