Chapter 7.6, Problem 39MS

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 $x=rx\left(1-x\right).$

$r=4$

(H). For $y=4x(1-x),$ sketch a cobweb pattern that indicates that there must be periodic points of period 3. (Hint: Start fairly near the lower-left part of the diagonal and create a stair-step pattern that ends near the top, thus pushing you back to where you started. Slide your starting point if necessary.)