The logistic map is a simple second-order function on the unit interval: $latex \displaystyle x_{n+1} = r x_n (1-x_n) \,, &fg=000000$ where $latex {x_n}&fg=000000$ is the variable value at stage $latex {n}&fg=000000$ and $latex {r}&fg=000000$ is the ``growth rate''. For $latex {1 \le r \le 4}&fg=000000$, the map sends the unit interval [0,1] into itself. … Continue reading The Logistic Map is hiding in the Mandelbrot Set →