Function Repository Resource:

SequentialCellularAutomaton

Cellular automaton evolution with the order of each cell update specified

Contributed by: Stephen Wolfram

ResourceFunction["SequentialCellularAutomaton"][rule,init,list]

evolves using the specified cellular automaton rule from initial condition init, updating cells whose positions are specified in list.

ResourceFunction["SequentialCellularAutomaton"][rule,i]

is an operator form which updates only the cell at position i according to the rule.

Details and Options

ResourceFunction["SequentialCellularAutomaton"] currently works only for 1D cellular automata

SequentialCellularAutomaton assumes periodic boundary conditions.

Compute the evolution of sequential rule 60, successively scanning from left to right:

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Update the cell at position 3 according to rule 0:

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Make a rule plot of the substitutions in the sequential cellular automaton:

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Use a totalistic 3-color cellular automaton:

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Run sequential rule 60 with a variety of updating orders:

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This should be extended to other CA rule cases, as well as to higher-dimensional CAs, etc.