In 2009 some guys (Daniel White, Paul Nylander and others) developed a kind of
3-space version of the mandelbrot set by trying to simulate the operations
within the (two dimensional) complex numbers with polar coordinates. As I
understood their approach so far.

At the end of this year (2009) David Wagner (waggy) proposed an implemtation
with POV with isosurfaces using (illegal, but still working) recursive function
calls at the newsgroups. Tor Olav Kristensen was so kind, to give an iterative
alternative to the recursive algorithm. Both sources can be found at:

http://news.povray.org/povray.binaries.scene-files/thread/%3C4b2c7b3f%40news.povray.org%3E/

Now I found this old treasures and played a little bit around with them. The
main parameters I changed was the iteration depth and the treshhold of the
isosurface used, which proved the more interesting issue. Here is a first close
up. I hope you enjoy it like me. I used Tor Olav's (POV-legal) version for this
images.

The texture is a very simple slope-pattern so far. The direction of the slope
pattern is choosen as the direction from  camera position to camera look at
which happens to be z in this case. red violet marks areas with normals opposing
z (slope=0), cyan marks areas perpendicular to z (slope=0.5), dark cyan is in
the middle of both (slope=0.25). In this situation slope values
above 0.5 are not visible.

Best regards,
Michael

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