The Logistic Map is hiding in the Mandelbrot Set

The logistic map is a simple second-order function on the unit interval: ${\displaystyle x_{n+1}=r{x}_n(1-x_n)}$, where $x_n$ is the variable value at stage {n} and {r} is the “growth rate”. 

For $1\le r\le 4$, the map sends the unit interval [0,1] into itself. It is a simple nonlinear difference equation, whose solutions exhibit both regular and erratic behaviour, and it is often used to demonstrate some important characteristics of chaotic motion. 

It describes behaviour found in a wide range of disciplines: physics, engineering, economics and biology.

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