Complexity Index of Outer-Totalistic Binary Cellular Automata with Arbitrary Dimension and Neighborhood

The concept of complexity index is of key importance in the systematic analysis of the dynamics of Cellular Automata (CA); nevertheless, it has been defined only for the special case of 1D elementary CA. In this paper, we first introduce a complexity index for outer-totalistic binary CA with arbitrary dimension and neighborhood by means of a rigorous mathematical theory, and then propose a method to find it easily, given only the truth table of an outer-totalistic binary CA rule. Through our technique, we study in detail both 1D and 2D elementary CA rules, including the well-known Game of Life.

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