Compute the Feigenbaum delta from the logistic map. The logistic map is given by

$,$

and the Feigenbaum delta is defined as

where

and where is the value of for which is in the orbit of the period$-$ cycle with $.$

Here is a resonable outline:

Loop $1$ Start at period$-$ with $,$ and increment with each iteration

Compute initial guess for using $,$ and $.$

Loop $2$ Iterate Newton's method, either a fixed number of times or until convergence

Initialize logistic map

Loop $3$ Iterate the logistic map times

Compute and

Loop $3($end$)$