Ducky, Thalis and co.

[s31415]

Hi,

I've been recently interested in the fractals producing patterns filling densely the plane, that can be created with formulas of the family of "Ducky" for Ultra Fractal and "Thalis" in fractal explorer. Most of these formulas are pretty complicated, with lots of parameters and it's not clear what is doing what. However, it turns out there is pretty simple algorithm that reproduces more or less all the patterns created by these formulas. I've explained the details of the algorithm and posted a few pictures there:
http://www.algorithmic-worlds.net/blog/blog.php?Post=20110227

I would be especially interested if someone knows more about the history of the Thalis/Ducky type fractals.

Best,

Sam

[s31415]

Actually, I've just found out about Kaleidoscopic IFS's, that generalize to 3 dimensions the 2d Butterfly Origami algorithm by Johnathan McCabe.

[Tglad]

Here is the original thread, where it is defined and explored:
http://www.fractalforums.com/3d-fractal-generation/kaleidoscopic-(escape-time-ifs)/
Developed independently of McCabe and uses only the shape preserving transforms of translation, rotation, scaling, reflection and (occasionally) sphere inversion.
By Buddhi:
<a href="http://www.youtube.com/v/JlUMRMpLzRo&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/JlUMRMpLzRo&rel=1&fs=1&hd=1</a>

[s31415]

Thanks I updated my blog post.