Racket program to output a mandelbrot fractal

racket_mandelbrot.rkt

#lang racket
(require racket/draw)

(define HEIGHT 200)
(define WIDTH 400)
(define UNIT_PER_PIXEL 0.012)

(define HEIGHT/2 (/ HEIGHT 2))
(define WIDTH/2 (/ WIDTH 2))

(define X_RANGE (in-range 0 WIDTH 1))
(define Y_RANGE (in-range 0 HEIGHT 1))
(define (x-pixel-to-coord x)
  (* (- x WIDTH/2) UNIT_PER_PIXEL))
(define (y-pixel-to-coord y)
  (* (- y HEIGHT/2) UNIT_PER_PIXEL))

(define (f z c) (+ (expt z 2) c))
(define (>2 z) (> (magnitude z) 2))

;(define (converges? c)
;  (let _converges? ([z 0] [c c] [i 30])
;    (cond
;       [(>2 z) #f]
;       [(positive? i) (_converges? (f z c) c (sub1 i))]
;       [(zero? i) (not (>2 z))])))

(define (converges? c [z 0] [i 30])
  (cond
    [(>2 z) #f]
    [(positive? i) (converges? c (f z c) (sub1 i))]
    [(zero? i) (not (>2 z))]))

(define bmp (make-bitmap WIDTH HEIGHT))
(define dc (new bitmap-dc% [bitmap bmp]))

(for ([x X_RANGE])
  (for ([y Y_RANGE])
    (let ([complex (make-rectangular (x-pixel-to-coord x) (y-pixel-to-coord y))])
      (when (converges? complex)
          (send dc set-pixel x y (make-color 10 10 10))))))

bmp
(send bmp save-file "mandelbrot.png" 'png)