(define env (turtles 500 300))

;;;---------Pentagon-------------

;; one-pentagon-side: number snapshot --> snapshot
;; Return an after-snapshot which is like "env",
;; except that it has a one side of a pentagon drawn, of size length,
;; along with the 72-degree turn.

(define (one-pentagon-side length env)
  (turn 72 (draw length env)))


;; many-pentagon-sides: WholeNum snapshot --> snapshot
;; returns a snapshot with n sides of a pentagon drawn
;; given the initial snapshot "env"

(define (many-pentagon-sides n length env)
  (if (zero? n)
      env
      (many-pentagon-sides (sub1 n) 
                           length
                           (one-pentagon-side length env))))

;;draw-pengtagon: number snapshot --> snapshot
;;draws a regular pentagon, each side being of length "length"
;;takes an initial snapshot and returns another snapshot
;;with the pentagon

(define (draw-pentagon length env)
  (many-pentagon-sides 5 length env))

;;testing!
(draw-pentagon 80 env)

;;concentric-pentagons: WholeNum number number snapshot --> snapshot
;;Draws "number" concentric pentagons with the length of one side
;;of the inner-most pentagon being of size "length".  The spacing
;;between each pentagon is determined by the variable "spacing",
;;the length between each pentagon, measured from angle point to
;;to next angle point.

(define (concentric-pentagons number spacing length env)
  (if (zero? number)
      env
      (concentric-pentagons 
       (sub1 number)
       spacing
       (+ (* 0.587785 spacing 2) length);; cos of 54deg =~ .587785
       (turn 126 
             (move spacing 
                   (turn -126 
                         (draw-pentagon length env)))))))
 
(concentric-pentagons 8 10 50 env)

;;----------Koch curve-------------

;; koch: natNum number snapshot --> snapshot
;; draws a koch curve of level levels deep, 
;; a distance of length, based 
;; on the snapshot env. It returns a new snapshot.
(define (koch level length env) 
    (if (zero? level)
        (draw length env)
        (koch (sub1 level) (/ length 3)
              (turn 60
                    (koch (sub1 level) (/ length 3)
                          (turn -120
                                (koch (sub1 level) (/ length 3)
                                      (turn 60
                                            (koch (sub1 level) (/ length 3) env)))))))))

;;testing!
(koch 6 200 env)

;;snowflake: WholeNum number --> snapshot
;;draws a snowflake of the given level and size
(define (snowflake level size)
  (koch level size
        (turn -120
              (koch level size
                    (turn -120
                          (koch level size
                                (turn 180 
                                      (move (/ size 2) 
                                            (turn 180 
                                                  (turtles 
                                                   (* 2 size) 
                                                   (* 2 size)))))))))))

;;testing
(snowflake 3 100)