I expected some actual 3D fractals (or rather, some shapes with 3 < dimensions < 4) such as a Sperpinski or Menger Sponge: https://en.m.wikipedia.org/wiki/Menger_sponge

For 3D fractals, have a look at mandelbulb: https://en.wikipedia.org/wiki/Mandelbulb

And for discussion of 3D analog of the original Mandelbrot, check out the Math Exchange discussion[1] and site dedicated to finding it.[2]

The vanilla zoomed mandelbrot[3] looks 3d to me. It's interesting that actually turning them into true 3d is such an elusive problem.

[1] http://math.stackexchange.com/questions/150117/is-a-3d-mande...

[2] http://www.skytopia.com/project/fractal/2mandelbulb.html

[3] http://www.skytopia.com/project/fractal/h-frac.jpg

For all things fractal, join the http://www.fractalforums.com community!

For Volumising Mandelbrot's Equation the Mandelbulb is worth a look:

"In 2006 Daniel White inspired by an idea of Rudy Rucker developed a mathematical equation with the potential for a real 3D equivalent to the famous 2D mandelbrot set. With a modification by Paul Nylander in 2009 the Mandelbulb was born on fractalforums.com"[1][2]

[1] http://www.fractalforums.com/still-frame/the-discovery-of-th... [2] http://www.skytopia.com/project/fractal/mandelbulb.html

If you want to play with 3D fractals in WebGL, you can also try:

http://www.alsonkemp.com/geekery/webgl-fractals/

If nothing else, I learned that you can write Python scripts for Blender. Neat.

Step 4 made my day.

Hey, the code is well commented and the math is explained in detail as well.