Draw Julia Set of f(z) = z^2 + (-0.765+0.12i) by Haskell

julia.hs

import Data.Complex

type R = Double  
type C = Complex R

-- 反復合成の定義
(^:) :: (C -> C) -> Int -> C -> C
(^:) f n = (flip (!!) n).(iterate f)

-- 計算する矩形領域
domain :: [C]
domain = [x :+ y | x <- interval, y <- interval]
  where interval = [-2.0,-1.999..2.0]

-- 反復する関数
f :: C -> C 
f z = z*z + ((-0.765):+0.12)

-- 計算した値をCSVに整形して出力
outputCSV :: [C] -> IO ()
outputCSV zs = mapM_ putStrLn $ map form zs
  where form z = (show $ realPart z)++","++(show $ imagPart z)


main :: IO ()
main = outputCSV $ map snd $ filter condition $ zip (map (f^:100) domain) domain
  where condition z = (realPart.abs.fst) z < 5