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Author Topic: Problem replicating Mandelbulb power 2  (Read 4400 times)
Description: Could someone please fix my formula?
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makc
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Posts: 272



« on: March 30, 2010, 09:10:57 PM »

I have a problem replicating Mandelbulb power 2 using formula from skytopia site:



Here's what I have:

<a href="http://vimeo.com/moogaloop.swf?clip_id=10556096&amp;server=vimeo.com&amp;fullscreen=1&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=01AAEA" target="_blank">http://vimeo.com/moogaloop.swf?clip_id=10556096&amp;server=vimeo.com&amp;fullscreen=1&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=01AAEA</a>
(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 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.
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makc
Strange Attractor
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Posts: 272



« Reply #1 on: March 31, 2010, 12:42:02 AM »

I just found this thread in povray archives where people had the same problem and the same shape I am getting. It appears, the error is in mandelbulb formula itself shocked
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KRAFTWERK
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Posts: 1439


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« Reply #2 on: March 31, 2010, 08:37:33 AM »

I am no mathematician, but I have been asking the same questions afro and it looks like you have the "cosine" version there


and you aim for the "original sine" version.



More variations in this thread:

http://www.fractalforums.com/theory/summary-of-3d-mandelbrot-set-formulas/
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makc
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Posts: 272



« Reply #3 on: March 31, 2010, 01:12:58 PM »

yes, that was the one, thanks!



still ugly as hell though...

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KRAFTWERK
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« Reply #4 on: March 31, 2010, 01:44:14 PM »

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:


High res:

http://fc02.deviantart.net/fs70/f/2010/060/b/3/DeathStar_Bulb_Power2_by_MANDELWERK.jpg
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bib
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At the borders...


100008697663777 @bib993
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« Reply #5 on: March 31, 2010, 08:13:21 PM »

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 smiley


http://www.fractalforums.com/index.php?action=gallery;sa=view;id=1993
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Between order and disorder reigns a delicious moment. (Paul Valéry)
KRAFTWERK
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« Reply #6 on: April 01, 2010, 08:57:56 AM »

Beautifully sliced bib!  afro
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