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I have a problem replicating Mandelbulb power 2 using formula from skytopia site (http://www.skytopia.com/project/fractal/2mandelbulb.html#formula):

(http://www.skytopia.com/project/fractal/new/iter/i2-4-s.png)(http://www.skytopia.com/project/fractal/new/iter/i2-6-s.png)(http://www.skytopia.com/project/fractal/new/iter/i2-200-s.png)

Here's what I have:

http://www.vimeo.com/10556096
^{(if this doesn't work when you read this, just take my word that it's really different, and remind me never use vimeo again)}

The code I use is:

      while ((r < 2)&&(i < N)) {

         double theta = atan2( sqrt(x*x + y*y), z);
         double phi = atan2(y, x);
         r = sqrt (x*x + y*y + z*z);
         double rn = pow (r, n);
         x = x0 + rn * sin(theta*n) * cos(phi*n);
         y = y0 + rn * sin(theta*n) * sin(phi*n);
         z = z0 + rn * cos(theta*n);
         // I used to have "r = ..." line here, and thought this caused the glitch
         // however, when I moved it up there, animation (and resulting shape)
         // changed very insignificantly
         //r = sqrt (x*x + y*y + z*z);

         i++;

Earlier (http://bit.ly/bsomvJ) I runned it with n=8 and got results that look correct, but apparently the error is there too, just less noticeable.

Can anyone spot my mistake here? Thanks.

I just found this thread in povray archives (http://bit.ly/aafpCC) where people had the same problem and the same shape I am getting. It appears, the error is in mandelbulb formula itself :o

I am no mathematician, but I have been asking the same questions O0 and it looks like you have the "cosine" version there
(http://www.fractalforums.com/index.php?action=dlattach;topic=2081.0;attach=1026;image)

and you aim for the "original sine" version.

(http://www.fractalforums.com/index.php?action=dlattach;topic=2081.0;attach=1022;image)

More variations in this thread:

http://www.fractalforums.com/theory/summary-of-3d-mandelbrot-set-formulas/

yes, that was the one, thanks!

(http://xs.to/thumb-3552_4BB32C4C.jpg) (http://xs.to/image-3552_4BB32C4C.jpg)

^{still ugly as hell though...}

It is a harder beast to render than the power 8 one... lots of irregularities and noise...


Here is one of my renderings with Subblues pixelbender script:
(http://fc03.deviantart.net/fs70/i/2010/060/6/c/DeathStar_Bulb_Power2_by_MANDELWERK.jpg)

High res:

http://fc02.deviantart.net/fs70/f/2010/060/b/3/DeathStar_Bulb_Power2_by_MANDELWERK.jpg

Yes it's always difficlut to properly render the power 2, there too many chaotic shapes and calculation artifacts. When I saw this post I wanted to try again, so I did this image called "Elephant Canyon". Nothing very original, but I like it :)

(http://www.fractalforums.com/gallery/1/492_31_03_10_8_11_18.jpeg)
http://www.fractalforums.com/index.php?action=gallery;sa=view;id=1993

Beautifully sliced bib!  O0