Tor Olav Kristensen wrote:
 > Ok. See the attached pov-file.

That is very nice, indeed, and far easier to read than my formulation. 
It probably renders faster than my recursive SDL hack, too.

A few quick renders seems to indicate your formula may match one of the 
bizarre "negative power" variations related to the tricorn fractal 
rather than one of the standard mandelbulb functions.  (You should still 
be able to get the "classic" mandelbulbs by messing with the phase and 
the signs of the powers.)  I don't have time right now to examine it in 
detail, but I would take a look at the use of the built-in f_ph() and 
f_th() functions; they don't correspond directly to published mandelbulb 
functions[1], nor to the conventional spherical coordinate system[2].

> But it may not be the easiest example for new users to learn from.

Plain old isosurfaces are tough for new users to tackle at all, and more 
power to those that do!

> Note that if one want to see more details at higher powers,
> then this smoothing expression should probably be changed:
> 
>   1/(I - ln(ln(_r)/ln_R_BO)/ln_R_Pwr)

Can you explain what you mean here, or post an example?

The smoothing function should not smooth the surface itself, it should 
just decrease the actual max_gradient of the function and make it easier 
for the root solver to find the surface.  To get to higher iteration 
surfaces, lower the isosurface threshold to a value closer to zero (from 
1/2 as it is now to 1/3, 1/4, and so on to get more and more fractal 
detail.)

~David

[1]
http://www.skytopia.com/project/fractal/2mandelbulb.html#formula

[2] 
http://en.wikipedia.org/wiki/Spherical_coordinate_system#Coordinate_system_conversions

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