{-
Red spiral by Michal Kot.

compile and run. result image will be saved as red.ppm and can be opened using a default image browser. (in windows, use IrfanView or similar)
please note that it could take about 30sec or longer depending on speed
-}
--draw function calculates values for each pixel
draw fx tx fy ty s iter = rows s s
    where
    rows y x | x == 0             = rows (y-1) s
    rows y x | y == 0             = []
    rows y x | (x > 0) && (y > 0) = iteration (fx+(x*cx)) (fy+(y*cy)) iter : rows y (x-1)
    cx = (tx-fx)/s
    cy = (ty-fy)/s
--creates a ppm file
ppm s cs = "P3\n" ++ show s ++ " " ++ show s ++ "\n255\n" ++ (f cs)
    where
    f []     = ""
    f (x:xs) = c (mod x 1000) 1000 ++ "\n" ++ f xs
--depending on interation, choose a color
c x max = fg (round ((1023/fromIntegral max) * fromIntegral x))
    where
    fg n | n < 256  = show n ++ " 0 0"
    fg n | n < 512  = "255 " ++ show (n-256) ++ " 0"
    fg n | n < 768  = "0 " ++ show (767-n) ++ " " ++ show (n-512)
    fg n | n < 1024 =  "0 0 " ++ show (1023-n)
--most important function that calculates values for each point. it is amazing how simply it could be implemented in haskell
iteration :: Double -> Double -> Int -> Int
iteration x0 y0 iter = loop x0 y0 0
    where
    loop x y i | ((x*x)+(y*y)) >4 = i
    loop x y i | i == iter        = 0
    loop x y i | otherwise        = loop (x*x - y*y + x0) (2*x*y + y0) (i+1)
--main: calculate all pixels, create ppm file and save
main = writeFile "red.ppm" (ppm 1000 (draw (-0.338533147167322) (-0.335124997593271) (-0.641201519795881) (-0.63736432972578) 1000 1000))