Second-order cellular automaton

The past cells affecting the state of a cell at time t in a 2nd-order cellular automaton

Elementary CA rule 18 (left) and its second-order counterpart rule 18R (right). Time runs downwards. Note the up/down asymmetric triangles in the nonreversible rule.

A second-order cellular automaton is a type of reversible cellular automaton (CA) invented by Edward Fredkin^[1]^[2] where the state of a cell at time $t$ depends not only on its neighborhood at time $t - 1$ , but also on its state at time $t - 2$ .^[3]

^ Margolus, N. (1984), "Physics-like models of computation", Physica D, 10: 81–95, doi:10.1016/0167-2789(84)90252-5. Reprinted in Wolfram, Stephen, ed. (1986), Theory and Applications of Cellular Automata, Advanced series on complex systems, vol. 1, World Scientific, pp. 232–246.
^ Cite error: The named reference vichniac was invoked but never defined (see the help page).
^ Wolfram, Stephen (2002), A New Kind of Science, Wolfram Media, pp. 437–440, 452, ISBN 1-57955-008-8.

[m84-1] Margolus, N. (1984), "Physics-like models of computation", Physica D, 10: 81–95, doi:10.1016/0167-2789(84)90252-5. Reprinted in Wolfram, Stephen, ed. (1986), Theory and Applications of Cellular Automata, Advanced series on complex systems, vol. 1, World Scientific, pp. 232–246.

[vichniac-2] Cite error: The named reference vichniac was invoked but never defined (see the help page).

[nkos-3] Wolfram, Stephen (2002), A New Kind of Science, Wolfram Media, pp. 437–440, 452, ISBN 1-57955-008-8.

[1]

[2]

[3]