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There is some complex mathmatical equation to them, I never quite understood. An interesting fact though, lightning strike victims usually have complex fractal patterns appear on their skin for several hours.

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My math professor for my class last year has done a lot of work with fractals ("Mandelbrot" sets, if you've heard of them are supposed to be named after him, but Mandelbrot stole it... he retaliated by naming those black figures seen in a lot of fractals "Mandelbugs".. Mandelbrot did not appreciate it). Anyway, he did a couple lectures on fractals, I can try to explain some of the math.



Each fractal actually corresponds to the roots of a mathematical equation. Newton's Method of Exhaustion is a technique used to find roots of complex equations that we could never figure out by hand. To sum it up, you guess an answer, plug it into a certain equation, you get another answer. Plug that into the same equation, you get another... etc. Eventually, your answers will get closer and closer to each other until you know you have a root to the equation.

[edit, screwed up this part a little, fixed it]

If you start out with a point in the black, it eventually converges to a root (hence it is in the 'Mandelbrot set'). If you start out in a point in the colors, it will explode into some random number that is not a root. The color actually correponds to how many iterations it takes to explode to a certain point.