Changing only three lines in the code given above one yields a somewhat similiar
but in detail very different image. The three changes are (1) returning 0 in
case of assumed boundedness, (2) returning 1 in case of (assumed) divergence and
(3) raising the isosurface threshold from 0 to 0.5. This results in a
dichotomous function representing the isosurface. In consequence to the left one
has only the values 1 (Cyan) and 0 (Red). I see more details but stronger
artifacts on the other side.

Under comparable conditions the rendering time was a bit shorter now: 7 h 48 m.

That is less than a half of the time the approach with the distance estimation
function needed which was intended to accelerate the solver originally. Since I
have no idea what solver POV uses to compute the surface of an isosurface (and I
have not the wits to work through the POV sources for it) I would be happy if
someone of the more involved can name the algorithm used by POV to solve this
unexpected riddle.

If someone finds a flaw in my modification of Tor Olav's code I would be happy
as well since four eyes see more then two.

Best regards,
Michael

A short note: Originally I wrote this post after the image was rendered while
watching a game of soccer between France and Germany at the late evening of
Friday 13/11/2015. During the game it became more and more clear that Paris got
under attack by IS terrorists. I was not in the mood to post something about
mandelbulbs while innocent people were killed at Paris.

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