Benoit Mandelbrot is a large, imposing man with a pleasant demeanor. The Mandelbrot Set was named after him. It can be represented as a coloring on the complex plane, where each color value represents the number of iterations of the function z_n = z_n-1² + c until the function becomes unbounded, that is, it goes off toward infinity. The initial value of z₀ = 0 and c = (i, j) on the complex plane represented in the image. In the applet to the left, regions where the function never becomes unbounded are black.

Click and drag a rectangle on the applet to zoom in on a particular region of the set. You can zoom in indefinitely, although the speed at which the applet recomputes slows down as you zoom in.

Source code can be found here