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Observations and Explanations

1. Color the points corresponding to the first three steps of the random walk in three different colors and turn tracing on for them. Observe the effects of rerandomization over several hundred cycles. Explain what you see.

2. Now turn off tracing for all but the point corresponding to the second step. Observe the effects of rerandomization. Describe in detail what you see. Where is the density of points the greatest? Is the density greater at one step from the starting point or at two steps from the start? Draw a rough graph that estimates the density.

3. Repeat number 2 for the point corresponding to the third step of the random walk.

The Three Points Sketch is helpful for observing the above three steps; it uses buttons to turn tracing on and off so that you can follow the possibilities of C3PO's walk.