 A function is equivariant under the shift map if the transformation on configurations described by commutes with the shift map; that is, for every configuration , it must be the case that .Intuitively, this means that every position of the configuration is updated by using the same rule as every other position.A cellular automaton is defined by a rule for computing the new value of each position in a configuration based only on the values of cells in a prior-fixed finite neighborhood surrounding the position, with all positions of the configuration being updated simultaneously based on the same update rule.