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Lost in the Desert

If you were lost in the desert and tried to walk a straight line back to civilization, chances are that you would end up walking in a (very large) circle -- and end up back where you began.

Click Go. There is just one turtle this time. Each time the turtle takes a step forward, it also turns a little bit to the right. With this very simple rule, the turtle ends up walking in a circle. (If you want to stop the turtle, click Go again.)

Think about the desert again. Chances are that you would inadvertently follow the same simple rule. No matter how hard you tried to walk straight, you would probably turn a tiny amount with each step (for example, one of your legs might be slightly stronger than the other). Eventually, you would end up where you began.

This way of making circles highlights a different aspect of circleness: circles have constant curvature. Every part of the circle looks exactly the same.

Notice that the turtle has no idea where the center of the circle is. In fact, the idea of "center" has no importance in this way of making (and thinking about) circles. At each step, the turtle's movement depends only on its current position and heading. The turtle is only acting locally, even if it seems to be thinking globally.

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Last modified: November 17, 2003
by Rupert Russell