Sierpinski Bug Jump

Author:
brinkmwj
In this simulation we are experimenting with a funny jumping bug. There are piles of food at 3 points: (0,0), (1,0), and (0.5,1), and each time the bug jumps it picks one of those three piles (at random), and then jumps exactly halfway there. The bug starts at (0,0). For example, the bug, on the first jump, might pick the pile at (0.5, 1.0), landing at (0.25, 0.5) since it only jumped halfway. Then at the next step it might randomly decide to jump towards (1,0), landing at (0.625, 0.25). Notice at each step we are averaging the x values, and also averaging the y values.