In 2009, after a two-year effort, a group of innovators from Fractal Forums found a way to project the Mandelbrot set and similar equations into three dimensional space.

This mathematical transformation that manifested the two-dimensional Mandelbrot set as the three-dimensional Mandelbulb, Daniel White and Paul Nylander (and the rest of the group at Fractal Forums) opened the door into a world populated by a previously unknown kind of object: the 3D fractal.

The Mandelbulb and the Mandelbox (discovered in 2010 by Tom Lowe) are ‘pure’ manifestations of the Mandelbrot equation and exhibit the same kind of bottomless, self-similar detail. The Mandelbulb and Mandelbox are sometimes described as “cousins.”

Beyond these two shapes exist a wild variety of endlessly detailed 3D fractals. They are formed using different projections of the Mandelbrot set, projections of other equations, folding and symmetry-making transformations, and hybridizations that mix the Mandelbrot set with other equations. As fractal-generating/imaging software evolves, the range of 3D fractal objects is growing.

3D fractals are a range of chaotic equation-based objects—most often derived from- or related to- the Mandelbrot set. These are also called “Mandelmorphs.” The term “Mandelmorphic art” is used to describe art made with with these kinds of forms. Most Mandelmorphic art is image and video based—but the Mandelbulb was even 3D printed shortly after its discovery.

Mandelmorphosis is 3D fractal generation, or formation. The term combines the prefix “Mandel-” referring to the work of Benoit Mandelbrot with the suffix “-morph” meaning “form.”

Visit the Mandelmorphosis page on Facebook, administrated by 3D fractal artist John Vega, for an astounding range Mandelmorphic art.