History [of second-order cellular automata]

The concept of getting reversibility in a cellular automaton by having a second-order rule was apparently first suggested by Edward Fredkin around 1970 in the context of 2D systems—on the basis of an analogy with second-order differential equations in physics. Similar ideas had appeared in numerical analysis in the 1960s in connection with so-called symmetric or self-adjoint discrete approximations to differential equations.