fast implementation
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haskell/flame-img.hs
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haskell/flame-img.hs
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module Main where
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import Data.HashMap as Dict -- cabal install HashMap
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import Data.Maybe as Maybe
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import Data.Word (Word8)
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import Codec.Picture -- cabal install juicyPixels FTW
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import Control.Monad
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import System.Environment (getArgs)
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data Global = Global { imgWidth :: Int
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, imgHeight :: Int
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, nbPoints :: Int }
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type YMap = Map (Int,Int) Int
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-- Basic functions
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-- -- nth element of a list
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-- l !! n = if n == 0 then head l else (tail l) !! (n-1)
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-- negative of a number (I don't like writing 0-x).
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neg x = 0-x
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rgb :: Int -> Int -> Int -> (Int,Int,Int)
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rgb = (,,)
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rgba = (,,,)
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-- Colors (theme is solarized)
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base03 = rgb 0 43 54
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base02 = rgb 7 54 66
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base01 = rgb 88 110 117
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base00 = rgb 101 123 131
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base0 = rgb 131 148 150
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base1 = rgb 147 161 161
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base2 = rgb 238 232 213
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base3 = rgb 253 246 227
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yellow = rgb 181 137 0
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orange = rgb 203 75 22
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red = rgb 220 50 47
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magenta = rgb 211 54 130
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violet = rgb 108 113 196
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blue = rgb 38 139 210
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cyan = rgb 42 161 152
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green = rgb 133 153 0
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-- Default text color
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mybase = rgba 108 113 196 (2/3)
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-- RANDOM PART
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nextint n =
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let
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a = 22695477
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c = 1
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m = 2^32
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in
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(a*n + c) `rem` m
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-- generate a random sequence of length k starting with some seed
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randlist seed k = if (k<0) then [] else (nextint seed):randlist (nextint seed) (k-1)
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-- generate a random sequence of points of length k starting with some seed
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randcouples seed k = if (k<0) then []
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else
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let ns = nextint seed
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nns = nextint ns
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in (ns,nns):randcouples nns (k-1)
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-- END OF PSEUDO RANDOM NUMBER GENERATION
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{-
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- Flame Set
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-
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- S = U_{i} F_i(S)
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-
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- F_i being transformations
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- General form:
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- F = affine . linearcomp [variation] . affine
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- affine is a linear function (x,y) -> (ax+by+c,dx+ey+f)
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- variation is some kind of function with some contraction properties
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ex: (x,y) -> (x,y), (sin x, sin y), etc...
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- linearcomp [f] is a linear composition of functions: (x,y) -> Sum vi*f(x,y)
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-}
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data Matrice = M Float Float Float Float Float Float
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aff (M a b c d e f) (x,y) = (a*x + b*y + c, d*x + e*y +f)
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-- Some affine functions to generate the sierpinsky set
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-- Equivalent to
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-- sierp = [ \(x,y)->(x/2,y/2)
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-- , \(x,y)->((x+1)/2,y/2)
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-- , \(x,y)->(x/2,(y+1)/2) ]
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sierp = [ aff $ M
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0.5 0.0 0.0
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0.0 0.5 0.0
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, aff $ M
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0.5 0.0 0.5
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0.0 0.5 0.0
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, aff $ M
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0.5 0.0 0.0
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0.0 0.5 0.5
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]
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-- Some variations
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vs = [ \(x,y) -> (x,y)
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, \(x,y) -> (sin x, sin y)
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, \(x,y) -> let r2 = x*x+y*y in (x/r2,y/r2)
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, \(x,y) -> let r2 = x*x+y*y in (x*(sin r2) - y*(cos r2),x*(cos r2) + y * (sin r2))
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, \(x,y) -> let r = sqrt (x^2+y^2) in ((x - y)*(x + y)/r,2*x*y/r)
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]
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-- Some final functions
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fs :: [(Float,Float) -> (Float,Float)]
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fs = [ (vs !! 3) . (sierp !! 0)
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, (vs !! 3) . (sierp !! 1)
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, (vs !! 3) . (sierp !! 2)]
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-- Transformation functions
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-- translate
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trans (tx,ty) = aff $ M 1 0 tx 0 1 ty
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-- rotate
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rot phi = aff $ M (cos phi) (sin phi) 0.0 (neg (sin phi)) (cos phi) 0.0
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-- zoom
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zoom z = aff $ M z 0 0 0 z 0
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-- The final transformation to transform the final result (zoom,rotate,translate)
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final = trans (280,200) . zoom 300 . rot (neg 0.747)
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sierpset :: (Float,Float) -> [Int] -> YMap -> YMap
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sierpset startpoint rands tmpres =
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if rands == []
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then tmpres
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else
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let
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roundPoint (x,y) = (round x,round y)
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randval=(head rands) `rem` (length fs)
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newpoint = (fs !! randval) startpoint
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savepoint = roundPoint ( final newpoint )
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oldvalue = Dict.lookup savepoint tmpres
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newvalue = 1 + (Maybe.fromMaybe 0 oldvalue)
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newtmpres = savepoint `seq` newvalue `seq` Dict.insert savepoint newvalue tmpres
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in
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sierpset newpoint (tail rands) newtmpres
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sierpinsky :: Int -> YMap
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sierpinsky n = sierpset (0.0,0.0) (randlist 0 n) Dict.empty
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scene env =
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let
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w = imgWidth env
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h = imgHeight env
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n = nbPoints env
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inpoint ((x,y),_) = x>=0 && x<=w && y>=0 && y<=h
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in (Prelude.filter inpoint) . Dict.toList $ (sierpinsky n)
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initGlobalParams args =
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Global { imgWidth = read (args !! 0)
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, imgHeight = read (args !! 1)
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, nbPoints = read (args !! 2) }
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imageFromDict :: YMap -> Int -> Int -> Image PixelRGB8
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imageFromDict dict width height = generateImage colorOfPoint width height
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where
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maxnb :: Int
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maxnb = Dict.fold max 0 dict
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colorOfPoint :: Int -> Int -> PixelRGB8
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colorOfPoint x y = let nb = fromMaybe 0 (Dict.lookup (x,y) dict)
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val :: Word8
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val = fromIntegral $ div (255*nb) maxnb
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in if nb == 0 then PixelRGB8 0 0 0
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else PixelRGB8 val val val
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writeImage :: Int -> Int -> Int -> YMap -> IO ()
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writeImage w h n dict = writePng "flame.png" $ imageFromDict dict w h
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main :: IO ()
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main = do
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args <- getArgs
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if (length args<3)
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then print $ "Usage flame w h n"
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else do
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env <- return (initGlobalParams args)
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w <- return (imgWidth env)
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h <- return (imgHeight env)
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n <- return (nbPoints env)
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-- mapM_ (print) (scene env)
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writeImage w h n (sierpinsky n)
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