Fractals (to me):

Graphic representations of mathematical formulas. Yup, that's the basics of it, but there are several things that also characterize fractal images:
Self-similarity which means that the larger image contains, within itself, smaller pieces which look the same (but not exactly the same--which leads to the look of randomness at times.)
Reiteration: inputting the equations' results back into the equation again causes a sort of 'growth' at times--imitating the forces of nature..? Small inital changes lead to huge final variation----the 'butterfly's wings' theory at play.

Artistically: Enjoy the odd harmony of chaotic and orderly forces working together.

Mathematically: don't worry about it unless you're really into math---you'll begin to recognize/anticipate the effects of a given math function after a while, but the exploration can keep you busy for years!

RosemaryR
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"This...this is magnificent!"
"Oh, yeah. Ooooo. Aaaaah. That's how it starts.
Then, later, there's ...running. And....screaming."