Function Repository Resource:

FindNestPeriod

Try to find the repetition period for nesting of a function

Contributed by: Richard Phillips

ResourceFunction["FindNestPeriod"][f,expr]

attempts to find the repetition period for applying f repeatedly starting from expr.

ResourceFunction["FindNestPeriod"][f,expr,n]

tries at most n times.

Details and Options

ResourceFunction["FindNestPeriod"][f,…] uses SameQ to compare results of applying the function f.

If the period is not found, ResourceFunction["FindNestPeriod"] returns a Failure object.

Find the period for successive nesting of a function:

In[1]:=

Out[1]=

If the period is not found, FindNestPeriod returns a Failure object:

In[2]:=

Out[2]=