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Alex Geeks Fractals

"The Fractalist: Memoir of a Scientific Maverick” just arrived at KPL. It is by Benoit B. Mandelbrot, the holocaust survivor and genuis who coined the term "fractal" and opened our eyes to the math behind so many beautiful events of nature, such as trees, clouds, and mountains.

 World Book Online defines a fractal as "a complex geometric figure made up of patterns that repeat themselves at smaller and smaller scales," where "any of its smallest structures is similar in shape to a large structure, which, in turn, is similar to an even larger one, and so on." I'm sorry, what? To be honest, defining fractals is easier with real world examples, like the Romanesco broccoli. But I think the heart of why I geek fractals is that they encourage exploration and discovery. Computer-generated fractal images, such as the Mandelbrot Set, can be "zoomed" in forever, and essentially, the more you look, the more you find.

While basic patterns of the image are repeated at different scales, self-similar fractal patterns are always unique, never exactly the same, and “roughly” similar at different scales of space or time (yes there are temporal fractals, too). Because mapping fractals requires extensive calculation, only since the 1980s have computers allowed us to gain a more comprehensive understanding of their presence and dynamics. I hope that our continued exploration of fractals will create better understandings of human ecology, while potentially solving aspects of our energy production and energy storage issues.

Also, they just look really cool, and since the brain itself is fractal, my hunch is that observing fractals kind of tickles the perception - like letting one’s neural networks glance into a mirror reflecting their own fractal nature.