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Friday math movie: Fractals without a computer

By Murray Bourne, 12 Nov 2010

This is neat - a simple way to produce fractals without even turning on a computer.

A key concept of fractals is that many of them are "self-similar". What this means is if you zoom in far enough, you'll see the same patterns you saw when you started. And likewise, when you zoom out far enough, you will once again see the same shapes. (You can see some of this idea in this 3-D fractal journey).

In the video below, they point a video camera at 3 screens, and project the image form the camera onto the screens. It's a bit like being in a room with mirrors on opposite walls - you see infinite versions of yourself going off into space.

Since there is a slight delay as the image signal reaches the 3 screens, it provides opportunities to create Sierpinski triangles (which are examples of "exact self-similarity"), Julia sets and various other fractals, all without a computer. (Normally you need to generate them using complex numbers, various random generators or even chaotic differential equations.)

This 3-screen fractal idea could be a good activity for a math event (or a science fair) in schools or a math club.

See the 2 Comments below.

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