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Catch the Spirit of Mathematical Practices

Mathematics Investigations

Chaos Game Rules: Starting point is any point in the

plane of triangle ABC. Second point is half the distance

from current position and one of the vertices (A, B, or C) that has been randomly selected. (C)

Continue plotting points following the above rules.

Vertex B Vertex A Vertex B Vertex C, and so on . . .

1

2

3

45

6

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Catch the Spirit of Mathematical Practices

Mathematics Investigations

Playing the Chaos Game . . Players (2) Materials: Chaos Game

transparency, ruler, overhead pen, number cube.

Player 1: Plot a starting point on the transparency (any place on the paper)

Player 2: Roll the number cube to determine vertex A, B, or C. [0 or 1 (A); 2 or 3 (B); 4 or 5 (C)]Player 1: Using the ruler, plots the next point which is ½ the distance from the starting point and the vertex determined.

Continue this process and plot at least 30 points.Player 2 determines the next vertex and Player 1 finds the next point..

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Catch the Spirit of Mathematical Practices

Mathematics Investigations

Playing the Chaos Game . . In your group, stack your individual

transparency results from playing the Chaos Game. Be sure and align the transparencies so the triangle ABC looks like one triangle.

Do you see any patterns? Share results on a document camera.

Now, let’s try stacking everyone’s transparencies to see if we can see any patterns developing.

Discuss findings.

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Catch the Spirit of Mathematical Practices

Mathematics Investigations

Playing the Chaos Game . . Let’s see what we find if we use

technology.

A program was written for the Chaos Game. The triangle ABC is defined. When prompted to enter the distance to the new point, enter ½.

Watch to see if any patterns develop. The points will be plotted much faster and more accurate than we could do with our tools.

Use Graphing Calculator

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Catch the Spirit of Mathematical Practices

Mathematics Investigations

Playing the Chaos Game . . Let’s try the Chaos Game again but

this time use a different distance than ½ and see what happens.

Do you see any patterns developing?

Here’s a link with some good information about chaos and when fractals are developed.

Use Graphing Calculator