More Clojure Mandelbrot Goodness

Wed, 20 May 2009 23:39:23 -0700

After my brief stint in the world of fractal geometry and Clojure, I decided to make a real Mandelbrot set viewer. The resulting source code is here. Here's a simple output (click for bigger version):

It's a pretty naive implementation, barely 100 lines of code, but even with my brute-force approach, given a liberal sprinkling of type hints it runs fast enough. Programming Swing from Clojure couldn't be easier (though I doubt programming Swing from any language is ever really enjoyable, it's a painful bunch of libraries).

There's a discussion of different coloring algorithms on Wikipedia, but even after reading that, getting this thing to look good was difficult. I don't know enough math for it. I ended up cheating and I colored a couple of them in the GIMP, so I could use them as desktop wallpapers.

There are some more PNGS over here including one that's 16000x16000 (producing it almost melted my CPU last night).

Clojure: ASCII Mandelbrot Set

Tue, 12 May 2009 18:46:01 -0700

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)
"
~~~~~~~~~~~~}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
~~~~~~~~~~~~}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
~~~~~~~~~~}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
~~~~~~~~~}}}}}}}}}}}}|||||||||}}}}}}}}}}}}}}}}}}}}
~~~~~~~}}}}}}}}|||||||||||||||||||||}}}}}}}}}}}}}}
~~~~~~}}}}}||||||||||||||{{{{zlxz{{{||||}}}}}}}}}}
~~~~~}}}}|||||||||||||{{{{{zzyxpvlz{{{||||}}}}}}}}
~~~~}}}|||||||||||||{{{{{{zzyxvnpwyzz{{{||||}}}}}}
~~~}}|||||||||||||{{{{{{zzyyws   .vyzzz{{|||||}}}}
~~~}||||||||||||{{{{{zzxwwwvus   muvxyywz{|||||}}}
~~}|||||||||||{{{zzzzyyu= p         oteqpz{|||||}}
~~||||||||||{zzzzzzyyyvtm              oxz{{|||||}
~}|||||{{{zyvwxxxxxxxwrG                vuz{|||||}
~||{{{{{zzzywsMsqRovvs                  pxz{{|||||
~|{{{{{zzzyxsq      pj                  `xz{{|||||
~{{{{yyyxwsrp                           wyz{{|||||
~?:3 3 #                              ovxzz{{|||||
~{{{{yyyxwsrp                           wyz{{|||||
~|{{{{{zzzyxsq      pj                  `xz{{|||||
~||{{{{{zzzywsMsqRovvs                  pxz{{|||||
~}|||||{{{zyvwxxxxxxxwrG                vuz{|||||}
~~||||||||||{zzzzzzyyyvtm              oxz{{|||||}
~~}|||||||||||{{{zzzzyyu= p         oteqpz{|||||}}
~~~}||||||||||||{{{{{zzxwwwvus   muvxyywz{|||||}}}
~~~}}|||||||||||||{{{{{{zzyyws   .vyzzz{{|||||}}}}
~~~~}}}|||||||||||||{{{{{{zzyxvnpwyzz{{{||||}}}}}}
~~~~~}}}}|||||||||||||{{{{{zzyxpvlz{{{||||}}}}}}}}
~~~~~~}}}}}||||||||||||||{{{{zlxz{{{||||}}}}}}}}}}
~~~~~~~}}}}}}}}|||||||||||||||||||||}}}}}}}}}}}}}}
~~~~~~~~~}}}}}}}}}}}}|||||||||}}}}}}}}}}}}}}}}}}}}
~~~~~~~~~~}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}}
"
)

And here's some obligatory Jonathan Coulton.

briancarper.net Tag: Mandelbrot

More Clojure Mandelbrot Goodness

Clojure: ASCII Mandelbrot Set