Showing posts with label fractals. Show all posts
Showing posts with label fractals. Show all posts

Thursday, January 28, 2010

Fractals

I took another stab at understanding fractals this morning. I was familiar with the psychedelic and spiral graphics, but wondered what defines them. Dictionary definitions do little to help. Even the Wikipedia page was a bit dense for someone with no mathematical inclination. I had the weakest of grasps on the concepts of self-similarity, iteration, and recursion. I thought I understood the example of a shoreline having the same configuration as you zoomed in on it, but wasn't getting the overall picture. Well, it was all laid out very nicely by British science fiction author Arthur C. Clarke (1917-2008) in the film Fractals: The Color of Infinity (click to watch in its entirety). Clarke explains how French/American mathematician Benoît B. Mandelbrot, the "father of fractal geometry," discovered the deceptively simple math formula behind real-world, nonlinear things like coastlines, plants, blood vessels, etc. (There is also a Nova episode about fractals.) It's all about how irregular things repeat their shapes to infinity when magnified. In other words, a small part of the shape has a similar appearance to the overall shape, as explained in understandable terms on Fractalus.com. If you want to know more, try Fractals Unleashed. If you like the math and science of factals, you may be interested in a comparison of fractals at the atomic and astronomical levels (Fractal Universe), a description of the types of fractals, or a guided look at finding these forms all around you (Fractals Everywhere). Armed with a basic understanding, it wondrous to appreciate the spiral of a shell, the tributaries of a river, or the texture of a broccoli (pictured). There is an extensive fractal gallery on Flickr.

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