Arther C. Clarke explores the Mandelbrot set in this fantastic hour long documentary. Click on the link above for full screen or watch the video as sized below.
There are many free programs on the web for exploring the Mandelbrot set, here is one.
For the details of the calculation, this site has a nice simple explanation. That link is also where I got these beautiful images that seem... well, like they could be the fingerprint of a god.
I'll be on vacation for the next few weeks, so expect something inspired when I get back!
-pythagoruz
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