This draws a random figure with some number of sides (you can choose), and then connects the midpoints of that figure, then connects the midpoints of the next figure, and so on forever. It makes a very nice picture, especially with the random colors (spider webs for less-than-10 numbers and curves for larger numbers). You can choose auto mode, where it draws the figures without waiting, or you can choose the step-by-step mode, where it draws the next figure every time you press space. Note that the program does not know when to end, so what I mean by "end" is stopping the program once each new figure is just a point.
All credit goes to me. I am not responsible if you waste half an hour watching large numbers play through. I suggest using turbo mode to speed things up, but sometimes it's nice to see it play out slowly. Post below the most amount of sides you've sat though, and a screenshot!