What Is The Mandelbrot Set?

Discovered by Benoit Mandelbrot in 1980, the set which bears his name is a geometric or mathematical universe you can explore on your computer. Sometimes referred to as the sum of all Julia sets (a family of quadratic polynomials f(x) = x² - µ, where µ is an imaginary parameter). As µ varies, the graph of the Julia set will vary on the complex plane. Some of these Julia sets will be connected and these connected sets comprise the Mandelbrot set. So the set is the plot of all points in the plane where x varies from -1 to 2 and y varies from -1.2 to 1.2. As you explore this plot by zooming into its edges, you find many beautiful and surprising pictures.

How To Use This Applet

Click the "Full Set" button to generate the entire Mandelbrot Set. Once the entire set is drawn, you can click the "Zoom In" button and then click on an area in the set you are interested in, and use the "Zoom Out" button to zoom back out.

Source Code And Documentation

MandelbrotApplet.java
Mandelbrot Javadocs