Cellular Automata, Langevin Equations, and Unstable States
Martin Grant, J. D. Gunton · Physical Review Letters · 1986
Beginning with rules for a large class of continuum analogs of cellular automata, we derive Langevin equations for the slow variables of the system by projection-operator methods. For purely dissipative rules, we obtain an exact result: The slow variable is linearly unstable due to a "fluctuation-enhancement" relation. This means that this slow variable for the cellular automata grows exponentially for early times. We discuss how this may be related to, for example, kinetic models of the growth of ordered structures.