mandel_timing.java

 // Do note that the following java code takes about 8-15 microseconds also

 public class Timing {
    public static void main(String[] Args) {
       for(int i = 0; i < 10000; i++){ // warmup
         thing();
       }
       long start_time = System.nanoTime();
       thing();
       System.out.println(System.nanoTime() - start_time); // tends to print out 8000-15000 which is 8-15 microseconds
    }
 
    public static long thing(){
       double zre = 0;
       double zim = 0;
       double cre = -1.08;
       double cim = 0.07;
       double new_zre = 0;
       double new_zim = 0;
 
       long dwell = 2001;
 
       for(long i = 0; i < 2000; i++){ // this is not an attempt at calculating the its, just make the formula run 2000 times
         if(zre*zre + zim*zim > 4.0 || i == dwell) {
             break;
         } else {
             new_zre = zre*zre - zim*zim + cre;
             new_zim = 2.0*zre*zim + cim;
             zre = new_zre;
             zim = new_zim;
             i = i;
             dwell = dwell;
         }
       }
       return 2000;
    }
 }

mandelbrot_final.clj

;; Winner winner, chicken dinner.  This calcs (mandel (complex. 0 0) 2000) in 15 μs after warmup

(deftype complex [^double real ^double imag])

(defn plus
  "(a + bi) + (c + di) == (a + b) + (c + d)i"
  [^complex z1 ^complex z2]
  (complex. (+ (.real z1) (.real z2)) (+ (.imag z1) (.imag z2))))

(defn magnitude-squared
  "|z|^2 == a^2 + b^2"
  [^complex z]
  (+ (* (.real z) (.real z)) (* (.imag z) (.imag z))))

(defn times
  "(a + bi)*(c + di) == (ac - bd) + (ad + bc)i"
  [^complex z1 ^complex z2]
  (complex.
    (- (* (.real z1) (.real z2)) (* (.imag z1) (.imag z2)))
    (+ (* (.real z1) (.imag z2)) (* (.imag z1) (.real z2)))))

(defn mandel
  "Calculates the number of iterations taken to escape, up to a bailout
  (mandel (complex. 0 0) 100) => 100 since [0,0] is in the set"
  ([^complex c ^long dwell]
    (mandel (complex. 0 0) c 0 dwell))
  ([z c ^long its ^long dwell]
    (if (or (> (magnitude-squared z) 4.0) (= its dwell))
      its
      (recur (plus (times z z) c) c (inc its) dwell))))