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
- 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
- Select a direction perpendicular to the rope to be the positive
direction. The opposite direction will be the negative direction.
- Student #3 grasps the rope approximately in the middle.
- Flip the coin. Heads or tails determines the direction the person
in the middle will move in Step 5 below.
- 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
- Now Students #4 and #5 take up a position in the middle of each
- 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.
- Continue this process, randomly deflecting the midpoint
perpendicular to each straight segment, until you run out of either rope
- Take a picture of the resulting ``coastline.''
This is exactly the algorithm used in the accompanying JAVA applet.
Return to: Coastline