Why does the chaos game converge to the Sierpinski triangle?

Here is a simple process— also known as the “chaos game”— to generate a shape: #. Draw an equilateral triangle on a piece of paper and mark a random initial point. #. Mark the next point midway to one of the vertices of the triangle, chosen randomly. #. Repeat step 2 ad infinitum or ad nauseum, whichever comes first. If you haven’t seen this before (and maybe even if you have): what shape do you expect to emerge? Now, try simulating the game below: ...

April 28, 2020 · 17 min · 3617 words · Arun Tejasvi Chaganty