After playing the Chaos Game a few times, have students return to their teams. The teams should discuss and write up a strategy for hitting the target in the fewest number of moves at the novice level, writing out an algorithm to express their strategy. Select volunteers to present their strategies to the class. Fractals abound in nature. Remind them that the shape of the object or curve must be irregular and self-similar.
Some possibilities are sea shells, shorelines, clouds, mountains, leaves, trees, and crystals.
But the result is surprising. What appeared to be random actually had an invisible pattern to it. Although different strategies may work, one possible algorithm involves coloring all the triangles on the board. The Java program's algorithm works by finding the midpoints of all the vertices and then calling a triangle routine on the three triangles created by the midpoints. In the picture above, these three triangles are the bigger red, blue, and green triangles.