The chaos game is simple but very interesting. A single die is needed to play the game, and the vertices of an equilateral triangle. Assign two outcomes of the die to each of the 3 vertices. For example, rolling a 1 or 2 could be assigned the top vertex. Rolling a 3 or 4 could be assigned the bottom left vertex, and 5 or 6 could be the bottom right vertex.

Start the chaos game by placing a random point in the interior of the triangle; call it x_0. Roll the die. Measure half the distance from your initial point to the vertex corresponding to the number showing on the die. Mark a new point there; calling it x_1. Repeat the process, each time placing new points at the location of 1/2 the distance from the current point to the vertex indicated by the roll of the die. Continue accumulating points in the interior of the triangle. Is there any pattern to the placement of the points inside the triangle? That is, is there any order in chaos?