This interactive diagram shows a Mandelbrot fractal. Given a simple function fc(z) = z2 + c, the Mandelbrot set is the set of numbers c where the function does not diverge to infinity when iterated a large number of times.
The interactive mode shows a few iterations of fc(z). When fc(z) diverges on a large number of iterations, the nodes will be red; when it doesn't diverge, the nodes will be green. Try playing around by moving z and the c with the mouse and arrow keys respectively.
If we move z to the origin, move c over each pixel of the screen, and color the pixels which diverge as green, then a cool fractal pattern appears. This is the Mandelbrot set. Press the button to see the fractal.