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Yann Esposito (Yogsototh) 1a6066ea2b regeneration
2012-02-20 15:41:09 +01:00

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<h1>
Mandelbrot avec haskell
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<p>Voici le code &ldquo;obfusqué&rdquo;&nbsp;:</p>
<div class="code"><div class="file"><a href="/Scratch/fr/blog/Haskell-Mandelbrot/code/animandel.hs"> &#x27A5; animandel.hs </a></div><div class="withfile">
<pre class="twilight">
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)
<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>)
<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)
r(<span class="Constant">C</span>(x,y))=x;i(<span class="Constant">C</span>(x,y))=y
f c z 0=0;f c z n=<span class="Keyword">if</span>(r(<span class="Entity">abs</span>(z))&gt;2)<span class="Keyword">then</span> n <span class="Keyword">else</span> f c ((z*z)+c) (n-1)
h j k = <span class="Entity">map</span> (\z-&gt;(f (<span class="Constant">C</span> z) (<span class="Constant">C</span>(0,0)) 32,(<span class="Entity">fst</span> z&gt;l - q/2))) [(x,y)|y&lt;-[p,(p+((o-p)/a))..o],x&lt;-[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
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">&quot;</span> .,`'°<span class="StringConstant">\&quot;</span>:;-+oO0123456789=!%*§&amp;$@#<span class="String">&quot;</span></span>!!i):rst p;rst <span class="Constant">True</span>=<span class="String"><span class="String">&quot;</span><span class="StringConstant">\n</span><span class="String">&quot;</span></span>;rst <span class="Constant">False</span>=<span class="String"><span class="String">&quot;</span><span class="String">&quot;</span></span>
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">&quot;</span><span class="StringConstant">\x</span>1b[H<span class="StringConstant">\x</span>1b[25A<span class="String">&quot;</span></span>++im (n+1)
</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&nbsp;:</p>
<pre class="twilight">ghc --make animandel.hs <span class="Keyword">&amp;&amp;</span> animandel
</pre>
<p>Voici le résultat après 50 itérations.</p>
<pre>
###@@@@@@@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&amp;&amp;&amp;&amp;&amp;WWOOClbUOWW&amp;&amp;$$$$$$$$$$$$$$
##@@@@@@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&amp;&amp;&amp;&amp;&WWUCUb; ,jUOWW&amp;&amp;&amp;$$$$$$$$$$$$
#@@@@@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&amp;&amp;&amp;WWWWWUb ooCWW&amp;&amp;&amp;&amp;&amp;&amp;$$$$$$$$
@@@@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&amp;&amp;WWWWWWWWOU uUOWWWW&amp;&amp;&amp;&amp;&amp;&amp;$$$$$
@@@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&amp;&amp;&amp;WOUObUOOOUUUCbi rbCUUUOWWWWWOUW&amp;$$$
@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&amp;&amp;&amp;&amp;&amp;&amp;WWWUcr,iiCb o wUUUUUC;OW&amp;$$
$$$$$$$$$$$$$$$$$$$$$$$$$$&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;WWWWOUC, j llW&amp;&amp;$
$$$$$$$$$$$$$$$$$$$$$&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;WWWWWWOCCbi bWWW&amp;&amp;
$$$$$$$$$$$$$$$$$&amp;&amp;WWWWWWW&amp;&amp;&amp;WWWWWWWWOUo jUOWW&amp;&amp;
$$$$$$$$$$$$$$&amp;&amp;&amp;WWOwOOWWWOUUOWWWWWOOUbw j.blW&amp;
$$$$$$$$$$$&amp;&amp;&amp;&amp;&amp;WWWObiijbUCl bCiUUUUUCj, bOW&amp;
$$$$$$$$$&amp;&amp;&amp;&amp;&amp;&amp;&amp;WWWOUbw ; oobCbl jUWW&amp;
$$$$$$$&amp;&amp;&amp;&amp;&amp;&amp;&amp;WWWWOcbi ij jUW&amp;&amp;
$$$$$&amp;&amp;WWWWWWWOwUUCbw WW&amp;&amp;
WWWOWWWWWWWWWUUbo UWWW&amp;&amp;
: wbUOWW&amp;&amp;&amp;
WWWOWWWWWWWWWUUbo UWWW&amp;&amp;
$$$$$&amp;&amp;WWWWWWWOwUUCbw WW&amp;&amp;
$$$$$$$&amp;&amp;&amp;&amp;&amp;&amp;&amp;WWWWOcbi ij jUW&amp;&amp;
$$$$$$$$$&amp;&amp;&amp;&amp;&amp;&amp;&amp;WWWOUbw ; oobCbl jUWW&amp;
$$$$$$$$$$$&amp;&amp;&amp;&amp;&amp;WWWObiijbUCl bCiUUUUUCj, bOW&amp;
$$$$$$$$$$$$$$&amp;&amp;&amp;WWOwOOWWWOUUOWWWWWOOUbw j.blW&amp;
$$$$$$$$$$$$$$$$$&amp;&amp;WWWWWWW&amp;&amp;&amp;WWWWWWWWOUo jUOWW&amp;&amp;
$$$$$$$$$$$$$$$$$$$$$&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;WWWWWWOCCbi bWWW&amp;&amp;
$$$$$$$$$$$$$$$$$$$$$$$$$$&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;&amp;WWWWOUC, j llW&amp;&amp;$
@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&amp;&amp;&amp;&amp;&amp;&amp;WWWUcr,iiCb o wUUUUUC;OW&amp;$$
</pre>
<p>Here is the more readable version. I believe with this far more readable version, no more explanation is needed.</p>
<pre class="twilight">
nbvert = 30
nbhor = 79
zoomfactor = 1.01
init_bottom_left = <span class="Constant">C</span> (-2.0,-2.0)
init_top_right = <span class="Constant">C</span> (3.0,2.0)
interrest = <span class="Constant">C</span> (-1.713,-0.000)
<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>)
<span class="Keyword">instance</span> <span class="Constant">Num</span> <span class="Constant">Complex</span> <span class="Keyword">where</span>
<span class="Entity">fromInteger</span> n = <span class="Constant">C</span> (<span class="Entity">fromIntegral</span> n,0.0)
<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)
<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)
<span class="Entity">real</span> :: <span class="Constant">Complex</span> -&gt; <span class="Constant">Float</span>
real (<span class="Constant">C</span> (x,y)) = x
<span class="Entity">im</span> :: <span class="Constant">Complex</span> -&gt; <span class="Constant">Float</span>
im (<span class="Constant">C</span> (x,y)) = y
<span class="Entity">cabs</span> :: <span class="Constant">Complex</span> -&gt; <span class="Constant">Float</span>
cabs = real.<span class="Entity">abs</span>
<span class="Entity">f</span> :: <span class="Constant">Complex</span> -&gt; <span class="Constant">Complex</span> -&gt; <span class="Constant">Int</span> -&gt; <span class="Constant">Int</span>
f c z 0 = 0
f c z n = <span class="Keyword">if</span> (cabs z &gt; 2) <span class="Keyword">then</span> n <span class="Keyword">else</span> f c ((z*z)+c) (n-1)
bmandel bottomleft topright = <span class="Entity">map</span> (\z -&gt; (f (<span class="Constant">C</span> z) (<span class="Constant">C</span>(0,0)) 32, (<span class="Entity">fst</span> z &gt; right - hstep/2 ))) [(x,y) | y &lt;- [bottom,(bottom + vstep)..top], x&lt;-[left,(left + hstep)..right]]
<span class="Keyword">where</span>
top = im topright
bottom = im bottomleft
left = real bottomleft
right = real topright
vstep=(top-bottom)/nbvert
hstep=(right-left)/nbhor
<span class="Entity">mandel</span> :: (<span class="Constant">Complex,Complex</span>) -&gt; <span class="Constant">String</span>
mandel (bottomleft,topright) = <span class="Entity">concat</span> $ <span class="Entity">map</span> treat $ bmandel bottomleft topright
<span class="Keyword">where</span>
treat (i,jump) = <span class="String"><span class="String">&quot;</span> .,:;rcuowijlbCUOW&amp;$@#<span class="String">&quot;</span></span> !! (<span class="Entity">div</span> (i*22) 32):rst jump
rst <span class="Constant">True</span> = <span class="String"><span class="String">&quot;</span><span class="StringConstant">\n</span><span class="String">&quot;</span></span>
rst <span class="Constant">False</span> = <span class="String"><span class="String">&quot;</span><span class="String">&quot;</span></span>
<span class="Entity">cdiv</span> :: <span class="Constant">Complex</span> -&gt; <span class="Constant">Float</span> -&gt; <span class="Constant">Complex</span>
cdiv (<span class="Constant">C</span>(x,y)) r = <span class="Constant">C</span>(x/r, y/r)
<span class="Entity">cmul</span> :: <span class="Constant">Complex</span> -&gt; <span class="Constant">Float</span> -&gt; <span class="Constant">Complex</span>
cmul (<span class="Constant">C</span>(x,y)) r = <span class="Constant">C</span>(x*r, y*r)
<span class="Entity">zoom</span> :: <span class="Constant">Complex</span> -&gt; <span class="Constant">Complex</span> -&gt; <span class="Constant">Complex</span> -&gt; <span class="Constant">Float</span> -&gt; (<span class="Constant">Complex,Complex</span>)
zoom bl tr center magn = (f bl, f tr)
<span class="Keyword">where</span>
f point = ((center <span class="Entity"><span class="Entity">`</span>cmul` magn) + point ) `cdiv<span class="Entity">`</span></span> (magn + 1)
main = <span class="Keyword">do</span>
x &lt;- <span class="Entity">getContents</span>
<span class="Entity">putStrLn</span> $ infinitemandel 0
<span class="Keyword">where</span>
window n = zoom init_bottom_left init_top_right interrest (zoomfactor**n)
infinitemandel n = mandel (window n) ++ <span class="String"><span class="String">&quot;</span><span class="StringConstant">\x</span>1b[H<span class="StringConstant">\x</span>1b[25A<span class="String">&quot;</span></span> ++ infinitemandel (n+1)
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Écrit le : 10/07/2011
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