This activity is designed to help students generate the Sierpinski Triangle.

Materials:

ruler
paper
die
pencil

To play the chaos game, see student directions.These directions may be copied and distributed to students. Included, along with the directions for students, is a set of questions for students to complete. Answers to these questions will vary, and students may explore the possibilities to see if their conjectures are reasonable. Note, though, that changing the number of points results in Sierpinski pentagons, etc... An extension to this game could be changing the rules so that each move is one-third of the distance toward the vertex rather than one-half.

Additional Internet Resource on the Chaos Game:

http://math.bu.edu/DYSYS/chaos-game/node2.html

Non-Internet Resources:

Peitgen, Heinz-Otto, et. al. (1991). Fractals for the Classroom: Strategic Activities Volume One.
New York: Springer-Verlag.

Barnsley, Michael (1988). Fractals Everywhere. Boston: Harcourt Brace Jovanovich.