Sunday, 1 February 2009
Mandlebrot Fractals
The Mandlebrot Set is probably the most famous set of fractals. The maths behind it is dead simple and with just a few lines of code you can get some impressive results.
For any given pixel, you can work out a colour value thus:
(defn process-pixel [x y]
((fn [x y xc yc accum]
(let [x1 (+ (- (* x x) (* y y)) xc)
y1 (+ (* 2 x y) yc)
sq (+ (* x1 x1) (* y1 y1))]
(cond
(> accum *max-iteration*) *max-iteration*
(> sq 2.0) accum
:else (recur x1 y1 xc yc (inc accum))))) x y x y 0))
The harder part is translating a number between 0 and
Source code for version 0.1 is here. Next on the list:
For any given pixel, you can work out a colour value thus:
(defn process-pixel [x y]
((fn [x y xc yc accum]
(let [x1 (+ (- (* x x) (* y y)) xc)
y1 (+ (* 2 x y) yc)
sq (+ (* x1 x1) (* y1 y1))]
(cond
(> accum *max-iteration*) *max-iteration*
(> sq 2.0) accum
:else (recur x1 y1 xc yc (inc accum))))) x y x y 0))
The harder part is translating a number between 0 and
*max-iteration* into a decent range of colours. I'll ignore this for now and stick with green!
Source code for version 0.1 is here. Next on the list:
- Make it look like the Math - write complex number library
- Make it run fast - optimize (uses more cores, minimize type coercions)
- Make it look nice - find a better colour mapping function
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