We have found that activities such as those discussed above serve to excite and to challenge students. Many of the chaos games were played in ``chaos clubs'' organized by Jonathan Choate, Beverly Mawn, and Mary Corkery in Boston public schools as after-school enrichment activities for students. While we compiled no concrete data, we have a lot of anecdotal evidence that students greatly enjoyed this kind of mathematics.
The mathematics involved in constructing and understanding chaos games runs the gamut from elementary algebra to linear algebra, from Euclidean to fractal geometry. Algorithmic thinking is a prerequisite for writing the simple graphing calculator program necessary to play the game with technology. Geometric transformations are at the root of the game. And probability and randomness lurk in the background. In short, chaos games provide the student with a wealth of different mathematical ideas and, at the same time, a glimpse at contemporary mathematics.
Note: This paper will appear in printed form in "New Directions
for Teaching and Learning Geometry," ed. R. Lehrer, Erlbaum Associates. It appeared in abbreviated form in FOCUS, Volume 15, No. 3, June 1995, published by the Mathematical Association of America.
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