(import '(javax.swing JFrame JPanel)
'(java.awt Color Dimension Graphics)
'(java.awt.image BufferedImage WritableRaster))
(defn mandelformula [x0 y0 max-iters]
"Applies the mandelbrot formula until max-iters iterations
are reached, or the magnitude of Z exceeds 2"
(let [x0 (double x0)
y0 (double y0)
max-iters (int max-iters)]
(loop [x (double x0)
y (double y0)
n (int 0)]
(if (== n max-iters)
n
(let [mag (+ (* x x) (* y y))]
(if (>= mag (double 4))
n
(let [new-x (+ x0 (- (* x x) (* y y)))
new-y (+ y0 (* (double 2) (* x y)))]
(recur new-x new-y (inc n)))))))))
;; Colours used to draw the set
(def *grad-colour-a* [255, 255, 0]) ;yellow
(def *grad-colour-b* [0, 0, 255]) ;blue
(def *set-colour* [0, 0, 0]) ;black
(defn grad-colour
"Returns the colour that is the given fraction of the way between
the first and second colours given. Returns as a vector of three
integers between 0 and 255."
[colA colB frac]
(vec (map #(+ (* frac (- %2 %1)) %1) colA colB)))
(defn iter-colour
"Returns the colour needed to paint a point with the given number
of iterations"
[num-iters max-iters]
(grad-colour *grad-colour-a* *grad-colour-b*
(/ (double num-iters) max-iters)))
(def iter-colour (memoize iter-colour))
(defn coord-colour
"Returns a colour for which to draw the given coordinate. If the coordinate
is within the mandelbrot set, black is returned. Otherwise, a colour within
a gradient is given based on the number of iterations of the mandelbrot set
that have been evaluated."
[[xcoord ycoord] max-iters]
(let [num-iters (mandelformula xcoord ycoord max-iters)]
(if (= max-iters num-iters)
*set-colour*
(iter-colour num-iters max-iters))))
(defn get-coord
"Returns the coordinates of the given pixel in the complex plane"
[x y xstart ystart xsize ysize width height]
[(+ xstart (* (/ x width) xsize))
(+ ystart (* (/ y height) ysize))])
(defn get-pixels [width height]
"Returns a sequence of vectors representing pixels in a grid of
the given width and height"
(for [y (range height) x (range width)]
[x y]))
(defn render [xstart ystart xsize ysize width height max-iters #^WritableRaster wr]
(doseq [pixel (get-pixels width height)]
(let [[x y] pixel]
(.setPixel wr (int x) (int y)
(int-array
(coord-colour
(get-coord (double x) (double y) xstart ystart xsize ysize width height)
max-iters))))))
(defn get-img [width height]
(BufferedImage. width height (BufferedImage/TYPE_INT_RGB)))
(defn get-panel [width height img]
(proxy [JPanel] [] (paint [g] (.drawImage g img 0 0 (Color/red) nil))))
(defn construct-frame [width height panel]
"Creates and displays a JFrame of the given dimensions with
the panel added to it"
(let [frame (JFrame.)]
(.setPreferredSize panel (Dimension. width height))
(doto frame
(.add panel)
.pack
(.setLocationRelativeTo nil)
.show)))
(defn mandelbrot [xstart ystart xsize ysize width height max-iters]
"Returns a function to render the mandelbrot set with the
given parameters on a frame"
(let [img (get-img width height)
panel (get-panel width height img)
wr (.getRaster img)]
(construct-frame width height panel)
(fn []
(do
(render xstart ystart xsize ysize width height max-iters wr)
(.repaint panel)))))
(def my-mandelbrot (mandelbrot -2 -1.25 3 2.5 600 500 50))
(future (my-mandelbrot))
