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Here you are "In the Mandelbulb garden":

(http://fc06.deviantart.net/fs50/f/2009/324/4/7/In_the_Mandelbulb_garden_by_MakinMagic.jpg)

If no picture above then look here:

http://makinmagic.deviantart.com/art/In-the-Mandelbulb-garden-144177767 (http://makinmagic.deviantart.com/art/In-the-Mandelbulb-garden-144177767)

Hi Fractal Forums.
Playing around with mandelbulb for a few days.
Flying inside this thing is so addictive!
(http://img526.imageshack.us/img526/8607/mandelbulb81.png) (http://img87.imageshack.us/img87/1480/mandelbulb81.jpg)
(click for 2560x1600)
BTW, there should be faster way to approximate distance, analytic derivative takes way too much time..

I'm guessing from the above that you're using the normal (outside) distance estimator method for rendering from an "inside" viiewpoint ? If so then it will be inefficient because the distance estimator (as in the definition given in *the thread* by iq and as implimented in *the thread* by Jos Leys) is *not* really valid for "inside" points - for that a correct distance estimation is considerably more complicated - it is possible to derive one that *should* be considerably more optimum than using the "outside" version on the inside :)

Those are taken from outside.
I was actually referring to explicit computation of derivative  p*z^(p-1)*dz+1. It effectively doubles computation time.

Here is another idea: pre-compute both z^p (or other arbitrary complex formula) and derivative (scalar) into 4 channel 3D-texture. Or pre-compute rotation only.

Stereo view (cross-eyed) of degree 8 Mandelbulb (-sine version):
(http://img526.imageshack.us/img526/4787/stereo1.jpg)

Without using some sort of distance estimator you can obviously resort to a "brute-force" approach that simply guesses the steps and tests for hitting "inside" etc. but that method is decidedly inefficient at best and grossly inaccurate at worst :)

I know of 4 possible methods that are pretty much optimum - the analytical DE I take it that you're using and two other similiar methods that Ron Barnett (fractalrebel) has implimented in his ray-tracing formulas for Ultra Fractal (one of which does not require the derivative) and finally my own "delta DE" method, to be honest there's not much to choose between them in terms of performance but the method you're using is the best in my experience.
Note that it can be made dramatically better if you're using the trig version of getting the derivative bacause you can apparently get the derivative without the trig :)

@Enforcer:

If using trig on the GPU then use a texture lookup for the sines and cosines - I believe that's what iq is doing.

http://www.fractalforums.com/3d-fractal-generation/true-3d-mandlebrot-type-fractal/msg8698/#msg8698 (http://www.fractalforums.com/3d-fractal-generation/true-3d-mandlebrot-type-fractal/msg8698/#msg8698)

thanks for the stereo view, I could almost feel it with my fingers :)

I like the metallic look of these renders.