Deterministic cellular automata

Iever89] Levermore, C.D. and B.M.Boghosian, Deterministic cellular automata with diffusive behavior, pages 118-129 in [mann89j. 

The rules governing cell movement may be deterministic or probabilistic. Deterministic cellular automata use a fixed set of rules, the values of which are... 

Two other approaches treat a spatially distributed system as consisting of a grid or lattice. The cellular automaton technique looks at the numbers of particles, or values of some other variables, in small regions of space that interact by set rules that specify the chemistry. It is a deterministic and essentially macroscopic approach that is especially useful for studying excitable media. Lattice gas automata are mesoscopic (between microscopic and macroscopic). Like their cousins, the cellular automata, they use a fixed grid, but differ in that individual particles can move and react through probabilistic rules, making it possible to study fluctuations. 

The smallest recurrence time obtained for a fluctuation to induce a chemical wave is 10 seconds. This is the shortest recurrence time from a stochastic calculation considering of (1) experimentally obtained critical perturbations, (2) calculated critical perturbations from the deterministic reaction-diffusion equations, and (3) calculated critical perturbations from cellular automaton calculations. It is the recurrence time predicted by the reaction-diffusion equations of a modified Oregonator model for a fluctuation in the bromide concentration to achieve its critical concentration within a sphere of radius 0.5 /xm in an excitable medium. 

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