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Fractal art was one of the topics that got me really interested in computer programming, eventually leading to my degree in computer science. I used to play around a lot with a public domain DOS program, called Fractint. It had iterators for several different fractal sets, and gave you a mind-numbing array of tweaks to the inputs and outputs, so you could generate a limitless array of stunning scenes.
On a related topic, Jonathan Coulton (a geek rock star) wrote a song a couple years ago, “Mandelbrot Set”, which is all about Benoit and his discoveries. It was inspired by his reading of “The Fractal Geometry…” in high school.
If you’re interested in fractals then you shouldn’t miss it’s cousin the ‘strange attractor’.
As just for it’s sheer beauty, the organic attractor: http://petervandernoord.nl/blog/2010/11/the-strange-beauty-of-the-gumowski-mira-attractor/