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Clojure: ASCII Mandelbrot Set

Did you know there's this neat Lisp message board where from time to time someone posts a short problem similar in spirit to the infamous RubyQuiz?

Not a lot of people have participated so far, hopefully that changes. I participated this time; the problem is to render the Mandelbrot Set in ASCII. Here's my Clojure version (based loosely on this one).

(ns mandelbrot
  (:refer-clojure :exclude [+ * <])
  (:use (clojure.contrib complex-numbers)
        (clojure.contrib.generic [arithmetic :only [+ *]]
                                 [comparison :only [<]]
                                 [math-functions :only [abs]])))

(defn- mandelbrot-seq [x y]
  (let [z (complex x y)]
    (iterate #(+ z (* % %)) z)))

(defn- mandelbrot-char [x y]
  (loop [c 126
         m (mandelbrot-seq x y)]
    (if (and (< (abs (first m)) 2)
             (> c 32))
      (recur (dec c) (rest m))
      (char c))))

(defn- mandelbrot-line [xs y]
  (apply str (map #(mandelbrot-char % y) xs)))

(defn- m-range [min max num-steps]
  (range min
         max
         (/ (+ (abs min)
               (abs max))
            num-steps)))

(defn mandelbrot [rmin rmax imin imax]
  (let [rows 30
        cols 50
        xs (m-range rmin rmax cols)
        ys (m-range imin imax rows)]
    (dorun (map #(println (mandelbrot-line xs %)) ys))))

(comment
  ;Example run:
  (mandelbrot -2.0 1.0 -1.5 1.5)
"
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"
)

And here's some obligatory Jonathan Coulton.

May 12, 2009 @ 11:46 AM PDT
Cateogory: Programming