• Connection between Mandelbrot set and bifurcation diagrams

Chaotic systems change from stable to chaotic behaviour via bifurcations.

This movie shows the bifurcation diagram for the Mandelbrot set (along the x-axis).

... Glimpses of infinity, but beyond comprehension

The bifurcation diagram is drawn by repeating the calculation

xn+1  =  xn2 + x0

using initial values of x0 between -2.5 and 0.25, where the Mandelbrot set exists.

Calculating the coloured Mandelbrot set part of the animation is described on this page.