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<title>Mandelbrot avec haskell</title>
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<a href="/Scratch/en/blog/Haskell-Mandelbrot/" onclick="setLanguage('en')">in English</a>
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<h1>
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Mandelbrot avec haskell
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</h1>
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<p>Voici le code “obfusqué” :</p>
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<div class="codefile"><a href="/Scratch/fr/blog/Haskell-Mandelbrot/code/animandel.hs">➥ animandel.hs</a></div>
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<pre><code class="haskell">a=27;b=79;c=C(-2.0,-1.0);d=C(1.0,1.0);e=C(-2.501,-1.003)
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newtype C = C (Double,Double) deriving (Show,Eq)
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instance Num C where C(x,y)*C(z,t)=C(z*x-y*t,y*z+x*t);C(x,y)+C(z,t)=C(x+z,y+t);abs(C(x,y))=C(sqrt(x*x+y*y),0.0)
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r(C(x,y))=x;i(C(x,y))=y
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f c z 0=0;f c z n=if(r(abs(z))>2)then n else f c ((z*z)+c) (n-1)
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h j k = map (\z->(f (C z) (C(0,0)) 32,(fst z>l - q/2))) [(x,y)|y<-[p,(p+((o-p)/a))..o],x<-[m,(m + q)..l]] where o=i k;p=i j;m=r j;l=r k;q=(l-m)/b
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u j k = concat $ map v $ h j k where v (i,p)=(" .,`'°\":;-+oO0123456789=!%*§&$@#"!!i):rst p;rst True="\n";rst False=""
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main = putStrLn $ im 0 where cl n (C (x,y))=let cs=(1.1**n-1) in C ((x+cs*(r e))/cs+1,(y+cs*(i e))/cs+1);bl n=cl n c;tr n=cl n d;im n=u (bl n) (tr n)++"\x1b[H\x1b[25A"++im (n+1)
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</code></pre>
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<p>Pour le lancer, <a href="http://haskell.org">haskell</a> doit être installé. Puis vous devez écrire dans un terminal :</p>
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<pre><code class="zsh">ghc --make animandel.hs && animandel</code></pre>
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<p>Voici le résultat après 50 itérations.</p>
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<pre>
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###@@@@@@@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&WWOOClbUOWW&&$$$$$$$$$$$$$$
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##@@@@@@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&WWUCUb; ,jUOWW&&&$$$$$$$$$$$$
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#@@@@@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&WWWWWUb ooCWW&&&&&&$$$$$$$$
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@@@@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&WWWWWWWWOU uUOWWWW&&&&&&$$$$$
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@@@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&WOUObUOOOUUUCbi rbCUUUOWWWWWOUW&$$$
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@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&WWWUcr,iiCb o wUUUUUC;OW&$$
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$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&WWWWOUC, j llW&&$
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$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&WWWWWWOCCbi bWWW&&
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$$$$$$$$$$$$$$$$$&&WWWWWWW&&&WWWWWWWWOUo jUOWW&&
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$$$$$$$$$$$$$$&&&WWOwOOWWWOUUOWWWWWOOUbw j.blW&
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$$$$$$$$$$$&&&&&WWWObiijbUCl bCiUUUUUCj, bOW&
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$$$$$$$$$&&&&&&&WWWOUbw ; oobCbl jUWW&
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$$$$$$$&&&&&&&WWWWOcbi ij jUW&&
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$$$$$&&WWWWWWWOwUUCbw WW&&
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WWWOWWWWWWWWWUUbo UWWW&&
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: wbUOWW&&&
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WWWOWWWWWWWWWUUbo UWWW&&
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$$$$$&&WWWWWWWOwUUCbw WW&&
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$$$$$$$&&&&&&&WWWWOcbi ij jUW&&
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$$$$$$$$$&&&&&&&WWWOUbw ; oobCbl jUWW&
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$$$$$$$$$$$&&&&&WWWObiijbUCl bCiUUUUUCj, bOW&
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$$$$$$$$$$$$$$&&&WWOwOOWWWOUUOWWWWWOOUbw j.blW&
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$$$$$$$$$$$$$$$$$&&WWWWWWW&&&WWWWWWWWOUo jUOWW&&
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$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&WWWWWWOCCbi bWWW&&
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$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&WWWWOUC, j llW&&$
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@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&WWWUcr,iiCb o wUUUUUC;OW&$$
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</pre>
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<p>Here is the more readable version. I believe with this far more readable version, no more explanation is needed.</p>
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<pre><code class="haskell">nbvert = 30
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nbhor = 79
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zoomfactor = 1.01
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init_bottom_left = C (-2.0,-2.0)
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init_top_right = C (3.0,2.0)
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interrest = C (-1.713,-0.000)
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newtype Complex = C (Float,Float) deriving (Show,Eq)
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instance Num Complex where
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fromInteger n = C (fromIntegral n,0.0)
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C (x,y) * C (z,t) = C (z*x - y*t, y*z + x*t)
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C (x,y) + C (z,t) = C (x+z, y+t)
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abs (C (x,y)) = C (sqrt (x*x + y*y),0.0)
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signum (C (x,y)) = C (signum x , 0.0)
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real :: Complex -> Float
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real (C (x,y)) = x
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im :: Complex -> Float
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im (C (x,y)) = y
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cabs :: Complex -> Float
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cabs = real.abs
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f :: Complex -> Complex -> Int -> Int
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f c z 0 = 0
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f c z n = if (cabs z > 2) then n else f c ((z*z)+c) (n-1)
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bmandel bottomleft topright = map (\z -> (f (C z) (C(0,0)) 32, (fst z > right - hstep/2 ))) [(x,y) | y <- [bottom,(bottom + vstep)..top], x<-[left,(left + hstep)..right]]
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where
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top = im topright
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bottom = im bottomleft
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left = real bottomleft
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right = real topright
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vstep=(top-bottom)/nbvert
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hstep=(right-left)/nbhor
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mandel :: (Complex,Complex) -> String
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mandel (bottomleft,topright) = concat $ map treat $ bmandel bottomleft topright
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where
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treat (i,jump) = " .,:;rcuowijlbCUOW&$@#" !! (div (i*22) 32):rst jump
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rst True = "\n"
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rst False = ""
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cdiv :: Complex -> Float -> Complex
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cdiv (C(x,y)) r = C(x/r, y/r)
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cmul :: Complex -> Float -> Complex
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cmul (C(x,y)) r = C(x*r, y*r)
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zoom :: Complex -> Complex -> Complex -> Float -> (Complex,Complex)
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zoom bl tr center magn = (f bl, f tr)
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where
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f point = ((center `cmul` magn) + point ) `cdiv` (magn + 1)
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main = do
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x <- getContents
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putStrLn $ infinitemandel 0
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where
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window n = zoom init_bottom_left init_top_right interrest (zoomfactor**n)
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infinitemandel n = mandel (window n) ++ "\x1b[H\x1b[25A" ++ infinitemandel (n+1)
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</code></pre>
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Écrit le : 10/07/2011
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modifié le : 26/10/2011
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