scratch/content/html/fr/blog/Haskell-Mandelbrot.md

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isHidden:       false
menupriority:   1
kind:           article
created_at:     2011-07-10T12:41:26+02:00
title: Mandelbrot avec haskell
author_name: Yann Esposito
author_uri: yannesposito.com
# tags:
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Voici le code "obfusqué" :

<code class="haskell" file="animandel.hs">
a=27;b=79;c=C(-2.0,-1.0);d=C(1.0,1.0);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);C(x,y)+C(z,t)=C(x+z,y+t);abs(C(x,y))=C(sqrt(x*x+y*y),0.0)
r(C(x,y))=x;i(C(x,y))=y
f c z 0=0;f c z n=if(r(abs(z))>2)then n else f c ((z*z)+c) (n-1)
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
u j k = concat $ map v $ h j k where v (i,p)=(" .,`'°\":;-+oO0123456789=!%*§&$@#"!!i):rst p;rst True="\n";rst False=""
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)
</code>

Pour le lancer, [haskell](http://haskell.org) doit être installé. Puis vous devez écrire dans un terminal :

<code class="zsh">ghc --make animandel.hs && animandel</code>

Voici le résultat après 50 itérations.

<pre>
###@@@@@@@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&WWOOClbUOWW&&$$$$$$$$$$$$$$
##@@@@@@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&WWUCUb; ,jUOWW&&&$$$$$$$$$$$$
#@@@@@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&WWWWWUb       ooCWW&&&&&&$$$$$$$$
@@@@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&WWWWWWWWOU         uUOWWWW&&&&&&$$$$$
@@@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&WOUObUOOOUUUCbi      rbCUUUOWWWWWOUW&$$$
@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&WWWUcr,iiCb                o wUUUUUC;OW&$$
$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&WWWWOUC,                         j    llW&&$
$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&WWWWWWOCCbi                              bWWW&&
$$$$$$$$$$$$$$$$$&&WWWWWWW&&&WWWWWWWWOUo                                 jUOWW&&
$$$$$$$$$$$$$$&&&WWOwOOWWWOUUOWWWWWOOUbw                                  j.blW&
$$$$$$$$$$$&&&&&WWWObiijbUCl bCiUUUUUCj,                                    bOW&
$$$$$$$$$&&&&&&&WWWOUbw  ;      oobCbl                                     jUWW&
$$$$$$$&&&&&&&WWWWOcbi             ij                                      jUW&&
$$$$$&&WWWWWWWOwUUCbw                                                       WW&&
WWWOWWWWWWWWWUUbo                                                         UWWW&&
:                                                                      wbUOWW&&&
WWWOWWWWWWWWWUUbo                                                         UWWW&&
$$$$$&&WWWWWWWOwUUCbw                                                       WW&&
$$$$$$$&&&&&&&WWWWOcbi             ij                                      jUW&&
$$$$$$$$$&&&&&&&WWWOUbw  ;      oobCbl                                     jUWW&
$$$$$$$$$$$&&&&&WWWObiijbUCl bCiUUUUUCj,                                    bOW&
$$$$$$$$$$$$$$&&&WWOwOOWWWOUUOWWWWWOOUbw                                  j.blW&
$$$$$$$$$$$$$$$$$&&WWWWWWW&&&WWWWWWWWOUo                                 jUOWW&&
$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&WWWWWWOCCbi                              bWWW&&
$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&WWWWOUC,                         j    llW&&$
@$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&WWWUcr,iiCb                o wUUUUUC;OW&$$
</pre>

Here is the more readable version. I believe with this far more readable version, no more explanation is needed.

<code class="haskell">
nbvert = 30
nbhor = 79
zoomfactor = 1.01
init_bottom_left = C (-2.0,-2.0)
init_top_right   = C (3.0,2.0)
interrest        = C (-1.713,-0.000)

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 -> Float
real (C (x,y))    = x
im :: Complex -> Float
im   (C (x,y))    = y

cabs :: Complex -> Float
cabs = real.abs

f :: Complex -> Complex -> Int -> Int
f c z 0 = 0
f c z n = if (cabs z > 2) then n else f c ((z*z)+c) (n-1) 


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]]
    where
        top = im topright
        bottom = im bottomleft
        left = real bottomleft
        right = real topright
        vstep=(top-bottom)/nbvert
        hstep=(right-left)/nbhor

mandel :: (Complex,Complex) -> String
mandel (bottomleft,topright) = concat $ map treat $ bmandel bottomleft topright
    where
        treat (i,jump) = " .,:;rcuowijlbCUOW&$@#" !! (div (i*22) 32):rst jump
        rst True = "\n"
        rst False = ""

cdiv :: Complex -> Float -> Complex
cdiv (C(x,y)) r = C(x/r, y/r) 
cmul :: Complex -> Float -> Complex
cmul (C(x,y)) r = C(x*r, y*r) 

zoom :: Complex -> Complex -> Complex -> Float -> (Complex,Complex)
zoom bl tr center magn = (f bl, f tr)
    where
        f point = ((center `cmul` magn) + point ) `cdiv` (magn + 1)
    

main = do
    x <- getContents
    putStrLn $ infinitemandel 0
    where
        window n = zoom init_bottom_left init_top_right interrest (zoomfactor**n) 
        infinitemandel n = mandel (window n) ++ "\x1b[H\x1b[25A" ++ infinitemandel (n+1)
</code>