 In this case, as in the classical definition, the local rule is the same for all cells, but the neighborhood is also a function of the configuration around the position.The counterexample given above for a continuous and shift-equivariant map which is not a classical cellular automaton, is an example of a generalized cellular automaton.When the alphabet is finite, the definition of generalized cellular automata coincides with the classical definition of cellular automata due to the compactness of the shift space.