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<link rel="alternate" lang="fr" xml:lang="fr" title="Mandelbrot avec haskell" type="text/html" hreflang="fr" href="/Scratch/fr/blog/Haskell-Mandelbrot/" />
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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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<p>Voici le code “obfusqué” :</p>
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<div class="code"><div class="file"><a href="/Scratch/fr/blog/Haskell-Mandelbrot/code/animandel.hs"> ➥ animandel.hs </a></div><div class="withfile">
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<pre class="twilight">
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a=27;b=79;c=<span class="Constant">C</span>(-2.0,-1.0);d=<span class="Constant">C</span>(1.0,1.0);e=<span class="Constant">C</span>(-2.501,-1.003)
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<span class="Keyword">newtype</span> <span class="Constant">C</span> = <span class="Constant">C</span> (<span class="Constant">Double</span>,<span class="Constant">Double</span>) <span class="Keyword">deriving</span> (<span class="Constant">Show</span>,<span class="Constant">Eq</span>)
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<span class="Keyword">instance</span> <span class="Constant">Num</span> <span class="Constant">C</span> <span class="Keyword">where</span> <span class="Constant">C</span>(x,y)*<span class="Constant">C</span>(z,t)=<span class="Constant">C</span>(z*x-y*t,y*z+x*t);<span class="Constant">C</span>(x,y)+<span class="Constant">C</span>(z,t)=<span class="Constant">C</span>(x+z,y+t);<span class="Entity">abs</span>(<span class="Constant">C</span>(x,y))=<span class="Constant">C</span>(<span class="Entity">sqrt</span>(x*x+y*y),0.0)
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r(<span class="Constant">C</span>(x,y))=x;i(<span class="Constant">C</span>(x,y))=y
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f c z 0=0;f c z n=<span class="Keyword">if</span>(r(<span class="Entity">abs</span>(z))>2)<span class="Keyword">then</span> n <span class="Keyword">else</span> f c ((z*z)+c) (n-1)
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h j k = <span class="Entity">map</span> (\z→(f (<span class="Constant">C</span> z) (<span class="Constant">C</span>(0,0)) 32,(<span class="Entity">fst</span> z>l - q/2))) [(x,y)|y←[p,(p+((o-p)/a))..o],x←[m,(m + q)..l]] <span class="Keyword">where</span> o=i k;p=i j;m=r j;l=r k;q=(l-m)/b
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u j k = <span class="Entity">concat</span> $ <span class="Entity">map</span> v $ h j k <span class="Keyword">where</span> v (i,p)=(<span class="String"><span class="String">"</span> .,`'°<span class="StringConstant">\"</span>:;-+oO0123456789=!%*§&$@#<span class="String">"</span></span>!!i):rst p;rst <span class="Constant">True</span>=<span class="String"><span class="String">"</span><span class="StringConstant">\n</span><span class="String">"</span></span>;rst <span class="Constant">False</span>=<span class="String"><span class="String">"</span><span class="String">"</span></span>
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main = <span class="Entity">putStrLn</span> $ im 0 <span class="Keyword">where</span> cl n (<span class="Constant">C</span> (x,y))=<span class="Keyword">let</span> cs=(1.1**n-1) <span class="Keyword">in</span> <span class="Constant">C</span> ((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)++<span class="String"><span class="String">"</span><span class="StringConstant">\x</span>1b[H<span class="StringConstant">\x</span>1b[25A<span class="String">"</span></span>++im (n+1)
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</pre>
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</div></div>
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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 class="twilight">ghc --make animandel.hs <span class="Keyword">&&</span> animandel
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</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 class="twilight">
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nbvert = 30
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nbhor = 79
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zoomfactor = 1.01
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init_bottom_left = <span class="Constant">C</span> (-2.0,-2.0)
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init_top_right = <span class="Constant">C</span> (3.0,2.0)
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interrest = <span class="Constant">C</span> (-1.713,-0.000)
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<span class="Keyword">newtype</span> <span class="Constant">Complex</span> = <span class="Constant">C</span> (<span class="Constant">Float</span>,<span class="Constant">Float</span>) <span class="Keyword">deriving</span> (<span class="Constant">Show</span>,<span class="Constant">Eq</span>)
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<span class="Keyword">instance</span> <span class="Constant">Num</span> <span class="Constant">Complex</span> <span class="Keyword">where</span>
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<span class="Entity">fromInteger</span> n = <span class="Constant">C</span> (<span class="Entity">fromIntegral</span> n,0.0)
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<span class="Constant">C</span> (x,y) * <span class="Constant">C</span> (z,t) = <span class="Constant">C</span> (z*x - y*t, y*z + x*t)
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<span class="Constant">C</span> (x,y) + <span class="Constant">C</span> (z,t) = <span class="Constant">C</span> (x+z, y+t)
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<span class="Entity">abs</span> (<span class="Constant">C</span> (x,y)) = <span class="Constant">C</span> (<span class="Entity">sqrt</span> (x*x + y*y),0.0)
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<span class="Entity">signum</span> (<span class="Constant">C</span> (x,y)) = <span class="Constant">C</span> (<span class="Entity">signum</span> x , 0.0)
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<span class="Entity">real</span> :: <span class="Constant">Complex</span> → <span class="Constant">Float</span>
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real (<span class="Constant">C</span> (x,y)) = x
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<span class="Entity">im</span> :: <span class="Constant">Complex</span> → <span class="Constant">Float</span>
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im (<span class="Constant">C</span> (x,y)) = y
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<span class="Entity">cabs</span> :: <span class="Constant">Complex</span> → <span class="Constant">Float</span>
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cabs = real.<span class="Entity">abs</span>
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<span class="Entity">f</span> :: <span class="Constant">Complex</span> → <span class="Constant">Complex</span> → <span class="Constant">Int</span> → <span class="Constant">Int</span>
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f c z 0 = 0
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f c z n = <span class="Keyword">if</span> (cabs z > 2) <span class="Keyword">then</span> n <span class="Keyword">else</span> f c ((z*z)+c) (n-1)
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bmandel bottomleft topright = <span class="Entity">map</span> (\z → (f (<span class="Constant">C</span> z) (<span class="Constant">C</span>(0,0)) 32, (<span class="Entity">fst</span> z > right - hstep/2 ))) [(x,y) | y ← [bottom,(bottom + vstep)..top], x←[left,(left + hstep)..right]]
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<span class="Keyword">where</span>
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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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<span class="Entity">mandel</span> :: (<span class="Constant">Complex,Complex</span>) → <span class="Constant">String</span>
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mandel (bottomleft,topright) = <span class="Entity">concat</span> $ <span class="Entity">map</span> treat $ bmandel bottomleft topright
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<span class="Keyword">where</span>
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treat (i,jump) = <span class="String"><span class="String">"</span> .,:;rcuowijlbCUOW&$@#<span class="String">"</span></span> !! (<span class="Entity">div</span> (i*22) 32):rst jump
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rst <span class="Constant">True</span> = <span class="String"><span class="String">"</span><span class="StringConstant">\n</span><span class="String">"</span></span>
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rst <span class="Constant">False</span> = <span class="String"><span class="String">"</span><span class="String">"</span></span>
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<span class="Entity">cdiv</span> :: <span class="Constant">Complex</span> → <span class="Constant">Float</span> → <span class="Constant">Complex</span>
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cdiv (<span class="Constant">C</span>(x,y)) r = <span class="Constant">C</span>(x/r, y/r)
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<span class="Entity">cmul</span> :: <span class="Constant">Complex</span> → <span class="Constant">Float</span> → <span class="Constant">Complex</span>
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cmul (<span class="Constant">C</span>(x,y)) r = <span class="Constant">C</span>(x*r, y*r)
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<span class="Entity">zoom</span> :: <span class="Constant">Complex</span> → <span class="Constant">Complex</span> → <span class="Constant">Complex</span> → <span class="Constant">Float</span> → (<span class="Constant">Complex,Complex</span>)
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zoom bl tr center magn = (f bl, f tr)
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<span class="Keyword">where</span>
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f point = ((center <span class="Entity"><span class="Entity">`</span>cmul` magn) + point ) `cdiv<span class="Entity">`</span></span> (magn + 1)
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main = <span class="Keyword">do</span>
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x ← <span class="Entity">getContents</span>
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<span class="Entity">putStrLn</span> $ infinitemandel 0
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<span class="Keyword">where</span>
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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) ++ <span class="String"><span class="String">"</span><span class="StringConstant">\x</span>1b[H<span class="StringConstant">\x</span>1b[25A<span class="String">"</span></span> ++ infinitemandel (n+1)
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</pre>
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