Lab 3: Fractional Dimension: The 3/2 Curve
Start with an ordinary piece of graph paper, if you have graph paper with smaller squares, so much the better. Set the paper horizontally and draw a line across the paper starting about half of the way down the short side of the paper. Make your line 32 units long, 64 units long if you have the room (stage 0).
Next take eight line segments, one-fourth of the length of the original (8 units if you began with 32 units, 16 units if you began with 64 units), and assemble them as the wiggle you see in stage 1.
Your goal at each stage is to replace each line segment with eight line segments that are each one-fourth of the length of the original. You want to arrange the eight smaller line segments over the original in the same orientation that you see when you compare stage 0 to stage 1. See if you can draw stage 2 and compare it to the figure below.
Your assignment is to complete stage 3. Notice that at each stage the length of the curve doubles. If you like, you can view a magnified image of stage 4.
