;; !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
;; Remember to use the draw.ss teachpack
;; !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!


;; Number -> Boolean
;; termination case: returns whether the side of a square
;; is too small to continue dividing
(define (too-small? len)
  (< len 1))

;; Posn Posn Posn Posn -> true
;; draw a square from the input posns and return true
;; side effect: square is drawn on screen
(define (draw-square a b c d)
  (and (draw-solid-line a b)
       (draw-solid-line b c)
       (draw-solid-line c d)
       (draw-solid-line d a)))

;; Number Posn -> true
;; draws a fractal using side length len and top corner p
;; this fractal is recursively four squares inside another
;; square, like so.
;;
;; *----------*----------*----------*
;; |          |          |          |
;; |          |          |          |
;; |          |          |          |
;; |          |          |          |
;; |          |          |          |
;; |          *----------*          |
;; |                                |
;; *----------*          *----------*
;; |          |          |          |
;; |          |          |          |
;; |          |          |          |
;; |          |          |          |
;; |          |          |          |
;; *----------*          *----------*
;; |                                |
;; |          *----------*          |
;; |          |          |          |
;; |          |          |          |
;; |          |          |          |
;; |          |          |          |
;; |          |          |          |
;; *----------*----------*----------*
(define (fractal len p)
  (cond
    [(too-small? len) true]
    [else
     (local ((define x (posn-x p))
             (define y (posn-y p))
             (define a (make-posn (+ x len) y))
             (define b (make-posn (+ x len) (+ len y)))
             (define c (make-posn x (+ len y)))
             (define newlen (/ len 3))
             (define p1 (make-posn x (+ newlen y)))
             (define p2 (make-posn (+ x newlen) y))
             (define p3 (make-posn (+ x (* 2/3 len)) (+ y newlen)))
             (define p4 (make-posn (+ x newlen) (+ y (* 2/3 len)))))
               
     (and
      (draw-square p a b c) 
      (fractal newlen p1)
      (fractal newlen p2)
      (fractal newlen p3)
      (fractal newlen p4)))]))

(start 600 600)

(fractal 500 (make-posn 10 10)