Second-order Cellular Automaton
A second-order cellular automaton is a type of reversible cellular automaton (CA) invented by Edward Fredkin. Reprinted in . where the state of a cell at time depends not only on its neighborhood at time , but also on its state at time .. General technique In general, the evolution rule for a second-order automaton may be described as a function that maps the neighborhood of a cell to a permutation on the states of the automaton. In each time step , for each cell of the automaton, this function is applied to the neighborhood of to give a permutation . Then, this permutation is applied to the state of cell at time , and the result is the state of the cell at time . In this way, the configuration of the automaton at each time step is computed from two previous time steps: the immediately previous step determines the permutations that are applied to the cells, and the time step before that one gives the states on which these permutations operate. The reversed time dynamics o ...
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