HandsOn 4 - Creating a Rubber Band Coastline

Construct a coastline using a rubber band. You will need

• a rubber band,
• a single die, and
• nine or more thumb tacks.

1. Place a blank sheet of white paper on a bulletin board and over it stretch the rubber band between two thumb tacks (as shown in Figure 2.4) a vertical distance 20 centimeters apart. Treat the doubled rubber band as a single line.

2. Locate the midpoint of the rubber band. You are going to move this midpoint right or left a random amount and hold it there with a third thumb tack. Here is how:

3. Roll the die.

• If you get 1, push the midpoint left by 4 centimeters, hold it with the thumb tack.

• If you get 2, push the midpoint left by 2 centimeters, hold it with the thumb tack.

• If you get 3, leave the midpoint where it is, but hold it with a thumb tack.

• If you get 4, push the midpoint right by 2 centimeters, hold it with the thumb tack.

• If you get 5, push the midpoint right by 4 centimeters, it with the thumb tack.

• If you get 6, roll again.

4. Now look at the two segments that make up your coastline. Repeat the above process on each of the segments, pushing the midpoint to one side or the other perpendicular to the direction of the segment. Pin each relocated midpoint to obtain a four-segment coastline.

5. Repeat one more time on the four segments to get an eight-segment coastline. Trace the final coastline on the white paper backing and leave it on the bulletin board.

 Q2.7: Did the previous two activities teach you anything about the process of forming natural fractals? Can you draw parallels between your own creation of an artificial coastline using a rope or rubber band and the natural process that creates real coastlines?

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