Category: Mandelbrot

Posted in 3D Chaos Theory Flame Harmonograph Julia Set Mandelbrot Natural

The Very Best Fractal & Mathematical Pictures

This gallery showcases some of our best fractal & mathematical pictures. Start here! We have Mandelbrot & Julia Sets, Lorenz attractors, The Burning Ship, Flame fractals, Harmonographs, Buddhabrots, Menger Sponges, Sierpinskis, 3D Fractals, Fractal Zooms, Lyapunov Fracatals, etc. Oh, and …

Posted in Mandelbrot

Mandelbrot Gallery

Benoit B. Mandelbrot  (20 November 1924 – 14 October 2010) was a Polish-born, French and American mathematician, noted for developing a “theory of roughness” and “self-similarity” in nature and the field of fractal geometry to help prove it, which

Posted in Mandelbrot

Buddhabrots – Ghosts of the Mandelbrot Set

The Buddhabrot is an interesting variation on the well-known Mandelbrot Set, invented by Melinda Green in 1993. It’s a density plot of the orbits of points outside the Mandelbrot Set. The Mandelbrot Set is defined as the set of …

Posted in Mandelbrot

Orbits of The Starship Mandelbrot, in 3D

Orbits of The Starship Mandelbrot, in 3D.

In fractal mathematics, an orbit is the sequence of points in the complex plane traced out by the iteration of the function that generates the fractal. In the case of the Mandelbrot Set, …

Posted in Mandelbrot Program

Mandrian’s Mandelbrot Music

Mandrian is a Python + Pygame program to render the Mandelbrot Set  by sub-dividing square areas into sub-squares. If the square’s corners all have the same iteration count from the escape function we assume there’s no internal detail to render. …

Posted in Mandelbrot Zoom

Beyer’s Mandelbrot Zoom

Mandelbrot Zoom sequence up to 1:60,000,000,000, created by Wolfgang Beyer with the program Ultra Fractal 3.

  • Mandelbrot set. Initial image of a zoom sequence: Mandelbrot set with continuously colored environment.
  • Coordinates of the center: Re(c) = -.7, Im(c) =
Posted in Mandelbrot Program

Mandelbrot Set in Python & Pygame