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Fluctuations in the overall increase of sequences

Fluctuations in the overall increase of sequences from the previous page. In cases (c) and (d), the fluctuations have a regular nested form, and turn out to be directly related to the base 2 digit sequence of n. In the other cases, the fluctuations are more complicated, and seem in many respects random. All the rules shown start with f[1]=f[2]=1.


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