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A method for constructing a variety of probabilistic lattice-gas cellular automata for chemically reacting systems is described. The microscopic reactive dynamics give rise to a general fourth-order polynomial rate law for the average particle density. The reduction of the microdynamical equations to a discrete or continuous Boltzmann equation is presented. Connection between the linearized Boltzmann equations and a reaction-diffusion macroscopic equation is discussed. As an example of the general formalism a set of cellular automata rules that yield the Schl\"ogl phenomenological model is constructed. Simulation results are presented.
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Dab et al. (1990) studied this question.
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