Welcome to the Mandelbrot set page. This fractal is named after Benoit Mandelbrot,
who coined the word "fractal." Like many other fractals, it can be produced by
iterating a function (often millions of times). To produce the Mandelbrot set, you
iterate the following function:
The variables Z and C are both complex numbers. The first value
for Z must be 0+0i, and C is simply the value of the point you are
plotting. The function is iterated until the absolute value of Z exceeds two, or
until an arbitrarily assigned maximum number of iterations is reached. If the latter
occurs, then the point is in the set.
Points are sometimes colored according to whether or not they are in the set, but often
they are color-coded based on the number of iterations that were required to stop the
Now that you've seen how to create a Mandelbrot set, here are some programs I wrote
that you can run/download. All the source code is included, so you can compile them
on other machines.
Two Mandelbrot Set programs are available for download. The Turbo Pascal version is DOS compiled and contains source code. And, the QBasic version is extremely simple, and well suited for beginners.
Also, a Java applet is available that will create a Mandelbrot Set on your computer.