Art, Math, Science? - all of the above

Last night I was doing some Christmas shopping. I was looking at some different toy websites and saw something that reminded me of the spirograph I had as a child. I loved that toy! I still enjoy toys especially puzzles, legos, toy cars, and coloring books, and Christmas time makes me a little nostalgic for some of my childhood toys. Think what you will about that, but I personally think the world would be better off if more adults played liked kids on occasion. Anyway, I was curious if some version of the spirograph was still made so I did a Google search. Lots of websites having to do with fractals came up, and the science geek in me took over. I found this website, Mandelbrot Explorer, that allows you to zoom in and out on the Mandelbrot set. The image above is one that I "created".

Now what exactly is the Mandelbrot set, you might be wondering? Here is a basic definition I found on a website. "The Mandelbrot set named after Benoit Mandelbrot, is a fractal. Fractals are objects that display self-similarity at various scales. Magnifying a fractal reveals small-scale details similar to the large-scale characteristics. Although the Mandelbrot set is self-similar at magnified scales, the small scale details are not identical to the whole. In fact, the Mandelbrot set is infinitely complex. Yet the process of generating it is based on an extremely simple equation involving complex numbers." The website also gives a basic explanation of how the image is generated. Wikipedia also has good info.

I'm sure a few of you have noticed that the above image bears a striking resemblance to some sea shells - particularly the nautilus and the fossil ammonites. All natural objects, living or not, exhibit fractal geometry at some level, and this observation is part of the math known as Chaos Theory. I'm going to stop there - I believe that's enough education for one day, and Chaos Theory kind of makes my head hurt. If you want to have some fun, go to the Mandelbrot Explorer and play around. Be careful, though, it is definitely a timesuck.

By the way, I never did find out about the spirograph. I am definitely too easily distracted!