Discovering the 3D Mandelbulb

There is some exciting news this week in the world of fractals. Daniel White, on his website, describes what is apparently a completely new type of fractal, and the closest analog so far to a true 3-dimensional Mandelbrot set!

Although White mentions that this is probably not the “true” 3D Mandelbrot, the new fractal is undoubtedly a sight to behold, especially considering the renderings he showcases on his webpage.

Unable to contain my enthusiasm, I quickly wrote up a small program that uses OpenGL to actually display this shape in 3D, in real time, to get a feel for what this beast looks like from all angles. Don’t get too excited; the program does not render the shape in real time, it just displays the points rendered so far in real time. The actual rendering process can take a minute or so.

Download the program using the link below, and read further for instructions and screen shots.


The program basically renders the 3D shape by constructing a “point cloud” that approximates the edge of the fractal.

Everything in the program should be relatively self-explanatory, but here’s a brief overview of the features so far:

  • The program lets you click-and drag the rendered shape to rotate it in trackball fashion (left mouse button), as well as zooming in and out (right mouse button).
  • The program lets you select the “power” of the Mandelbulb formula, as well as the number of iterations to perform.
  • The program lets you select the resolution of the point cloud.
  • It gives you a “selection cube” with which you can select a subset of the shape to zoom in on (with the “zoom to cube” button).
  • It has a number of other minor features like fog and anti-aliasing.
  • It uses multiple threads to render the shape, so it will take advantage of multiple cores/processors.

Here are some additional screen shots:

Manipulating the selection cube:

After zooming in on the cube:

Zooming in further:

Looking inside:

Colorized points:

The program was written in C# with WinForms, using the Open Toolkit Library (OpenTK) which provides an excellent OpenGL wrapper.

Of course, this program is very much in its early stages, so don’t expect it to be perfect. As always, suggestions are welcome!