Fractals

Start/Stop music

In 1982 Benoit Mandelbrot published his book The Fractal Geometry of Nature. When I saw this book a few years later in the house of a friend, I was at once fascinated. But it was expensive, so I copied a few pages with the mathematics, and at home I tried to program the formula's . At that time I had an AT PC with a 286 processor and a CGA adaptor, Borland Pascal 4.0 just had appeared on the market.

The programming was easy, but it took me some time to find out where in the complex plane I had to look for the results..:-). I still remember the feeling of triumph when for the first time I was able to print out a very crude Julia fractal on my matrix printer.

To make a screen picture (4 colors, 320x200 resolution, imagine that now!) took time, sometimes several days. But I got addicted, bought an EGA adapter (16 colors, wow) and a mathematical coprocessor, bought the beautiful book The Beauty of Fractals(1986) by Peitgen, and spent many hours with my PC, always amazed about the beauty of these wonderful shapes.

I have given lectures about fractals to audiences varying from high school students to senior citizens. I have written a (very pedestrian) tutorial. And the fascination has never ended. But I don't write the programs myself anymore, there is a wide choice of software available now.

A good fractal generator is Fractint. You can find the official Fractint website here

The following pictures have been made with Fractint. Click for a larger image

Both pictures map the same region of the complex plane, only the color scheme is different.

Here are two zoom sequences of the Mandelbrot Set


Mandelbrot Zoom

Another Mandelbrot Zoom

Have you ever heard about Fractal Music?
The chaotic behaviour of the Mandelbrot fractal (and others) can be translated to a tone scale. If you do nothing more than that, the result generally will be boring, but with musical talent you can make this translation quite interesting.
My favourite composer is Yo Kubota from Japan.
He has composed a wonderful suit for micro tone piano: Mandelbrot Suit I
It consists of 12 pieces and has a length of 40 minutes.
You are listening now to part number 9: Fuga

If you like to experiment with the Mandelbrot fractal yourself, you can use the applet below.