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 Author Topic: 3D Pickover Stalks  (Read 17487 times) Description: 0 Members and 1 Guest are viewing this topic.
David Makin
Global Moderator
Fractal Senior

Posts: 2286

 « 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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The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
David Makin
Global Moderator
Fractal Senior

Posts: 2286

 « 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
 Logged

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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