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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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<link rel="alternate" lang="en" xml:lang="en" title="ASCII Haskell Mandelbrot" type="text/html" hreflang="en" href="/Scratch/en/blog/Haskell-Mandelbrot/" />
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<title>ASCII Haskell Mandelbrot</title>
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<h1>
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ASCII Haskell Mandelbrot
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<p>Here is the obfuscated code:</p>
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<div class="code"><div class="file"><a href="/Scratch/en/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<span class="Keyword">;</span>b=79<span class="Keyword">;</span>c=C(-2.0,-1.0)<span class="Keyword">;</span>d=C(1.0,1.0)<span class="Keyword">;</span>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)<span class="Keyword">;</span>C(x,y)+C(z,t)=C(x+z,y+t)<span class="Keyword">;</span>abs(C(x,y))=C(sqrt(x*x+y*y),0.0)
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r(C(x,y))=x<span class="Keyword">;</span>i(C(x,y))=y
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f c z 0=0<span class="Keyword">;</span>f c z n=<span class="Keyword">if</span>(r(abs(z))<span class="Keyword">></span>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 = map (<span class="Constant">\z</span>-<span class="String"><span class="String">>(</span>f (C z<span class="String">)</span></span> (C(0,0)) 32,(fst z<span class="Keyword">></span>l - q/2))) [(x,y)<span class="Keyword">|</span>y<span class="Keyword"><</span>-[p,(p+((o-p)/a))..o],x<span class="Keyword"><</span>-[m,(m + q)..l]] where o=i k<span class="Keyword">;</span>p=i j<span class="Keyword">;</span>m=r j<span class="Keyword">;</span>l=r k<span class="Keyword">;</span>q=(l-m)/b
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u j k = concat $ map v $ h j k where v (i,p)=(<span class="String"><span class="String">"</span> .,<span class="String"><span class="String">`</span>'°\":;-+oO0123456789=!%*§&$@#"!!i):rst p;rst True="\n";rst False=""</span></span>
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<span class="String"><span class="String">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)</span></span>
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</pre>
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</div></div>
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<p>To launch it, you’ll need to have <a href="http://haskell.org">haskell</a> installed and to run:</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>Here is some image after 50 iterations:</p>
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<pre class="twilight">
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<span class="Comment"><span class="Comment">#</span>##@@@@@@@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&WWOOClbUOWW&&$$$$$$$$$$$$$$</span>
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<span class="Comment"><span class="Comment">#</span>#@@@@@@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&WWUCUb; ,jUOWW&&&$$$$$$$$$$$$</span>
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<span class="Comment"><span class="Comment">#</span>@@@@@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&WWWWWUb ooCWW&&&&&&$$$$$$$$</span>
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@@@@<span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span>$<span class="Keyword">&&</span>WWWWWWWWOU uUOWWWW<span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span>$
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@@@<span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Keyword">&&</span><span class="Keyword">&</span>WOUObUOOOUUUCbi rbCUUUOWWWWWOUW<span class="Keyword">&</span><span class="Variable"><span class="Variable">$</span>$</span>$
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@<span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span>$<span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&&</span>WWWUcr,iiCb o wUUUUUC<span class="Keyword">;</span>OW<span class="Keyword">&</span><span class="Variable"><span class="Variable">$</span>$</span>
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<span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&&</span>WWWWOUC, j llW<span class="Keyword">&&</span>$
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<span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span>$<span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&&</span>WWWWWWOCCbi bWWW<span class="Keyword">&&</span>
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<span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span>$<span class="Keyword">&&</span>WWWWWWW<span class="Keyword">&&</span><span class="Keyword">&</span>WWWWWWWWOUo jUOWW<span class="Keyword">&&</span>
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<span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Keyword">&&</span><span class="Keyword">&</span>WWOwOOWWWOUUOWWWWWOOUbw j.blW<span class="Keyword">&</span>
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<span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span>$<span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&</span>WWWObiijbUCl bCiUUUUUCj, bOW<span class="Keyword">&</span>
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<span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span>$<span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&</span>WWWOUbw <span class="Keyword">;</span> oobCbl jUWW<span class="Keyword">&</span>
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<span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span>$<span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&</span>WWWWOcbi ij jUW<span class="Keyword">&&</span>
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<span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span>$<span class="Keyword">&&</span>WWWWWWWOwUUCbw WW<span class="Keyword">&&</span>
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WWWOWWWWWWWWWUUbo UWWW<span class="Keyword">&&</span>
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: wbUOWW<span class="Keyword">&&</span><span class="Keyword">&</span>
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WWWOWWWWWWWWWUUbo UWWW<span class="Keyword">&&</span>
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<span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span>$<span class="Keyword">&&</span>WWWWWWWOwUUCbw WW<span class="Keyword">&&</span>
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<span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span>$<span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&</span>WWWWOcbi ij jUW<span class="Keyword">&&</span>
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<span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span>$<span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&</span>WWWOUbw <span class="Keyword">;</span> oobCbl jUWW<span class="Keyword">&</span>
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<span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span>$<span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&</span>WWWObiijbUCl bCiUUUUUCj, bOW<span class="Keyword">&</span>
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<span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Keyword">&&</span><span class="Keyword">&</span>WWOwOOWWWOUUOWWWWWOOUbw j.blW<span class="Keyword">&</span>
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<span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span>$<span class="Keyword">&&</span>WWWWWWW<span class="Keyword">&&</span><span class="Keyword">&</span>WWWWWWWWOUo jUOWW<span class="Keyword">&&</span>
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<span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span>$<span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&&</span>WWWWWWOCCbi bWWW<span class="Keyword">&&</span>
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<span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&&</span>WWWWOUC, j llW<span class="Keyword">&&</span>$
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@<span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span><span class="Variable"><span class="Variable">$</span>$</span>$<span class="Keyword">&&</span><span class="Keyword">&&</span><span class="Keyword">&&</span>WWWUcr,iiCb o wUUUUUC<span class="Keyword">;</span>OW<span class="Keyword">&</span><span class="Variable"><span class="Variable">$</span>$</span>
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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 = 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 -<span class="Keyword">></span> Float
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real (C (x,y)) = x
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im :: Complex -<span class="Keyword">></span> Float
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im (C (x,y)) = y
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cabs :: Complex -<span class="Keyword">></span> Float
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cabs = real.abs
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f :: Complex -<span class="Keyword">></span> Complex -<span class="Keyword">></span> Int -<span class="Keyword">></span> Int
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f c z 0 = 0
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f c z n = <span class="Keyword">if</span> (cabs z <span class="Keyword">></span> 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 = map (<span class="Constant">\z</span> -<span class="Keyword">></span> (f (C z) (C(0,0)) 32, (fst z <span class="Keyword">></span> right - hstep/2 ))) [(x,y) <span class="Keyword">|</span> y <span class="Keyword"><</span>- [bottom,(bottom + vstep)..top], x<span class="Keyword"><</span>-[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) -<span class="Keyword">></span> 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) = <span class="String"><span class="String">"</span> .,:;rcuowijlbCUOW&<span class="StringVariable"><span class="StringVariable">$</span>@</span>#<span class="String">"</span></span> <span class="Keyword">!</span><span class="Keyword">!</span> (div (i*22) 32):rst jump
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rst True = <span class="String"><span class="String">"</span>\n<span class="String">"</span></span>
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rst False = <span class="String"><span class="String">"</span><span class="String">"</span></span>
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cdiv :: Complex -<span class="Keyword">></span> Float -<span class="Keyword">></span> Complex
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cdiv (C(x,y)) r = C(x/r, y/r)
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cmul :: Complex -<span class="Keyword">></span> Float -<span class="Keyword">></span> Complex
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cmul (C(x,y)) r = C(x*r, y*r)
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zoom :: Complex -<span class="Keyword">></span> Complex -<span class="Keyword">></span> Complex -<span class="Keyword">></span> Float -<span class="Keyword">></span> (Complex,Complex)
|
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zoom bl tr center magn = (f bl, f tr)
|
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where
|
|
f point = ((center <span class="String"><span class="String">`</span>cmul<span class="String">`</span></span> magn) + point ) <span class="String"><span class="String">`</span>cdiv<span class="String">`</span></span> (magn + 1)
|
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main = <span class="Keyword">do</span>
|
|
x <span class="Keyword"><</span>- getContents
|
|
putStrLn $ infinitemandel 0
|
|
where
|
|
window n = zoom init_bottom_left init_top_right interrest (zoomfactor**n)
|
|
infinitemandel n = mandel (window n) ++ <span class="String"><span class="String">"</span>\x1b[H\x1b[25A<span class="String">"</span></span> ++ infinitemandel (n+1)
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</pre>
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