Have you ever heard of the Chaos Game? I didn't before. If you recall back to the pendulum with the 3 magnets, we can do something similiar to create fractals by playing the Chaos Game. Watch this video to learn how to play. Stop at about the 1 minute mark.
Now it's your turn. Grab a piece of paper and mark 3 vertices of an equilateral triangle. Following the instrctions in the video, mark about 20-40 dots, given on how much time you have. Get a friend involved. See what obvious spaces are in the triangle where there are no dots. Why do you think that is? You could answer that becuase we are going half-way between a current location and a randomly chosen vertex, we'll never hit the middle of the triangle.
Use this Applet by Shodor that allows the user to play the Chaos Game with 1-10 vertices by clicking the box below. The user can also change the probabilities of a vertex being randomly chosen.
Now some follow-up questions:
Why do we see the Sierpinski triangle with the equilateral triange?
Why do even numbered polygons have dots in the middle but odd numbered polygons tend to have a blank area in the middle?
What was noticed when you changed the probabilities of vertices?
You can view my Technology-Enhanced Activity Plan of this Activity here.
Note: I take no credit for the Shodor Applet or pictures. I am using them for educational purposes only. Credit goes to respective owners.