Directions to students:

To play the chaos game, begin with three points at the vertices of an equilateral triangle. Label the vertices 1,2, and 3. Using a standard cubic die, let a roll of 1 or 2 correspond to vertex 1 ,a roll of 3 or 4 correspond to vertex 2 and a roll of 5 or 6 correspond to vertex 3. Begin with any point in the interior of the triangle, called the seed point. Roll the die and move the seed point half way to the vertex that corresponds to your roll. Let this point be the new seed point, and keep rolling, continuing the process. (See diagram below)

In the above example, beginning with seed point 1, the first roll resulted in a move toward vertex 1, and the second move resulted in a move toward vertex 3.

Play the game on the back of this paper, and answer the questions on the following page.


Chaos Game Questions

1. Do you think that the same pattern will always form from this game? Why or why not?

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2. What would happen if the triangle were not equilateral?
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3. What would happen if you started with four points rather than three? What about five or six points? How would you set up the game in order to make sure that each vertex had an equal chance of being chosen in each of the above scenarios?
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4. Can you think of any interesting ways to change this game to get some other patterns? If so, what are they?
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