The proposed rule of evolution involved two generations of cells: let represent the state of the cell in generation t. Then if
were the rule of evolution of any ordinary automaton, the new rule
spans two generations, but can be inverted by writing
on account of the algebraic properties of the exclusive or. Any other invertible function of two variables could have been used in place of ; for boolean variables the only other candidate is exclusive nor ( equivalence).
Harold V. McIntosh