added a very fast haskell version

haskell/flame.hs

@@ -0,0 +1,159 @@
+module Main where
+
+import Data.HashMap as Dict
+import Data.Maybe   as Maybe
+
+import Control.Monad
+import System.Environment (getArgs)
+data Global = Global { imgWidth  :: Int
+                     , imgHeight :: Int
+                     , nbPoints  :: Int }
+
+-- Basic functions
+
+-- -- nth element of a list
+-- l !! n = if n == 0 then head l else (tail l) !! (n-1)
+-- negative of a number (I don't like writing 0-x).
+neg x = 0-x
+
+rgb :: Int -> Int -> Int -> (Int,Int,Int)
+rgb = (,,)
+rgba = (,,,)
+-- Colors (theme is solarized)
+base03  = rgb 0   43  54
+base02  = rgb 7   54  66
+base01  = rgb 88  110 117
+base00  = rgb 101 123 131
+base0   = rgb 131 148 150
+base1   = rgb 147 161 161
+base2   = rgb 238 232 213
+base3   = rgb 253 246 227
+yellow  = rgb 181 137 0
+orange  = rgb 203 75  22
+red     = rgb 220 50  47
+magenta = rgb 211 54  130
+violet  = rgb 108 113 196
+blue    = rgb 38  139 210
+cyan    = rgb 42  161 152
+green   = rgb 133 153 0
+
+-- Default text color
+mybase = rgba 108 113 196 (2/3)
+
+-- RANDOM PART
+nextint n =
+    let
+      a = 22695477
+      c = 1
+      m = 2^32
+    in
+     (a*n + c) `rem` m
+
+-- generate a random sequence of length k starting with some seed
+randlist seed k = if (k<0) then [] else (nextint seed):randlist (nextint seed) (k-1)
+
+-- generate a random sequence of points of length k starting with some seed
+randcouples seed k = if (k<0) then []
+                     else
+                       let ns = nextint seed
+                           nns = nextint ns
+                       in (ns,nns):randcouples nns (k-1)
+-- END OF PSEUDO RANDOM NUMBER GENERATION
+
+
+{-
+ - Flame Set
+ -
+ - S = U_{i} F_i(S)
+ -
+ - F_i being transformations
+ - General form:
+ -   F = affine .  linearcomp [variation] . affine
+ -   affine is a linear function (x,y) -> (ax+by+c,dx+ey+f)
+ -   variation is some kind of function with some contraction properties
+        ex: (x,y) -> (x,y), (sin x, sin y), etc...
+ -   linearcomp [f] is a linear composition of functions: (x,y) -> Sum vi*f(x,y)
+-}
+
+data Matrice = M Float Float Float Float Float Float
+aff (M a b c d e f) (x,y) = (a*x + b*y + c, d*x + e*y +f)
+
+-- Some affine functions to generate the sierpinsky set
+-- Equivalent to
+-- sierp = [ \(x,y)->(x/2,y/2)
+--         , \(x,y)->((x+1)/2,y/2)
+--         , \(x,y)->(x/2,(y+1)/2) ]
+sierp = [ aff $ M
+          0.5  0.0  0.0
+          0.0  0.5  0.0
+        , aff $ M
+          0.5  0.0  0.5
+          0.0  0.5  0.0
+        , aff $ M
+          0.5  0.0  0.0
+          0.0  0.5  0.5
+        ]
+
+-- Some variations
+vs = [ \(x,y) -> (x,y)
+     , \(x,y) -> (sin x, sin y)
+     , \(x,y) -> let r2 = x*x+y*y in (x/r2,y/r2)
+     , \(x,y) -> let r2 = x*x+y*y in (x*(sin r2) - y*(cos r2),x*(cos r2) + y * (sin r2))
+     , \(x,y) -> let r = sqrt (x^2+y^2) in ((x - y)*(x + y)/r,2*x*y/r)
+     ]
+
+-- Some final functions
+fs = [ (vs !! 3) . (sierp !! 0)
+     , (vs !! 3) . (sierp !! 1)
+     , (vs !! 3) . (sierp !! 2)]
+
+-- Transformation functions
+-- translate
+trans (tx,ty) = aff $ M 1 0 tx 0 1 ty
+-- rotate
+rot phi = aff $ M (cos phi) (sin phi) 0.0 (neg (sin phi)) (cos phi) 0.0
+-- zoom
+zoom z = aff $ M z 0 0 0 z 0
+
+-- The final transformation to transform the final result (zoom,rotate,translate)
+final = trans (280,200) . zoom 300 . rot (neg 0.747)
+
+sierpset startpoint rands tmpres =
+  if rands == []
+    then tmpres
+    else
+      let
+        roundPoint (x,y) = (round x,round y)
+        randval=(head rands) `rem` (length fs)
+        newpoint = (fs !! randval) startpoint
+        savepoint = roundPoint ( final newpoint )
+        oldvalue = Dict.lookup savepoint tmpres
+        newvalue = 1 + (Maybe.fromMaybe 0 oldvalue)
+        newtmpres = Dict.insert savepoint newvalue tmpres
+      in
+        sierpset newpoint (tail rands) newtmpres
+
+sierpinsky n = sierpset (0.0,0.0) (randlist 0 n) Dict.empty
+
+scene env =
+  let
+    w = imgWidth  env
+    h = imgHeight env
+    n = nbPoints  env
+    inpoint ((x,y),_) = x>=0 && x<=w && y>=0 && y<=h
+  in (Prelude.filter inpoint) . Dict.toList $ (sierpinsky n)
+
+
+initGlobalParams args =
+  Global { imgWidth  = read (args !! 0)
+         , imgHeight = read (args !! 1)
+         , nbPoints  = read (args !! 2) }
+
+main :: IO ()
+main = do
+  args <- getArgs
+  if (length args<3)
+    then print $ "Usage flame w h n"
+    else do 
+      env  <- return (initGlobalParams args)
+      mapM_ (print) (scene env)