A continuous automaton can be described as a cellular automaton whereby the valid states a cell can take are not discrete, but continuous, for example, [0,1]. Such automata can be used to model certain physical reactions more closely, such as diffusion. One such diffusion model could conceivably consist of a transition function based on the average values of the neighbourhood of the cell. A cellular automaton (plural: cellular automata) is a discrete model studied in computability theory and mathematics. ... This article is about the physical mechanism of diffusion. ... Neighbourhood is also a term in topology. ...
Notice that the spatial entropy of a cellular automaton configuration may be considered as the temporal entropy of a pure shift mapping applied to the cellular automaton configuration.
space-time patch are determined according to the cellular automaton rules by the values in the ``rind'' of the patch, as indicated in fig.
The ratio of temporal to spatial entropy is thus bounded by the maximum propagation speed in the cellular automaton.
This is a continuous cellular automaton, otherwise known as a "coupled map lattice." (See CA 1D Elementary and CA 1D Totalistic if you are unfamiliar with cellular automata.) It operates just like a standard cellular automaton, except for the fact that its states are not discrete, but continuous values.
The rules are a cross between a totalistic cellular automaton and an iterated map.
The cellular automaton is totalistic, which means that at every time step, each cell's new state is determined by taking the average of itself and its nearest neighbors, and then passing it through the iterated map.
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