Continuous automaton

A continuous automaton can be described as a cellular automaton whereby the valid states a cell can take are not discrete (for example, the states consist of integers between 0 and 3), but continuous, for example, [0,1]. The cells however remain discretely seperated from each other

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. Many implementations of Finite Element Analysis (FEA) can be thought of as continuous automatons, though this degree of abstraction away from the physics of the problem is probably inappropriate.