Here is a zoom-in on the infinitely expanding, self-similar Mandelbrot Set, considered one of the most fascinating and beautiful constructs in mathematics, which links together notions of chaos, complexity, and fractals (roughly, a "fractal" is a geometric shape that is composed in part of smaller sections which themselves are similar in structure to the larger shape --- a sort of mathematical recursion):

A few sites with more info on this most famously-generated of mathematical fractals :

http://en.wikipedia.org/wiki/Mandelbrot_set (Wikipedia)

http://www.ddewey.net/mandelbrot/

http://en.wikipedia.org/wiki/Fractal (the Wikipedia entry for "fractals")

.... "If the brain was so simple that we could understand it, then we would be so simple that we couldn't." -- Emerson M. Pugh

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