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In this book, “A New Kind of Science,” Stephen Wolfram lists all the patterns we get with the 1-D cellular automata. As we know by now, there are 256 total possibilities; some are simple, while others are pretty complex. I agree with his statement: “What is perhaps most bizarre about the pictures is just how little trace they ultimately show of the simplicity of the underlying cellular automaton rule that was used to produce them.” (p.39)

Wolfram also talks about three-color totalistic cellular automaton where there are more rules and they are more complex – even though the rules are more complex, the resulting behavior is not. “... beyond a certain point, adding complexity to the underlying rules for a system does not ultimately lead to more complex behavior.” (p. 62)

How is that “certain point” determined? In the case of cellular automata, it is the 256 possibilities in which the resulting color can be either black or white. There are 8 possible on or off options/switches, giving us the total 256 possibilities. I was wondering how and why he came up with this particular number. Can the first 128 rules be seen as the point after which behavior does not get more complex after all? If, on the other hand, there are 9 switches instead giving us 512 possibilities, do we get new kinds of complex behavior, or are the behaviors from rule 257 to 512 simply a repeat of the first 256 rules?