New better code

multi/blog/Haskell-Mandelbrot.md

@@ -17,7 +17,6 @@ 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 -> C -> Int -> Int
 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=""
@@ -60,12 +59,12 @@ OO"-O0000000000Oo--oO0000000000O-:oO0000Oo::+++;;: ":"-++-';+oooOOoooo-::-oooo++
 Here is the more readable version. I believe with this far more readable version, no more explanation is needed.
 
 <code class="zsh">
--- Screen size
-nbvert = 27
+nbvert = 30
 nbhor = 79
-init_bottom_left = C (-2.0,-1.0)
-init_top_right   = C (1.0,1.0)
-interrest        = C (-2.5,-1.0)
+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
@@ -80,17 +79,15 @@ real (C (x,y))    = x
 im :: Complex -> Float
 im   (C (x,y))    = y
 
-f :: Complex -> Complex -> Int -> Complex
-f c z 0 = z
-f c z n = f c ((z*z)+c) (n-1) 
-
 cabs :: Complex -> Float
 cabs = real.abs
 
-tst :: Complex -> Bool
-tst c = (cabs (f c (C(0.0,0.0)) 32)) < 2
+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 -> (tst (C z), (fst z > right - hstep/2 ))) [(x,y) | y <- [bottom,(bottom + vstep)..top], x<-[left,(left + hstep)..right]]
+
+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
@@ -99,23 +96,28 @@ bmandel bottomleft topright = map (\z -> (tst (C z), (fst z > right - hstep/2 ))
         vstep=(top-bottom)/nbvert
         hstep=(right-left)/nbhor
 
-mandel :: Complex -> Complex -> String
-mandel bottomleft topright = concat $ map treat $ bmandel bottomleft topright
+mandel :: (Complex,Complex) -> String
+mandel (bottomleft,topright) = concat $ map treat $ bmandel bottomleft topright
     where
-        treat (True,jump) = " " ++ rst jump
-        treat (False,jump) = "@" ++ rst  jump
+        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
-        closer n (C (x,y)) = 
-            let cst = (1.1**n - 1) in
-                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) ++ "\x1b[H\x1b[25A" ++ infinitemandel (n+1)
+        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>