Chaos Game
In the chaos game, one of a few simple rules is selected at random and applied to a point, to yield a new point. This random step is repeated over and over again, to produce an "attractor". Here the attractor is a Sierpinski triangle. The figures illustrate (i) the first few points, (ii) the results after 1000 iterations, (iii) the same result at a higher resolution with outliers discarded, (iv) a magnification of (iii).
What happens when you change the rules?
