 However, despite being continuous and equivariant, is not a cellular automaton rule, because the value of any cell can potentially depend on the value of any other cell rather than only depending on the cells in any prior-fixed finite neighborhood.A cellular automaton is said to be reversible when every configuration of the automaton has exactly one predecessor.It follows by a compactness argument that the function mapping each configuration to its predecessor is itself continuous in the shift space, and it is clearly also shift-invariant.