Thursday, March 3, 2016

TOK 1: Fractals

Today we will discuss the wonderful world of Fractals.

Creating Fractals
To begin, you will attempt to make some fractals of your own.  You will need:

  • A large piece of paper
  • A pencil
  • A ruler
  • Perhaps a protractor
Follow the rules to create your fractal.

What do you notice about the image that you are creating? What can we say about these diverse images?  What would a definition of fractals be?

Fractals in Nature
For Benoit Mandelbrot, who gave fractals their name and their theory, one of the most startling aspect of what seems at first to be a purely mathematical exercise was the frequency with which we encounter fractals and fractal-like structures in nature.

Take a few minutes to consider, and try to list ten examples of natural fractals.

Finally, consider this TEDTalk from Ron Eglash, "The Fractals at the heart of African design"

Now, let's apply the principles we learned from Fractals to a real-world problem:

How Long is the Coastline of Great Britain?
This question is also the title of one of Mandelbrot's original treatments of the topic.

More Fractal Resources:
"Scientists find evidence of mathematical structures in classic books"

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