One-Term Nestedly Recursive Functions
Recursion relations with a very simple form can lead to surprisingly complex behavior.
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.