;;; Scheme Recursive Art Contest Entry
;;;
;;; Please do not include your name or personal info in this file.
;;;
;;; Title: <"Thallsophobia">
;;;
;;; Description:
;;;   <'Sea's darkest abyss/ You are a lifetime ago/ This a conclusion>



; TURTLE MOVEMENT
(define (move-right x)
	(setheading 90)
	(forward x))

; USEFUL PROCEDURES
(define (at_index s i)
	(if (= i 0)
		(car s)
		(at_index (cdr s) (- i 1))
	)
)

(define (len s)
	(define (helper s i)
		(if (null? s)
			i
			(helper (cdr s) (+ i 1))
		)
	)
	(helper s 0)
)




; ==== Variables ====
(define window_width (/ (screen_width) 1)) ;so they can be treated as variables instead of calling the functions everytime
(define window_height (/ (screen_height) 1))

(define c1 0)
(define c2 0.8)
;input the real and imaginary parts for the complex constant c in the recurrence relation.

(define (f x y c1 c2)
  (cons (+ (- (* x x) (* y y)) c1) (+ (* 2 x y) c2))
)
;Specify the function f for which the julia set is computed
;Outputs a pair with first element the real part of the image and the secnd element the complex part.


(define (escape_depth px py)
	(define x_normalization 1)
	(define y_normalization 1)

	(define x_scaled (- (/
			(*	(- 1 (- x_normalization))
				(- px (/ (- window_width) 2)))
			(-	(/ window_width 2)
				(/ (- window_width) 2))
		) x_normalization)) ; x coordinates normalized to julia set domain

	(define y_scaled (- (/
			(*	(- 1 (- y_normalization))
				(- py (/ (- window_height) 2)))
			(-	(/ window_height 2)
				(/ (- window_height) 2))
		) y_normalization)) ; y coordinates normalized to julia set domain


  (define (filled-julia depth max-depth x y)
  (cond
    ((and (< depth max-depth) (< [+ (* x x) (* y y)] 4))
      (define x-new (car (f x y c1 c2)))
      (define y-new (cdr (f x y c1 c2)))

      (filled-julia (+ depth 1) max-depth x-new y-new)
    )
      (else depth)
    )
  )

	(filled-julia 0 2500 x_scaled y_scaled)
  ;Run for 2500 iterations
)

(define (depth_row x y)
	(define (iterator i window_width row x)
		(cond ((< i window_width)
				(define row (append row (list (escape_depth x y))))
				(iterator (+ i 1) window_width row (+ x 1))
			)
			(else row)
		)
	)

	(iterator 0 window_width '() x)
)

(define (render-julia)
	(define x_0 (/ (- window_width) 2))
	(define y_0 (/ window_height 2))
	(define x x_0)
	(define y y_0)

	(define (iteratorator y y_0)
		(cond
			((> y (- y_0))
				(define row (depth_row x y))

				(define (iterator_2 i palette)
					(cond ((< i (len row))
							(define j i)
							(define (iterator_3 j)
								(if (and [< j (len row)] [= (at_index row j) (at_index row i)])
									(iterator_3 (+ j 1))
									j
								)
							)
							(define j (iterator_3 j))
							(define palette (append palette [list (list (at_index row i) (- j i))]))
							(if (> j i)
								(define i j)
								(define i (+ i 1))
							)
							(iterator_2 i palette)
						)
						(else palette)
					)
				)
				(define palette (iterator_2 0 '()))

				(define (for_iter i palette)
					(cond
						((< i (len palette))
							(define offset
								(* 255
									(- 1
										(/
											(log (+ [* (/ [at_index (at_index palette i) 0] 100) 150] 1))
											(log 256)
										)
									)
								)
							)
							(define offset (quotient offset 1)) ; truncation
							(define r (- 255 offset))
							(cond ((> r 255)
									(define r 230)
									(define g 230)
									(define b 230)
								)
								(else
									(define r 0)
									(define g 0)
									(define b (- 255 offset))
								)
							)
							(color (rgb (/ r 255) (/ g 255) (/ b 255)))
							(pendown)
							(move-right (at_index (at_index palette i) 1))
							(penup)
							(for_iter (+ i 1) palette)
						)
						(else nil)
					)
				)

				(for_iter 0 palette)

				(define y (- y 1))
				(setposition x y)
				(iterator y y_0)
			)
		)
		(else nil)
	)

	(iterator y y_0)
)

(speed 0)
(penup)
(setposition (/ (- window_width) 2) (/ window_height 2))
(pendown)

(define (draw)
	(render-julia)
	(setposition (/ window_width 13) (/ window_height 45))
	(addshape)
	(shape)
	(stamp)
  (exitonclick))

; Please leave this last line alone.  You may add additional procedures above
; this line.
(draw)