Mandelbrot 04

Source code: mandelbrot01    Built with Processing

Doctor Matt >> Graphics

This applet displays the so called Mandelbrot lemniscates. We defined the polynomial sequence P like this: let P₀=z, and, for n>0, P_n = P_n-1²+z. We then define the lemniscates as the set of points with |P_n(z)|=1.

This applet shows these lemniscates approximately. The number of "iterations" is n, and what is shown in white is the set of points z with ||P_n(z)|²-1|< error.

If you increase the number of iterations, and decrease the error, you can see the set of white points approaches the boundary of the Mandelbrot set.

Key controls:

Clicking on the image recenters and zooms in by a factor of 4.