(define triangle-box! 
  (lambda (image number side starth startv startcolor endcolor) 
    (let ((palette (make-vector number "BALLS")) 
          (tommy (turtle-new image))) 
      (turtle-teleport! tommy starth startv) 
      (let make-palette ((index1 0)) 
        (if (< index1 number) 
            (begin 
              (vector-set! palette index1 (rgb-new (/ (+ (* (- number index1) (rgb-red startcolor)) (* index1 (rgb-red endcolor))) number)
                                                   
                                                   (/ (+ (* (- number index1) (rgb-green startcolor)) (* index1 (rgb-green endcolor))) number)
                                                   
                                                   (/ (+ (* (- number index1) (rgb-blue startcolor)) (* index1 (rgb-blue endcolor))) number)))
              
              (make-palette (+ 1 index1))))) 
      (let draw-squares ((index2 0) 
                         (sidelength side)) 
        (if (< index2 number) 
            (begin 
              (turtle-set-color! tommy (vector-ref palette index2)) 
              (turtle-forward! tommy sidelength) 
              (turtle-turn! tommy 90) 
              (turtle-forward! tommy sidelength) 
              (turtle-turn! tommy 90) 
              (turtle-forward! tommy sidelength) 
              (turtle-turn! tommy 90) 
              (turtle-forward! tommy sidelength) 
              (turtle-turn! tommy 90) 
              (turtle-forward! tommy (/ sidelength 2)) 
              (turtle-turn! tommy 45) 
              (draw-squares (+ 1 index2) (* sidelength 0.7071067812))))))))

(define canvas (image-new 200 200))

(define prime? 
  (lambda (number) 
    (let kernel ((index 2)) 
      (if (<= index (sqrt number)) 
          (if (int? (/ number index)) #f (kernel (+ 1 index))) 
          #t))))

(define factorthis 
  (lambda (number) 
    (let listmaker ((index 1) 
                    (vectorlist null)) 
      (if (< index number) 
          (if (int? (/ number index)) 
              (listmaker (+ 1 index) (cons index vectorlist)) 
              (listmaker (+ 1 index) vectorlist)) 
          (list->vector (cons number vectorlist))))))

(define exp2 
  (lambda (base power) 
    (exp (* (log base) power))))

(define rgb-mod-new 
  (lambda (number modi) 
    (cond 
      ((<= number (/ modi 3)) 
       (rgb-new (* (/ 255 (/ modi 3)) (- (/ modi 3) number)) 
                (* (/ 255 (/ modi 3)) number) 
                0)) 
      ((<= number (* 2 (/ modi 3))) 
       (rgb-new 0 
                (* (/ 255 (/ modi 3)) (- (* 2 (/ modi 3)) number)) 
                (* (/ 255 (/ modi 3)) (- number (/ modi 3))))) 
      ((<= number modi) 
       (rgb-new (* (/ 255 (/ modi 3)) (- number (* 2 (/ modi 3)))) 
                0 
                (* (/ 255 (/ modi 3)) (- modi number)))))))



(define image-series 
  (lambda (n width height) 
    (let* ((img (image-new width height)) 
           (factorvector (factorthis n)) 
           (factorslength (vector-length factorvector))) 
      (image-show img) 
      (let kernel ((index 0)) 
        (if (< index factorslength) 
            (begin 
              (triangle-box! img 
                             5 
                             (* (vector-ref factorvector index) (/ height 1000)) 
                             (* (/ height 1000) (vector-ref factorvector index)) 
                             (* (/ height 1000) (vector-ref factorvector (- (- factorslength index) 1))) 
                             (rgb-mod-new (vector-ref factorvector index) n) 
                             (rgb-mod-new (vector-ref factorvector (- (- factorslength index) 1)) n)) 
              (kernel (+ 1 index))))))))