Activity 2: Creating a Coastline

In the previous activity, we found that coastlines can have a non-integer dimension. The shape of a coastline is called a fractal. Non-fractal objects have integer dimensions. For example, in the previous activity you saw that a line is one-dimensional. A piece of paper is two-dimensional.

In order to study coastlines further, create a sample coastline using the following instructions. You will need for this activity a rope, such as a clothesline, about 30 meters long, a single die, and a coin. Use an instant-picture camera if one is available. The activity takes place with the class in a wide hall, entrance hall, or outdoors. Select one class member to roll the die and another to flip the coin when told to.

1.

Two class members, Student #1 and Student #2, stand about 20 feet apart. Student #1 holds the end of the rope. Student #2 pulls the rope into a line, keeping the unused portion of the rope coiled at his or her feet.

2.

Select a direction perpendicular to the rope to be the positive direction. The opposite direction will be the negative direction.

3.

Student #3 grasps the rope approximately in the middle.

4.

Flip the coin. Heads or tails determines the direction the person in the middle will move in Step 5 below.

5.

Roll the die. The person in the middle of the rope takes a number of ``baby steps'' (steps that touch heel to toe) perpendicular to the rope. The number of steps is equal to the number on the die: from one to six. The direction of these steps is determined by the outcome (heads or tails) of the coin flip performed in step 4. Student #2 lets the rope slip out to provide the extra length as needed.

6.

Now Students #4 and #5 take up a position in the middle of each straight segment.

7.

Repeat items 4 through 6 for Student #4, who takes the number of baby steps indicated on the die in a direction perpendicular to the rope indicated by the coin flip. Do the same for Student #5.

8.

Continue this process, randomly deflecting the midpoint perpendicular to each straight segment, until you run out of either rope or students.

9.

Take a picture of the resulting ``coastline.''

This is exactly the algorithm used in the accompanying JAVA applet.