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Clojure Programming, Chapter 11

Visualizing the Mandelbrot Set in Clojure

This project contains a Mandelbrot Set implementation in Clojure that demonstrates the usage and impact of primitive type declarations on the runtime of numerically-intensive algorithms.


A canonical rendering of the Mandelbrot Set can be obtained by running the -main entry point in the com.clojurebook.mandelbrot namespace using Leiningen:

$ lein run mandelbrot.png -2.25 0.75 -1.5 1.5 :width 800 :height 800 

After running this, you'll see this in mandelbrot.png:

The run arguments correspond exactly to those required by com.clojurebook.mandelbrot/mandelbrot.

You can change the view you get by modifying the coordinates provided to that function:

$ lein run mandelbrot-zoomed.png -1.5 -1.3 -0.1 0.1 :width 800 :height 800

Of course, if you're going to do a bunch of exploration of the Mandelbrot Set using this implementation, you'll be way better off working from the REPL rather than paying the JVM and Leiningen startup cost repeatedly. Refer to the book or the sources here for REPL-oriented examples.

Optimization via primitive type declarations

A nearly order-of-magnitude improvement in the running time of com.clojurebook.mandelbrot/mandelbrot can be had by replacing its helper escape function with this implementation:

(defn- fast-escape
  [^double a0 ^double b0 depth]
  (loop [a a0
         b b0
         iteration 0]
      (< 4 (+ (* a a) (* b b))) iteration
      (>= iteration depth) -1
      :else (recur (+ a0 (- (* a a) (* b b)))
                   (+ b0 (* 2 (* a b)))
                   (inc iteration)))))

Aside from the ^double type declarations for the a0 and b0 arguments, this implemenation is otherwise unchanged compared to the default (boxing) escape function.

An alternative lein run alias — called :fast — is set up to use fast-escape:

$ lein run :fast mandelbrot.png -2.25 0.75 -1.5 1.5 :width 800 :height 800 

The above will run far faster than the first lein run invocation above.