vd: Fractals with Sierpinski Triangle/Carpet.

09a-fractals/vd01-sierpinski-triangle-carpet.rkt

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+#lang htdp/isl
+(require 2htdp/image)
+
+;
+; PROBLEM:
+;
+; Design a function that consumes a number and produces a Sierpinski
+; triangle of that size. Your function should use generative recursion.
+;
+; One way to draw a Sierpinski triangle is to:
+;
+;  - start with an equilateral triangle with side length s
+;
+;  ;  - inside that triangle are three more Sierpinski triangles
+;  ;
+;  - and inside each of those... and so on
+;
+; So that you end up with something that looks like this:
+;
+
+ (define IMG1 (bitmap "../imgs/023-sierpinski-triangle.png"))
+
+;
+; Note that in the 2nd picture above the inner triangles are drawn in
+; black and slightly smaller just to make them clear. In the real
+; Sierpinski triangle they should be in the same color and of side
+; length s/2. Also note that the center upside down triangle is not
+; an explicit triangle, it is simply formed from the other triangles.
+;
+
+(define CUTOFF 2)
+
+;; Number -> Image
+;; Produce a Sierpinski Triangle of given size.
+(check-expect (stri CUTOFF) (triangle CUTOFF "outline" "red"))
+(check-expect (stri (* CUTOFF 2))
+              (overlay (triangle (* 2 CUTOFF) "outline" "red")
+                       (local [(define sub1 (triangle CUTOFF "outline" "red"))]
+                         (above sub1
+                                (beside sub1 sub1)))))
+#;
+(define (genrec-fn d)
+  (cond [(trivial? d) (trivial-answer d)]
+        [else
+         (... d
+              (genrec-fn (next-problem d)))]))
+
+(define (stri s)
+  (cond [(<= s CUTOFF) (triangle s "outline" "red")]
+        [else
+         (overlay (triangle s "outline" "red")
+                  (local [(define sub (stri (/ s 2)))]
+                    (above sub
+                           (beside sub sub))))]))
+
+
+;
+; PROBLEM:
+;
+; Design a function to produce a Sierpinski carpet of size s.
+;
+; Here is an example of a larger Sierpinski carpet.
+;
+(define IMG2 (bitmap "../imgs/024-sierpinski-carpet.png"))
+
+
+
+; You make a square, and inside a square you put 8 copies of and
+; a blank square in the middle.
+;; Natural -> Image
+;; Produce box with white box inside.
+
+;; Test the TRIVIAL case.
+(check-expect (scarp CUTOFF) (square CUTOFF "outline" "red"))
+
+;; Test the case where it is "1" bigger than the cut-off point.
+;; There will be one recursion here.
+(check-expect (scarp (* CUTOFF 3))
+              (overlay (square (* CUTOFF 3) "outline" "red")
+                       (local [(define sub (square CUTOFF "outline" "red"))
+                               (define blk (square CUTOFF "solid" "white"))]
+                         (above (beside sub sub sub)
+                                (beside sub blk sub)
+                                (beside sub sub sub)))))
+
+;(define (scarp s) (square CUTOFF "outline" "red")) ;stub
+
+;; Incorrect...
+#;
+(define (scarp s)
+  (cond [(<= s CUTOFF) (square s "outline" "red")]
+        [else
+         (overlay (square s "outline" "red")
+                  (local [(define sub (square (/ s 3) "outline" "red"))
+                          (define blk (square (/ s 3) "solid" "white"))]
+                    (above (beside sub sub sub)
+                           (beside sub blk sub)
+                           (beside sub sub sub)))
+                  (scarp (/ s 3)))]))
+
+;; Correct solution. Compare with the incorrect one.
+(define (scarp s)
+  (cond [(<= s CUTOFF) (square s "outline" "red")]
+        [else
+         (overlay (square s "outline" "red")
+                  (local [(define sub (scarp (/ s 3)))
+                          (define blk (square (/ s 3) "solid" "white"))]
+                    (above (beside sub sub sub)
+                           (beside sub blk sub)
+                           (beside sub sub sub))))]))
+
+;; TODO:
+;; (scarp 150) produces a strange result, like, correct but looks
+;;             like there are lines instead of boxes.
+;; (scarp 200) produces a more good-looking thing. Why‽
+