Hold the Space bar and click and travel with the mouse along the perimeter of the Mandelbrot set. You will see the iteration orbit of each location and it should give you insights into the convergence/divergence behavior in the interior/exterior of the Mandelbrot set. Not surprisingly locations near the perimeter provides most interesting behaviors.
I learned how to create the Mandelbrot set during a course I taught on Theories of Infinity. I developed a similar demo then in Geometer's Sketchpad to explain the behavior of locations under iteration.
