Cellular Automata and Fractal Evolution

Outer Totalistic Cellular Automata Rules

For simplicity we consider only binary CA. The extension to S > 2 is straightforward.

Outer totalistic CA rules depend on only the number of live cells in a neighborhood, with the additional condition that we allow different outcomes if the central cell is alive or dead.

For one-dimensional, N = 3 rules the nbhd around the central cell can have 0, 1, or 2 cells alive.

Thus S = 2, N = 3 outer totalistic CA rules have six nbhd configurations. On the right we see how these are represented in our CA software. Note each configuration is represented by an example.

1. Central cell dead, 0 surrounding cells alive 2. Central cell alive, 0 surrounding cells alive 3. Central cell dead, 1 surrounding cell alive 4. Central cell alive, 1 surrounding cell alive 5. Central cell dead, 2 surrounding cells alive 6. Central cell alive, 2 surrounding cells alive

Here is an N=3 example.

Outer totalistic rules can be formulated for one-dimensional N = 5, two-dimensional von Neumann, and two-dimensional Moore CA. Here are the tables.

Here is a von Neumann example.

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