Benoit Mandelbrot, the father of fractal geometry, died last week. He fundamentally changed mathematics, and allowed us to start grasping the complexity that underlies the natural world in a new way. He developed math  that can be used to better understand things as disparate as coastlines, broccoli and clouds.
At left is a Mandelbox, named in his honor and found at Jos Leys' excellent mathematical imagery web page. It looks kind of like a Borg-ish cube, right? But if you look closer (below), you can see amazing intricacy. The whole cube arises from a single straightforward fractal.



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  2. Fractals also have important implications for how chaos behaves. just think about that - chaos actually BEHAVES and we can predict it (or are starting to). You can play with Mandelbrot sets (the 2-D version of this) at No matter how many times you zoom in, there's always a further level to go.