SICP Exercise 2.52

sicp

Question

Make changes to the square limit of wave shown in Figure 2.9 by working at each of the levels described above. In particular:

  1. Add some segments to the primitive wave painter of Exercise 2.49 (to add a smile, for example).
  2. Change the pattern constructed by corner-split (for example, by using only one copy of the up-split and right-split images instead of two).
  3. Modify the version of square-limit that uses square-of-four so as to assemble the corners in a different pattern. (For example, you might make the big Mr. Rogers look outward from each corner of the square.)

Answer

Let us step through this one by one. This was a little random, but I added a smiley face to the wave painter:

(define wave-segments
 (list
  (make-segment
   (make-vect 0.006 0.840) (make-vect 0.155 0.591))
  (make-segment
   (make-vect 0.006 0.635) (make-vect 0.155 0.392))
  (make-segment
   (make-vect 0.304 0.646) (make-vect 0.155 0.591))
  (make-segment
   (make-vect 0.298 0.591) (make-vect 0.155 0.392))
  (make-segment
   (make-vect 0.304 0.646) (make-vect 0.403 0.646))
  (make-segment
   (make-vect 0.298 0.591) (make-vect 0.354 0.492))
  (make-segment
   (make-vect 0.403 0.646) (make-vect 0.348 0.845))
  (make-segment
   (make-vect 0.354 0.492) (make-vect 0.249 0.000))
  (make-segment
   (make-vect 0.403 0.000) (make-vect 0.502 0.293))
  (make-segment
   (make-vect 0.502 0.293) (make-vect 0.602 0.000))
  (make-segment
   (make-vect 0.348 0.845) (make-vect 0.403 0.999))
  (make-segment
   (make-vect 0.602 0.999) (make-vect 0.652 0.845))
  (make-segment
   (make-vect 0.652 0.845) (make-vect 0.602 0.646))
  (make-segment
   (make-vect 0.602 0.646) (make-vect 0.751 0.646))
  (make-segment
   (make-vect 0.751 0.646) (make-vect 0.999 0.343))
  (make-segment
   (make-vect 0.751 0.000) (make-vect 0.597 0.442))
  (make-segment
   (make-vect 0.597 0.442) (make-vect 0.999 0.144))
  (make-segment
   (make-vect 0.45 0.78) (make-vect 0.5 0.75))
  (make-segment
   (make-vect 0.5 0.75) (make-vect 0.55 0.78))
  (make-segment
   (make-vect 0.5 0.87) (make-vect 0.5 0.82))
  (make-segment
   (make-vect 0.5 0.82) (make-vect 0.52 0.82))
  (make-segment
   (make-vect 0.43 0.89) (make-vect 0.45 0.91))
  (make-segment
   (make-vect 0.45 0.91) (make-vect 0.47 0.89))
  (make-segment
   (make-vect 0.53 0.89) (make-vect 0.55 0.91))
  (make-segment
   (make-vect 0.55 0.91) (make-vect 0.57 0.89))))
(define wave (segments->painter wave-segments))

This is what it looks like now:

Next, I modified corner-split so that the wave figures are holding hands.

(define (corner-split-1 p n)
  (if (= n 0)
      p
      (beside (below p (up-split (rotate180 p) (- n 1)))
              (below (right-split (flip-horiz p) (- n 1))
                     (corner-split (flip-vert p) (- n 1))))))

It now looks like this with an n of 1:

For our modified square-limit procedure, your fantasy is the only limit. I just tried to make something that looks cool.

(define (square-limit-1 painter n)
  (let ((combine4
         (square-of-four flip-vert
                         rotate180
                         identity
                         flip-horiz)))
    (combine4 (corner-split painter n))))

This is what it looks like with an n of 2: