287 lines
17 KiB
HTML
287 lines
17 KiB
HTML
|
<?xml version="1.0" encoding="utf-8"?>
|
||
|
|
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
|
||
|
|
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||
|
|
<html xmlns="http://www.w3.org/1999/xhtml" lang="fr" xml:lang="fr">
|
||
|
|
<head>
|
||
|
|
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8" />
|
||
|
|
|
||
|
|
|
||
|
|
<link rel="shortcut icon" type="image/x-icon" href="/Scratch/img/favicon.ico" />
|
||
|
|
<link rel="stylesheet" type="text/css" href="/Scratch/assets/css/main.css" />
|
||
|
|
<link rel="stylesheet" type="text/css" href="/Scratch/css/twilight.css" />
|
||
|
|
<link rel="stylesheet" type="text/css" href="/Scratch/css/idc.css" />
|
||
|
|
<link rel="alternate" type="application/rss+xml" title="RSS" href="http://feeds.feedburner.com/yannespositocomfr"/>
|
||
|
|
|
||
|
|
<link rel="alternate" lang="fr" xml:lang="fr" title="Mandelbrot avec haskell" type="text/html" hreflang="fr" href="/Scratch/fr/blog/Haskell-Mandelbrot/" />
|
||
|
|
<link rel="alternate" lang="en" xml:lang="en" title="ASCII Haskell Mandelbrot" type="text/html" hreflang="en" href="/Scratch/en/blog/Haskell-Mandelbrot/" />
|
||
|
|
<script type="text/javascript" src="/Scratch/js/jquery-1.3.1.min.js"></script>
|
||
|
|
<script type="text/javascript" src="/Scratch/js/jquery.cookie.js"></script>
|
||
|
|
<script type="text/javascript" src="/Scratch/js/index.js"></script>
|
||
|
|
<!--[if lt IE 9]>
|
||
|
|
<script src="http://ie7-js.googlecode.com/svn/version/2.1(beta4)/IE9.js"></script>
|
||
|
|
<![endif]-->
|
||
|
|
<!-- < % if containMaths %>
|
||
|
|
<script type="text/javascript" src="/Scratch/js/MathJax/MathJax.js"></script>
|
||
|
|
< % end %>
|
||
|
|
-->
|
||
|
|
<title>Mandelbrot avec haskell</title>
|
||
|
|
</head>
|
||
|
|
<body lang="fr">
|
||
|
|
<script type="text/javascript">// <![CDATA[
|
||
|
|
document.write('<div id="blackpage"><img src="/Scratch/img/loading.gif" alt="Chargement en cours..."/></div>');
|
||
|
|
// ]]>
|
||
|
|
</script>
|
||
|
|
|
||
|
|
<div id="content">
|
||
|
|
|
||
|
|
<div id="choix">
|
||
|
|
<div class="return"><a href="#entete">↓ Menu ↓</a></div>
|
||
|
|
<div id="choixlang">
|
||
|
|
<a href="/Scratch/en/blog/Haskell-Mandelbrot/" onclick="setLanguage('en')">in English</a>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
<div id="titre">
|
||
|
|
<h1>
|
||
|
|
Mandelbrot avec haskell
|
||
|
|
</h1>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div class="flush"></div>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
<div class="flush"></div>
|
||
|
|
<div id="afterheader">
|
||
|
|
<div class="corps">
|
||
|
|
<p>Voici le code “obfusqué” :</p>
|
||
|
|
|
||
|
|
<div class="code"><div class="file"><a href="/Scratch/fr/blog/Haskell-Mandelbrot/code/animandel.hs"> ➥ animandel.hs </a></div><div class="withfile">
|
||
|
|
<pre class="twilight">
|
||
|
|
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)
|
||
|
|
newtype C = C (Double,Double) deriving (Show,Eq)
|
||
|
|
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)
|
||
|
|
r(C(x,y))=x<span class="Keyword">;</span>i(C(x,y))=y
|
||
|
|
f :: C -<span class="Keyword">></span> C -<span class="Keyword">></span> Int -<span class="Keyword">></span> Int
|
||
|
|
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)
|
||
|
|
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
|
||
|
|
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>
|
||
|
|
<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>
|
||
|
|
</pre>
|
||
|
|
</div></div>
|
||
|
|
|
||
|
|
<p>Pour le lancer, <a href="http://haskell.org">haskell</a> doit être installé. Puis vous devez écrire dans un terminal :</p>
|
||
|
|
|
||
|
|
<pre class="twilight">ghc --make animandel.hs <span class="Keyword">&&</span> animandel
|
||
|
|
</pre>
|
||
|
|
|
||
|
|
<p>Voici le résultat après 50 itérations.</p>
|
||
|
|
|
||
|
|
<pre class="twilight">
|
||
|
|
5555666666666666666666666666666655555555554O+++ :o022334444444444444444444444444
|
||
|
|
5555556666666666666666666666665555555555543210O-+O112333344444444444444444444444
|
||
|
|
55555555666666666666666666665555555555444333210o<span class="String"><span class="String">`</span>O012333333444444444444444444444</span>
|
||
|
|
<span class="String">4555555555566666666666666555555555544444333331O+°°,'0233333334444444444444444433</span>
|
||
|
|
<span class="String">44444445555555556666555555555444444444433333210o-:O01122333333334444444444443333</span>
|
||
|
|
<span class="String">44444444444444445555444444444444444444333332211O+ -o1112222223333333344433333222</span>
|
||
|
|
<span class="String">444444444444433331133334444444444444433332221110o"+O0111222222222222222222222222</span>
|
||
|
|
<span class="String">34444444443333330OO03333334444444443332222221100O+-oO001122222222221110-O1111122</span>
|
||
|
|
<span class="String">22333333333332210--01223333333333322222222211000o-°+o00000122222111110o°;o001111</span>
|
||
|
|
<span class="String">11OO112222222111O;;O111222222211OO111122211000Oo-" :+ooOOOO.O0000000OOo'°oOO0000</span>
|
||
|
|
<span class="String">0O;+O01122211000O--O00011221110O+;O00000OO +oooo-: :-+oo++";oOO0000Ooo+;;+oooO00</span>
|
||
|
|
<span class="String">o+"+oO00OO OOOOoo::ooOOOO°OO00Oo+"+ooOooo+;°---",' ,,";--: ;-+oo+ +++;;°°;;-++:;</span>
|
||
|
|
<span class="String">,° °':°: <span class="String">`</span></span> <span class="String"><span class="String">"</span><span class="String"><span class="String">`</span>".°° °° "°". :'", '°<span class="String">`</span></span>°<span class="String">"</span></span>:<span class="String"><span class="String">`</span>°<span class="String">`</span></span> ,,<span class="String"><span class="String">`</span><span class="String">`</span></span> . . .°°<span class="String"><span class="String">'</span>°° ` .. `<span class="String">'</span></span>°.
|
||
|
|
+-<span class="String"><span class="String">`</span>-oo+oo+'+o+<span class="String">`</span></span>--°°<span class="Keyword">;</span>-<span class="String"><span class="String">`</span>+o+"+oo+oo-'-++;+++-:,:::"<span class="String">`</span></span> °::°° :-<span class="Keyword">;</span><span class="Keyword">;</span>--,<span class="Keyword">;</span>-<span class="Keyword">;</span> <span class="String"><span class="String">"</span> <span class="String">"</span></span> <span class="Keyword">;</span>-<span class="Keyword">;</span><span class="String"><span class="String">"</span>:</span>
|
||
|
|
<span class="String">OO<span class="String">"</span></span>-O0000000000Oo--oO0000000000O-:oO0000Oo::+++<span class="Keyword">;</span><span class="Keyword">;</span>: <span class="String"><span class="String">"</span>:<span class="String">"</span></span>-++-<span class="String"><span class="String">'</span>;+oooOOoooo-::-oooo++</span>
|
||
|
|
<span class="String">10;-111222222110O--O011222222111- 01111110oOOOoo-: :-ooooo`:OO000000OO+;;+OOO000</span>
|
||
|
|
<span class="String">22122222222222110++0112222222222111222222221000O+:,;.O000001111111100Oo:-OO00000</span>
|
||
|
|
<span class="String">3344444433333332-,°-2333333344444433322222221100o-;oO00011222222221111O<span class="String">'</span></span>+0111111
|
||
|
|
444444444444333320023333444444444444433322221110O.:O0011222222222222211-01112222
|
||
|
|
44444444444444443333444444444444444444333332211O. -o1112222222223333333333322222
|
||
|
|
44444444445555555555555555444444444444433333210O-<span class="String"><span class="String">"</span>oO1122223333333444444444433333</span>
|
||
|
|
<span class="String">444555555555666666666666555555555444444433333' '<span class="String"><span class="String">`</span>:+O0233333333444444444444444433</span></span>
|
||
|
|
</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">
|
||
|
|
-- Screen size
|
||
|
|
nbvert = 27
|
||
|
|
nbhor = 79
|
||
|
|
init_bottom_left = C (-2.0,-1.0)
|
||
|
|
init_top_right = C (1.0,1.0)
|
||
|
|
interrest = C (-2.5,-1.0)
|
||
|
|
|
||
|
|
newtype Complex = C (Float,Float) deriving (Show,Eq)
|
||
|
|
instance Num Complex where
|
||
|
|
fromInteger n = C (fromIntegral n,0.0)
|
||
|
|
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)
|
||
|
|
signum (C (x,y)) = C (signum x , 0.0)
|
||
|
|
|
||
|
|
real :: Complex -<span class="Keyword">></span> Float
|
||
|
|
real (C (x,y)) = x
|
||
|
|
im :: Complex -<span class="Keyword">></span> Float
|
||
|
|
im (C (x,y)) = y
|
||
|
|
|
||
|
|
f :: Complex -<span class="Keyword">></span> Complex -<span class="Keyword">></span> Int -<span class="Keyword">></span> Complex
|
||
|
|
f c z 0 = z
|
||
|
|
f c z n = f c ((z*z)+c) (n-1)
|
||
|
|
|
||
|
|
cabs :: Complex -<span class="Keyword">></span> Float
|
||
|
|
cabs = real.abs
|
||
|
|
|
||
|
|
tst :: Complex -<span class="Keyword">></span> Bool
|
||
|
|
tst c = (cabs (f c (C(0.0,0.0)) 32)) <span class="Keyword"><</span> 2
|
||
|
|
|
||
|
|
bmandel bottomleft topright = map (<span class="Constant">\z</span> -<span class="Keyword">></span> (tst (C z), (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]]
|
||
|
|
where
|
||
|
|
top = im topright
|
||
|
|
bottom = im bottomleft
|
||
|
|
left = real bottomleft
|
||
|
|
right = real topright
|
||
|
|
vstep=(top-bottom)/nbvert
|
||
|
|
hstep=(right-left)/nbhor
|
||
|
|
|
||
|
|
mandel :: Complex -<span class="Keyword">></span> Complex -<span class="Keyword">></span> String
|
||
|
|
mandel bottomleft topright = concat $ map treat $ bmandel bottomleft topright
|
||
|
|
where
|
||
|
|
treat (True,jump) = <span class="String"><span class="String">"</span> <span class="String">"</span></span> ++ rst jump
|
||
|
|
treat (False,jump) = <span class="String"><span class="String">"</span>@<span class="String">"</span></span> ++ rst jump
|
||
|
|
rst True = <span class="String"><span class="String">"</span>\n<span class="String">"</span></span>
|
||
|
|
rst False = <span class="String"><span class="String">"</span><span class="String">"</span></span>
|
||
|
|
|
||
|
|
main = <span class="Keyword">do</span>
|
||
|
|
x <span class="Keyword"><</span>- getContents
|
||
|
|
putStrLn $ infinitemandel 0
|
||
|
|
where
|
||
|
|
closer n (C (x,y)) =
|
||
|
|
let cst = (1.1**n - 1) <span class="Keyword">in</span>
|
||
|
|
C ( (x + cst*(real interrest))/cst+1,
|
||
|
|
(y + cst*(im interrest))/cst+1 )
|
||
|
|
bottomleftn n = closer n init_bottom_left
|
||
|
|
toprightn n = closer n init_top_right
|
||
|
|
infinitemandel n = mandel (bottomleftn n) (toprightn n) ++ <span class="String"><span class="String">"</span>\x1b[H\x1b[25A<span class="String">"</span></span> ++ infinitemandel (n+1)
|
||
|
|
</pre>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
<div id="choixrss">
|
||
|
|
<a id="rss" href="http://feeds.feedburner.com/yannespositocomfr">
|
||
|
|
s'abonner
|
||
|
|
</a>
|
||
|
|
</div>
|
||
|
|
<script type="text/javascript">
|
||
|
|
$(document).ready(function(){
|
||
|
|
$('#comment').hide();
|
||
|
|
$('#clickcomment').click(showComments);
|
||
|
|
});
|
||
|
|
function showComments() {
|
||
|
|
$('#comment').show();
|
||
|
|
$('#clickcomment').fadeOut();
|
||
|
|
}
|
||
|
|
document.write('<div id="clickcomment">Commentaires</div>');
|
||
|
|
</script>
|
||
|
|
<div class="flush"></div>
|
||
|
|
<div class="corps" id="comment">
|
||
|
|
<h2 class="first">commentaires</h2>
|
||
|
|
<noscript>
|
||
|
|
Vous devez activer javascript pour commenter.
|
||
|
|
</noscript>
|
||
|
|
|
||
|
|
<script type="text/javascript">
|
||
|
|
var idcomments_acct = 'a307f0044511ff1b5cfca573fc0a52e7';
|
||
|
|
var idcomments_post_id = '/Scratch/fr/blog/Haskell-Mandelbrot/';
|
||
|
|
var idcomments_post_url = 'http://yannesposito.com/Scratch/fr/blog/Haskell-Mandelbrot/';
|
||
|
|
</script>
|
||
|
|
<span id="IDCommentsPostTitle" style="display:none"></span>
|
||
|
|
<script type='text/javascript' src='/Scratch/js/genericCommentWrapperV2.js'></script>
|
||
|
|
|
||
|
|
</div>
|
||
|
|
|
||
|
|
<div id="entete" class="corps_spaced">
|
||
|
|
<div id="liens">
|
||
|
|
<ul><li><a href="/Scratch/fr/">Bienvenue</a></li>
|
||
|
|
<li><a href="/Scratch/fr/blog/">Blog</a></li>
|
||
|
|
<li><a href="/Scratch/fr/softwares/">Softwares</a></li>
|
||
|
|
<li><a href="/Scratch/fr/about/">À propos</a></li></ul>
|
||
|
|
</div>
|
||
|
|
<div class="flush"></div>
|
||
|
|
<hr/>
|
||
|
|
<div id="next_before_articles">
|
||
|
|
<div id="previous_articles">
|
||
|
|
articles précédents
|
||
|
|
|
||
|
|
<div class="previous_article">
|
||
|
|
<a href="/Scratch/fr/blog/Password-Management/"><span class="nicer">«</span> Password Management</a>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
|
||
|
|
<div class="previous_article">
|
||
|
|
<a href="/Scratch/fr/blog/2011-04-20-Now-hosted-on-github/"><span class="nicer">«</span> Hébergement github</a>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
|
||
|
|
<div class="previous_article">
|
||
|
|
<a href="/Scratch/fr/blog/2011-01-03-Why-I-sadly-won-t-use-coffeescript/"><span class="nicer">«</span> Pourquoi je n'utiliserai pas CoffeeScript (malheureusement)</a>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
|
||
|
|
</div>
|
||
|
|
<div id="next_articles">
|
||
|
|
articles suivants
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
|
||
|
|
</div>
|
||
|
|
<div class="flush"></div>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
|
||
|
|
|
||
|
|
<div id="bottom">
|
||
|
|
<div>
|
||
|
|
<a rel="license" href="http://creativecommons.org/licenses/by-sa/3.0/deed.fr">Droits de reproduction ©, Yann Esposito</a>
|
||
|
|
</div>
|
||
|
|
<div id="lastmod">
|
||
|
|
Écrit le : 10/07/2011
|
||
|
|
modifié le : 10/07/2011
|
||
|
|
</div>
|
||
|
|
<div>
|
||
|
|
Site entièrement réalisé avec
|
||
|
|
<a href="http://www.vim.org">Vim</a>
|
||
|
|
et
|
||
|
|
<a href="http://nanoc.stoneship.org">nanoc</a>
|
||
|
|
</div>
|
||
|
|
<div>
|
||
|
|
<a href="/Scratch/fr/validation/">Validation</a>
|
||
|
|
<a href="http://validator.w3.org/check?uri=referer"> [xhtml] </a>
|
||
|
|
.
|
||
|
|
<a href="http://jigsaw.w3.org/css-validator/check/referer?profile=css3"> [css] </a>
|
||
|
|
.
|
||
|
|
<a href="http://validator.w3.org/feed/check.cgi?url=http%3A//yannesposito.com/Scratch/fr/blog/feed/feed.xml">[rss]</a>
|
||
|
|
</div>
|
||
|
|
</div>
|
||
|
|
<div class="clear"></div>
|
||
|
|
</div>
|
||
|
|
<script type="text/javascript">
|
||
|
|
var clicky = { log: function(){ return; }, goal: function(){ return; }};
|
||
|
|
var clicky_site_id = 66374971;
|
||
|
|
(function() {
|
||
|
|
var s = document.createElement('script');
|
||
|
|
s.type = 'text/javascript';
|
||
|
|
s.async = true;
|
||
|
|
s.src = ( document.location.protocol == 'https:' ? 'https://static.getclicky.com/js' : 'http://static.getclicky.com/js' );
|
||
|
|
( document.getElementsByTagName('head')[0] || document.getElementsByTagName('body')[0] ).appendChild( s );
|
||
|
|
})();
|
||
|
|
</script>
|
||
|
|
<noscript><p><img alt="Clicky" width="1" height="1" src="http://in.getclicky.com/66374971ns.gif" /></p></noscript>
|
||
|
|
|
||
|
|
</body>
|
||
|
|
</html>
|