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.
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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I enjoyed the Arthur C. Clarke film immensely. Although I studied a bit of mathematics while pursuing my engineering degrees, I have always felt that it was a weak area for me (and my grades in math supported that feeling). So I had a very hard time understanding the coordinates for the spots on the screens were generated. However, upon seeing them I was immediately reminded of many experiences I had during the period 1968 to 1972, my college years. Unlike Arthur Clarke, I did use quite a number of illegal chemicals. There was an eerie similarity between the fractal images and many visual phenomena I experienced. And as was pointed out in the film, there are certain styles in art and decoration that are very reminiscent of the images generated with fractals. And those were exactly the kinds of art that we experimenting students sought out for clothes, wall hangings, etc. etc. I kept thinking that surely fractals must have been discovered in 1960 rather than 1980. They looked so familiar. Then to top it off, the sound track was performed by David Gilmour. He was lead guitarist for Pink Floyd, my favorite band right down to this day. I listen to them daily.
ReplyDeleteSo thank you. Absolutely fascinating.