Chapter 7.6, Problem 40MS

Logistic cobwebs. Let’s explore the relatively simple-looking transformation $y=rx\left(1-x\right)$ in the following three Mind scapes. A fixed point is one where $x=rx\left(1-x\right).$

$r=4.$

For $y=4x(1-x),$ start at two random points near your periodic point of period 3 and compute the first 10 values under repeated application of the transformation. Do these values seem to be converging toward the plot of the period 3 point or not?