Oct 27, 2010

5th Math Circle!!!


In nature, fractals are everywhere and have always been, but it is thanks to a brilliant mathematician (Benoit Mandelbrot) who drew attention to them in 1975, that the term ‘FRACTAL’ became a household concept. The best way to understand that something is fractal is to observe similarities between the whole and small parts of it. Here are a few images which share this:

Romanesque broccoli (left) and fern leave (right)

This “self-similarity” is ubiquitous in nature. Trees have fractal properties, and kids had a chance to draw some interesting branching trees:

The rules are simple. Start with a line, then branch it into two smaller lines, then branch each line into two smaller lines, etc. You can probably guess the rule fro getting the so called Sierpinski square below:

But there are other man-made fractals …. Mandelbrot set being the first one to be unveiled:

You can see what we mean by seeing similar shapes at smaller and smaller scales, by zooming in the fractal set:

We showed quite a few fractals that have connection with or are inspired by Halloween, here is just one of them (see http:\\zapatopi.net):

Finally (parents take notice!), there is a very interesting episode of NOVA (on PBS) called “The Hidden Dimension”,  which IS A MUST SEE for the whole family. In it Benoit Mandelbrot is featured among many others. This will hopefully answer your natural question: “Why do people study fractals?”

Watch it online at http://www.pbs.org/wgbh/nova/fractals/

Sadly, Benoit Mandelbrot died October 14, 2010, so he was still alive when we started our Math Circle!!!


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