5th Math Circle!!!
Today’s theme was FRACTALS !!! COOLEST THING ON EARTH!
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!!!
