Mandelbrot.hs

data Complex a = Complex a a deriving (Show)
 
pretty :: (Show a) => Complex a -> String
pretty (Complex a b) = show a ++ " + " ++ show b ++ "i"
 
pp :: (Show a) => Complex a -> IO ()
pp a = putStrLn . pretty $ a
 
cAdd :: (Floating a) => Complex a -> Complex a -> Complex a
cAdd (Complex a b) (Complex x y) = Complex (a + x) (b + y)
 
cMult :: (Floating a) => Complex a -> Complex a -> Complex a
cMult (Complex a b) (Complex x y) = Complex (a * x) (b * y)
 
cExp :: (Floating a) => Complex a -> a -> Complex a
cExp (Complex a b) e = Complex (a ** e) (b ** e)
 
cMagnitude :: (Floating a) => Complex a -> a
cMagnitude (Complex a b) = sqrt $ (a * a) + (b * b)
 
-- returns Nothing if stays below 2
-- returns Just Int for how many iterations before escaping past 2
_mandelbrot :: (Ord a, Floating a, Integral b) => Complex a -> Complex a -> b -> Maybe b
_mandelbrot _ _ 0 = Nothing
_mandelbrot (Complex zr zi) (Complex cr ci) iter
  | mag > 2 = Just iter
  | mag <= 2 = _mandelbrot (((Complex zr zi) `cExp` 2) `cAdd` (Complex cr ci)) (Complex cr ci) (iter - 1)
  where mag = cMagnitude (Complex zr zi)
 
mandelbrot :: (Ord a, Floating a, Integral b) => Complex a -> b -> Maybe b
mandelbrot (Complex cr ci) iter = _mandelbrot (Complex cr ci) (Complex cr ci) iter
 
main = do
  print $ mandelbrot (Complex (-1) 0.5) 50