Monday, April 22, 2013

Exploring Fractal National Park

I was introduced to 3D fractals a few years ago via the iPad and iPhone app, Mandelbulb HD, by Angisoft. These apps enable the user to explore the fractal geometry of the mandelbulb. It has often struck me that exploring this fractal landscape is akin to hiking through a national park and photographing the sights.

The iPad app is somewhat limited by the processing power of the iPad itself. To this end, I discovered Mandelbulb 3D (MB3D). MB3D is written for Windows, but can also run on OS X and Unix without having Windows installed, thanks to WINE, a compatibility layer that duplicates the functions of Windows. MB3D is capable of much higher resolution rendering than the iPad app, which is necessary to achieve high quality imagery.

Below are some recent renderings I've done while exploring "Fractal National Park". Be sure to click on the images to get a high rez view.

Click image to view larger

Click image to view larger

Click image to view larger

The amount of variation found within the mandelbulb—which is nothing more than a mathematical formula visualized with computer graphics—is nothing short of mind-blowing. And this is only one formula, many of which that can be explored.

Using MB3D, you can even hybridize various formulae to synthesize new worlds to explore. Imagine taking Rocky Mountain National Park and hybridizing it with Grand Canyon National Park. You'd end up with a new national park that exhibits features of both!

I have a feeling I'll be hiking through these parks for some time to come.


  1. Can one animate in 3D the experience of walking through these wonderlands?

    1. There is a wide variety of free and paid fractal programs on which to explore and create. My 2 favs are Xenodream and Apophysis. Just Google for info and where to download. These work on PC not iPad. Yes animations and stills abound; again search via Google.
      Also there is a national fractal art competition and results posted on www; another Google easy find (use images).
      Theses are all mind-blowing art. Xenodream has the best ability to control rather than search/find/ can imagine and create with it. Apo can also easily revise/explore many equations and has many free plug-ins to modify what you first find; as well as explore in 3D.
      Using Xenodream you can export a 3D model to use in other 3D programs.
      I have tried many auto paintings in P12 & using John's smart auto paint brushes but fractals don't go much further by making them look like paintings; but they are very useful to generate parts of or backgrounds for painting.

  2. Yes, these are capable of being animated. Here is an example:

    Google "mandelbulb 3d" to check out other animations created by users.

  3. Hi John,
    Your Artist's Brushes site ( is not working. Tried with three different browsers.

  4. Thanks, Greg. It's fixed and back up now. -john