The mathematics involved in constructing and understanding chaos games runs the gamut from elementary 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 of contemporary mathematics.
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Peitgen, H.-O., Jurgens, H., & Saupe, D. ( 1991). Fractals for the classroom. New York: Springer Verlag.