Created
October 29, 2012 11:10
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Complex Field Visualisation
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{-# LANGUAGE BangPatterns #-} | |
-- Preview on Youtube: http://www.youtube.com/watch?v=bK01Bgh32Sc | |
import Data.Complex | |
type C = Complex Float | |
type Color = (Float,Float,Float) | |
type Point = (Float,Float) | |
main :: IO () | |
main = flip mapM_ [0 :: Float, 0.1 .. 5] $ \t -> do -- 125 = 1 period | |
print t | |
let output = renderer (2000,1000) (-1.2,-1.5) (0.5,0.6) function t | |
writeFile ("temp/field/testimage_" ++ show t ++ ".ppm") output | |
function :: Float -> Point -> Color | |
function !t' !(x',y') = c2c $ n $ tc ** pc | |
where | |
pc = x :+ y | |
tc = 8 * (n $ t ** x :+ (y - t)) | |
x = x' + 0.6 | |
y = y' + 0.3 | |
t = 40 * (sin (t'/20) + 1) | |
c2c :: Complex Float -> Color | |
c2c !p@(r :+ i) = (r, i, (magnitude p)) | |
n :: C -> C | |
n !(x :+ y) = nf sin x :+ nf cos y | |
nf :: Fractional a => (t -> a) -> t -> a | |
nf !fun !x = (fun x + 1) / 2 | |
-- ppm | |
renderer :: (Int, Int) -> (Float, Float) -> (Float, Float) -> (Float -> Point -> Color) -> Float -> String | |
renderer !size !lowbound !highbound !fun !time = header size body | |
where | |
xs = steps (fst lowbound) (fst highbound) (fst size) | |
ys = steps (snd lowbound) (snd highbound) (snd size) | |
body = unlines $ map line ys | |
line y = decolor . point fun time y =<< xs | |
header :: (Show a, Show a1) => (a, a1) -> [Char] -> [Char] | |
header !(w,h) x = "P3\n" ++ show w ++ " " ++ show h ++ "\n255\n" ++ x | |
steps :: Float -> Float -> Int -> [Float] | |
steps !l !h !p = take p [l, l + (h - l) / fromIntegral p .. h] | |
point :: (t1 -> (t2, t3) -> t) -> t1 -> t3 -> t2 -> t | |
point !f !t !y !x = f t (x,y) | |
decolor :: Color -> String | |
decolor !(r,g,b) = ' ' : unwords [sf r, sf g, sf b] | |
-- The mod here is intentional, as part of the cool look comes from overflowing the bounds of the color values. | |
sf :: Float -> String | |
sf = (show :: Int -> String) . flip mod 255 . floor . (*255) |
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Here is an example image generated by this code: