Use the formula for the Mandelbrot but don't plot a fractal based on it, just do one pixel and connect each successive value of z with lines, up to a certain number of iterations. Which pixel that is will get to move around the screen slowly, and the number of iterations should be just enough that it doesn't slow down the animation too much. There are some spots where very small changes make a big change in the drawing; those are the spots on the borders of the shapes in the corresponding fractal image. In fact, show the fractal image too, behind the lines. See if you can find a way to slow the motion down when it comes to these borders (probably affect speed according to how many iterations pass without it either converging or diverging too much), and/or only stay within such areas. I've done this in C++ and it looks cool, except that instead of moving the pixel around automatically, I let the user move it with the mouse. I'd include the source but I lost it.