-What is a Manbelbulb ?
-It's a 3D fractal shape.
-OK, but what's a 3D fractal ?

To better understand what these pages are about, let's go back in time to the seventies when Benoit Mandelbrot a french-polish mathematician theorized fractals and presented what is known today as the Mandelbrot set, an example of which is seen below.

The Mandelbrot set

This 2D image was one the first spectacular complex graphic representations of " fractality " (i.e. the possibility to zoom into the image and always discover new details showing similar shapes and patterns as the whole image...

This particularity, " fractal self-similarity ", had not really been translated into 3D imagery until 2009 when Daniel White, an english pianist and mathematician, assisted by a group of fractal enthusiasts congregating on the bulletin board Fractal Forums, devised a new form of algebra he baptised " Triplex Algebra " that allowed the calculation and rendering of a 3D fractal shape. The first images calculated using his triplex formulas, by White and Thomas Ludwig, another member of Fractal Forums, did indeed show fractal properties which led Ludwig, to post the now historical phrase: " I can confirm bulbs on all axes ". By tweaking and honing their formulas the group came upon the now famous object known as the Mandelbulb, first presented by Paul Nylander (another member of Fractal Forums) on August 30, 2009, 04:25:45 PM .

First image of the Mandelbox



Spearheaded by Daniel White's Triplex Algebra, helped along by his cyber-colleagues at Fractal Forums (a very good example of successful collaborative research on the internet) 3D fractals had been born. Very quickly, fractal enthusiasts around the world sensed the potential of this discovery and more images of the Mandelbulb started appearing, followed by applications designed to better explore it.
In febuary 2010, Tom Lowe, also a member of Fractal Forums, came forth with another triplex algebra formula, giving birth to the spectacular Mandelbox.

Outside view of a Mandelbox


Since then other variations and formulas using triplex algebra keep showing up, and hybridation between different formulas has given birth to even more strange and fascinating shapes.

Fractal "Hybrid"


Today in January 2011, after a year of rendering frenzy by fractal enthusiasts around the world, 3D fractals, have become a new form of graphic creation, and have brought forth many images of landscapes, creatures and patterns never seen before, and yet often reminiscent of shapes from nature. Lately, the trend seems to be " Rotboxes " or Rotated Mandelboxes a variation on the Mandelbox, that yields many astounding and offworldly landscapes like the one you see here .

"Rotated Mandelbox" landscape

After only a year, the amount of ground covered in this infant field of 3D fractals is already huge, and makes one wonder what strange and exciting new shapes, creatures and landscapes will be discovered in the years to come...


Skytopia, Daniel White's website

Fractal Forums

Paul Nylander's website

Triplex Algebra

The Original Mandelbulb Thread on Fractal Forums

Tom Lowe's Mandelbox

Benoit Mandelbrot



There are already quite a few applications for creating 3D fractals and probably many more to arrive.
My two favorite ones, with which I've made almost all of the images on this site, are:


Visions of Chaos