Today the father of fractal geometry turns 83. Benoît Mandelbrot is known for the Mandelbrot set, a set of points in the complex plane that forms a fractal. To see if a point c belongs to the Mandelbrot set start with z0 = 0 and generate the sequence z1, z2, z3,.. by iterating the function zn+1 = zn2 + c. If the value z remains close to the origin, the value c belongs to the Mandelbrot set. If it runs away to infinity, it doesn’t. Plotting the set of points in the complex plane gives you this picture.

mandelbrot.jpg

The picture is the result of running a small program I wrote on the TI-83+ calculator. You can download it from here. The program runs for several hours. The zip-file also includes two of my other TI-Basic fractal programs. A Julia fractal and the Sierpinski triangle.


Aswin van Woudenberg

I'm a lecturer at the NHL Stenden University of Applied Sciences where I teach Artificial Intelligence, Algorithms and Concurrent Programming. Together with my students I'm building dialogue systems that can learn, reason and converse in a variety of domains.

1 Comment

Koen Vervloesem · November 20, 2007 at 1:57 pm

You can use the program Xaos on your pc to visualize the Mandelbrot set. The program exists for Windows, Linux and Mac OS X: http://www.vervloesem.eu/qed/?p=520

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