The Chaos Game

The Chaos Game is a mathematical method used to create a sequence of points iteratively using a simple set of rules. In the Chaos game we start with a random point, use the rules to generate each successive point, then plot the resulting set of points.
Here are the rules of the game:
* Define 3 vertices in the x-y plane that define an equilateral triangle
* Start with a random initial point .
* At each step, select one of the 3 vertices at random
* Determine the next point by moving halfway from the selected vertex to the current point
* Plot the next point