An Extraordinary 3D Mandelbulb Animation

The Mandelbulb is a three dimensional manifestation of the Mandelbrot set. It is an infinitely complex, naturally occurring fractal object.

The two dimensional Mandelbrot set, discovered in the early 20th century, is named for the mathematician Benoit Mandelbrot—the ‘Father of Fractal Geometry’—who studied and popularized it.

The Mandelbrot Set is the most widely recognized mathematical fractal form. Along with fractal geometry, it entered popular culture in the mid 1980s. About thirty years passed between the first digital rendering of the flat Mandelbrot set in the late 1970s and the first rendering of its three dimensional equivalent, the 3D Mandelbulb Animation, in 2009.

The 3D Mandelbulb Animation set has its origin in complex dynamics, a field first investigated by the French mathematicians Pierre Fatou and Gaston Julia at the beginning of the 20th century. The fractal was first defined and drawn in 1978 by Robert W. Brooks and Peter Matelski as part of a study of Kleinian groups. On 1 March 1980, at IBM’s Thomas J. Watson Research Center in Yorktown Heights, New York, Benoit Mandelbrot first visualized the set.

Mandelbrot studied the parameter space of quadratic polynomials in an article that appeared in 1980. The mathematical study of the 3D Mandelbulb Animation set really began with work by the mathematicians Adrien Douady and John H. Hubbard (1985), who established many of its fundamental properties and named the set in honor of Mandelbrot for his influential work in fractal geometry.

The mathematicians Heinz-Otto Peitgen and Peter Richter became well known for promoting the set with photographs, books (1986), and an internationally touring exhibit of the German Goethe-Institut (1985).