The Beauty of Fractals

I'm a reasonably intelligent galoot, but what I can't understand is this: That beauty such as this exists neatly tucked away in common, garden-variety complex numbers. Take a small area along the periphery of the region known as the Mandlebrot Set. For each complex number c in that area, iterate the following: 

Now, the magnitude of z(n+1) will either remain finite or not. If it's going to go infinite, it will exceed 2. If that happens, assign a color to that point based on the value of n when it happens. Otherwise, continue iterating until the maximum number of iterations is reached, and assign black to that point. Then plot out all of the points. I used to do this in FORTRAN on a VAX, plotting on an old low-res paintjet printer. It's a lot easier now.

Copyright © Peter L Berglund, 2006. All rights reserved; content may not be reproduced without permission of author.