A deterministic cellular automaton rule is presented which simulates the Ising model. On each cell in addition to an lsing spin is a space-time parity bit and a variable playing the role of a momentum conjugate to the spin. The procedure permits study of nonequilibrium phenomena, heat flow, mixing, and time correlations. The algorithm can make full use of multispin coding, thus permitting fast programs involving parallel processing on serial machines. (c) 1986 Academic Press, lnc.