Angry Robot Clown

[fractower]

Made with a hacked version of Mandelbulber.

[Sockratease]

Wonderful!   

[kram1032]

creepy clown

[KRAFTWERK]

wierd 

What is the hack fractower?

[fractower]

I suspect that many of you can infer the algorithm directly from the following two images. More detail is below the images, but please try to guess the algorithm before reading more.

Towers of Bauble


The children of the Little Prince aren't getting along.






The basic idea is much like the complex methods which perform an angular remapping of the unit sphere with a radial power.

Z <- S(Z/|Z|) * |Z|^p +C.

The spherical remapping is specified geometrically rather than algebraically.
1. Start with a identity mapped unit sphere.
2. Draw a circle on the sphere and remap the sphere into the circle.
3. Add another circle and repeat.
4. Use a line to separate circles that overlap.
5. Whine about it taking longer to render than the Mandelbulb.

This method produces a fractal with lots and lots of knobs to play with. I plan to produce a more detailed writeup for the theory forum.

Frac

P.S. Can you guess what is different between the walled towers and those without walls? I was originally surprised when the walled towers showed up due to a typo.