turtle

;;Lecture 10

;;3
(defun print-fact (x)
    (terpri)
  (princ "print-fact applied at ")
  (princ x)
  (let ((prev (if (= x 0) 1 (* x (print-fact (- x 1))))))
    (terpri)
    (princ "print-fact returns ")
    (princ prev)
    ))

;;4
(defun prints-fact (x)
  (labels ((fact (x depth)
             (terpri)
             (indent depth)
             (princ "prints-fact applied at ")
             (princ x)
             (let ((prev (if (= x 0)
                             1
                           (* x (fact (- x 1) (1+ depth))))))
               (terpri)
               (indent depth)
               (princ "prints-fact returns ")
               (princ prev))
             )
           (indent (x)
             (if (<= x 0)
                 0
               (progn (princ " ") (indent (- x 1))))
             ))
    (fact x 0)
    ))

;;5

(defun tri-fract (length)
  (labels ((step (length) (progn
                            (ngon length 4)
                            (turtle:move (/ length 2))
                            (turtle:turn pi/4)
                            (if (> length 1) (step (sqrt (* 2 (expt (/ length 2) 2)))) 0)
                            )))
    (step length)))


(defun ngon (length n)
  (labels ((draw (prev) (progn
                          (turtle:draw length)
                          (turtle:turn (* (/ 360 n) (/ pi 180)))
                          (if (< prev (- n 1)) (draw (1+ prev)) 0)
                          )))
    (draw 0)
    ))


(defun clear () (turtle:clear))



(defun sqr-fract (length)
    (labels ((step (length) (progn
                            (ngon length 4)
                            (turtle:move (* length 0.1))
                            (turtle:turn (/ pi 32))
                            (if (> length 1) (step (* length 0.88)) 0)
                            )))
    (step length)))


(defun leaf (length)
  (if (> length 1) (progn
                     (turtle:draw length)
                     (turtle:excursion
                       (turtle:turn (/ pi 6))
                       (leaf (* length 0.4))
                       )
                     (turtle:excursion
                       (turtle:turn (* -1 (/ pi 6)))
                       (leaf (* length 0.4))
                       )
                     (turtle:turn (/ pi 24))
                     (leaf (* length 0.7))
                     0
                     )
    0
    ))

;;6
(defun draw-bt (tree length)
  (if (not (null tree)) (progn
                          (if (not (null (cdr tree))) (turtle:excursion (turtle:turn (/ pi 3)) (turtle:draw length) (turtle:turn (* -1 (/ pi 3))) (draw-bt (cadr tree) (/ length 2))))
                          (if (not (null (cddr tree))) (turtle:excursion (turtle:turn (* -1 (/ pi 3))) (turtle:draw length) (turtle:turn (/ pi 3)) (draw-bt (caddr tree) (/ length 2))))
                          0)
    0))