Lab 2: Space-Filling Curves: The Harter-Heighway Dragon
Start with an ordinary sheet of graph paper and draw a horizontal line segment one unit long near the center (see stage 0).
For stage 1 hold the right-hand endpoint fixed and rotate a copy of the line segment 90 degrees clockwise about this fixed point. Now you have two line segments that form a right angle, and a new endpoint.
For stage 2 hold this new endpoint fixed and rotate a copy of the "L"-shape 90 degrees clockwise about the new fixed point. Now you have four line segments and another new endpoint.
Continue on, stage by stage, each time holding the new endpoint fixed and rotating a copy of the figure 90 degrees clockwise about that new fixed point. It actually may be easier to use two pieces of graph paper and trace over a copy of the previous stage in order to reach the next stage.
Your assignment is to continue until you reach stage 9. If you continue indefinitely you will create an interesting, highly regular shape called the Harter-Heighway Dragon. How many line segments have you drawn in stage 9?
If you enough time, patience and paper, you could generate an image of stage 15. How many line segments would that require?
