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The authors propose a deterministic approach to lattice diffusion in two dimensions. This method is implemented on a cellular automaton special purpose computer in order to study the properties of the interface of particles diffusing from a source to a sink. Fractal properties of the diffusion front of this non-equilibrium process are compared with results from percolation theory. The observed agreement indicates that diffusion fronts and gradient percolation coincide asymptotically and that the cellular automata method is a viable alternative to standard simulations for this class of problems.
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Chopard et al. (1989) studied this question.
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