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Author Topic: 3D Pickover Stalks  (Read 12755 times)
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David Makin
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Posts: 2283



Makin' Magic Fractals
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« on: November 08, 2009, 01:43:41 PM »

After Paul (bugman) posted examples of 3D Pickover Stalks and I managed to get a fairly decent algorithm for 3D orbit traps I decided to try Pickover Stalks myself, so here's an example.
This is a Julia Set using particularly esoteric 3D maths for z^2+c where the unit vector multiplication table is:

   *  |  r   i   j
   ----------------
   r  |  r   j  -i
   i  |  j  -i   r
   j  | -i   r  -j



If no image above then look here:

http://makinmagic.deviantart.com/art/3D-Pickover-Stalks-test-142906488
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http://www.fractalgallery.co.uk/
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David Makin
Global Moderator
Fractal Senior
******
Posts: 2283



Makin' Magic Fractals
WWW
« Reply #1 on: November 08, 2009, 05:37:56 PM »

After Paul (bugman) posted examples of 3D Pickover Stalks and I managed to get a fairly decent algorithm for 3D orbit traps I decided to try Pickover Stalks myself, so here's an example.
This is a Julia Set using particularly esoteric 3D maths for z^2+c where the unit vector multiplication table is:

   *  |  r   i   j
   ----------------
   r  |  r   j  -i
   i  |  j  -i   r
   j  | -i   r  -j


Just in case anyone's interested:

Here's a rotation of the z^2+c Mandy for this system:

http://www.fractalgallery.co.uk/EMF.mov

Also this multiplication table was inspired by the idea of any two of three perpendicular forces coming together producing a perpendicular result and is based on the obvious unit vector multiplication table for such a system, i.e.

   * |   r      i       j
   --------------------
   r  | +/-r  +/-j  +/-i
   i  | +/-j  +/-i  +/-r
   j  | +/-i  +/-r  +/-j

Obviously this gives 512 possibilities depending on the signs used - I tried a few and settled on one based on the fact that it was the most visually interesting Mandy smiley
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The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
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