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Network systems with rules depending on the number of distinct nodes

Network systems in which the rule depends on the number of distinct nodes reached by going up to distance two away from each node. The plots show the total number of nodes obtained at each step. In cases (a) and (b), the behavior of the system is eventually repetitive. In case (c), it is nested—the size of the network at step t is related to the number of 1's in the base 2 digit sequence of t.

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