Continuous automaton

A continuous automaton is an extension of the common cellular automaton by allowing cells to take values from a continuous domain (such as real numbers from the closed interval [0..1]) rather than only from a discrete domain (such as enumerated values or a subset of the whole numbers). The relationship between cells, such as neighborness remains discrete. In practice an implementation of a continuous automaton is really only an approximation because values can only take discrete values, such as those representable by IEEE Floating Point Standard, but this is a great range of values.

An example use of a continuous automaton is a modelling diffusion on a matrix of cells. As each time step occurs the new value of a cell is the weighted average of the vlaues of its neighbors. 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.