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We show how to construct a deterministic nearest-neighbour cellular automaton(CA) with four states which emulates diffusion on a one-dimensional lattice.The pseudo-random numbers needed for directing random walkers in the diffusionprocess are generated with the help of rule 30. This CA produces densityprofiles which agree very well with solutions of the diffusion equation, and wediscuss this agreement for two different boundary and initial conditions. Wealso show how our construction can be generalized to higher dimensions.

Four state deterministic cellular automaton rule emulating random diffusion