One technical tip: if you can't see a fractal with fine details clearly because it is too small, you can enlarge the image in Scheme by using the resize-image procedure, which is built-in to our Scheme. For example,
(resize-image (line 0 0 1 1) 400)would give you an image of a line from the center of the image to the upper-right corner, but it would be much larger than usual.
Rather than typing in the definition of c-curve, you can click on the
following file in Netscape and save it somewhere in your home
Some notes on Exercise 4.7 are in order. We do expect you to be able to prove that the length of the C-curve is determined by the pattern. One way to do this is to determine a formula L(d, n) for the length of a level-n C-curve between two points distance d apart. You can then use induction on n to prove that the formula is correct for all d and for all nonnegative integers n. If you do the proof this way, you will be proving a theorem with two variables in it, d and n. Note that when you write the induction hypothesis, you should rename both variables, but only add a restriction to the one corresponding with n. For an example of this, see page 55. The theorem on that page involves the two variables a and b. The induction hypothesis renames them to i and k, and adds the restriction k < b.