The chaos game is a way to construct (an approximation) of Sierpinski triangle. It's clear (using Thales' theorem!) that if we begin with a point on the sierpinski triangle, then we will never leave it. However, the choice of the beginning point is not important! The final shape will be quite like the *real* triangle, even if the first point is not on the triangle! Why?

Thanks!

P.S. I'm still working on my tomorrow's lecture!