[plt-scheme] Fractals

From: Ahmad Issa (ahmadissa at gmail.com)
Date: Wed Sep 20 07:32:34 EDT 2006

Hi, I decided to make a (toy) fractals program. MzScheme (or PLT-Scheme in
general) has a reasonable advantage in being able to handle complex numbers
so well. However, I unfortunately could not get the code running fast
enough. I understand Scheme's more of a scripting language and is probably
not the best decision when it comes to number crushing, but i would
appreciate any way to get this running faster!

Here's the code:

;;;; General fractal generator, Mandelbrot Set example

(require (lib "etc.ss"))

;; This function takes a function trans which it uses to create
;; another function which, given a point in the complex plane,
;; returns the number of iterations until the point diverges
(define (pix-gen trans upper max-it)
    (define max-iterations max-it)
    (lambda (point)
        (define (strength)
            (let next ((new-point point) (iter 0))
                (cond ((>= (magnitude new-point) upper) iter)
                        ((>= iter max-it) iter)
                        (else (next (trans new-point) (+ iter 1))))))
        ;; if the value of (strength) belongs to the set,
        ;; return black (zero)
        (let ((val (strength)))
            (cond ((= val max-iterations) 0)
                  (else val)))))

(define (gen-fract gen x-start x-end y-start y-end x-steps y-steps)
    ; this part calculates the step on each iteration
    (define x-int (/ (- x-end x-start) (sub1 x-steps)))
    (define y-int (/ (- y-end y-start) (sub1 y-steps)))
    ; build a vector of number of iterations to diverge
    (build-vector x-steps
                  (lambda (m)
                      (build-vector y-steps
                                    (lambda (n)
                                        (gen (make-rectangular (* m x-int)
(* n y-int))))))))

;; here's a sample that creates a mandelbrot function,
;; which a maximum depth of 255, and a critical value of 2
;; note: I eventually will want the depth > 1000
(define mand (pix-gen (lambda (x) (* x x)) 2 255))

;; test this out!
(time (printf "~a~n" (gen-fract mand 0.0 1.0 0.0 1.0 30 30)))
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