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Neat, I find the majority of mathematics pretty dull, but fractals are kinda neat and their implications are pretty mind blowing.
I haven't heard about fractals since the little snippets my high school math teacher told us to make math seem cool, and do not remember much of the basic principles. All I do remember is that the image is infinite. That is, you can zoom in all you want on any specific section and it will keep going, never ending.
Anyways, I googled Fractals to find more information on them and found these nice videos that somewhat explain what they are without getting too "mathy" and still stay understandable to those who have no chance of even becoming a janitor, at MIT.
If you have never heard of fractals, check'em out. You might appreciate Sprott's Gallery better.
I use a fractal generator called Apophysis, it is freeware and you can render some pretty interesting things. The first fractal generator I ever used was on a Timex Sinclair computer, and it typically took 24-36 hrs to generate a decent mandlebrot fractal, in it's 4 color glory on a 10" color tv for a monitor. Took another 2 hrs to print on the thermal printer we had on a 4" wide piece of paper. Needless to say, with quad processors and off site rendering available, these math equations can generate some really neat abstract art. I have a render going now, which looks like a red jellyfish. Cool stuff for geeks. Below is the render I am referring to, not very complex, but cool none the less.
Rob