One-Term Nestedly Recursive Functions

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Recursion relations with a very simple form can lead to surprisingly complex behavior.

Contributed by: Stephen Wolfram (March 2011)
Based on: A live experiment at the 2003 NKS Summer School (NKS|Online)
Open content licensed under CC BY-NC-SA



The recursion relations are set up so that whenever they sample below , the is taken to have value 1.

It is quite common to see a long "transient," with complex behavior, followed by simple, essentially repetitive, behavior thereafter.

is the simplest example that seems never to yield simple behavior.

Functions like these were mentioned in A New Kind of Science, but first studied in detail in Stephen Wolfram's Live Experiment at the opening of the first NKS Summer School, in June 2003.

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