Thursday, October 26, 2006

Inside Julia Sets in areas of Strange Attraction

This is just a quick mention of the interesting results from viewing the inside of Julia Sets from areas of strange attraction.
It's particularly interesting when a conditional spherical inversion or reflection is applied to force a "normal" fractal formula to not diverge or at least diverge less often.

Here are two examples:

THE BATCAVE




EGGSHELL



Both are just views of the inside of Julia Sets from the standard Mandelbrot (z^2+c) simply modified by applying a circular inversion (The Batcave) or circular reflection (Eggshell) whenever z is outside the given circle of inversion/reflection.

One of the benefits of this method of creating fractal images is that you get very interesting results from very low maximum iteration counts - typically 10 to 30 - so render times are small.

The main formula that created the above was "Attractors" from mmf4.ufm which is in the Ultrafractal formula database. The formula also allows rendering of strange attractors and other interesting orbits with a dedicated colouring algorithm in mmf4.ucl.

1 Comments:

Blogger Philip Northover said...

Intriguing dimensionality. The eggshell image looks almost faberge.

10/30/2006 8:40 AM

 

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