Julia Sets

The Julia set is closely related to the Mandelbrot set. For example, it is possible to determine whether a Julia set will be connected or a Cantor dust based on the Mandelbrot set. To calculate the Julia set, iterate the following function as you would the Mandelbrot function (that is, iterate until your maximum number of iterations is exceeded or until the absolute value of Z exceeds two):

Z_n=Z_n-1²+C

Does the function look similar to something else you have seen? It is the same as the Mandelbrot function. The difference is that the value of C is fixed at an arbitrary value and the value of Z is the current point that you are plotting. If you want the set to be connected, the value for C should come from inside the Mandelbrot set. The most interesting patterns occur in values on the edge of the Mandelbrot set.

Numerous programs are available to create the Julia Set. All ZIP files contain source code, and a DOS compiled executable (not in BASIC style languages, of course). Click on a language listed below to download the program.

Also, a Java applet is online to generates the Julia Set on your computer, complete with a graphical user interface.