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Examples of general substitution systems and their causal networks

Examples of general substitution systems and the causal networks that emerge from them. In the pictures shown here, every replacement that is found to fit in a left-to-right scan is performed at each step. Rules (a) and (b) act like neighbor-independent substitution systems of the type discussed on page 84, and yield exponentially growing tree-like causal networks. The plots at the bottom show the growth rates of the patterns produced by rules (f) and (g). In the case of rule (f) the pattern turns out to be repetitive, with a period of 796 steps.

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From Stephen Wolfram: A New Kind of Science [citation]