--http://en.wikipedia.org/wiki/Mandelbrot_set

import System.Environment
import Control.Monad (mapM_)

xmin = -2 :: Double
xmax = 1 :: Double
ymin = -1 :: Double
ymax = 1 :: Double

escapesRec :: Int -> Double -> Double -> Double -> Double -> Bool
escapesRec 0 _ _ _ _ = False
escapesRec iter cr ci zr zi
  | (zr*zr + zi*zi) > 4   = True
  | otherwise             = next_zr `seq` next_zi `seq` escapesRec (iter-1) cr ci next_zr next_zi
  where
    next_zr = zr*zr - zi*zi + cr
    next_zi = 2*zr*zi + ci

escapes :: Int -> Double -> Double -> Bool
escapes iter cr ci = escapesRec iter cr ci 0 0

row xs iters ci = map toChar [escapes (iters+1) cr ci  | cr <- xs]
  where
    toChar b = if b then ' ' else 'X'

rows xs ys iters = map (row xs iters) ys

main = do
  args <- getArgs
  let xstep_str = args !! 0
  let xstep = read xstep_str :: Int
  let ystep_str = args !! 1
  let ystep = read ystep_str :: Int
  let iter_str = args !! 2
  let iters = read iter_str :: Int
  -- row and column values (a little clunky but want to duplicate the other calculations exactly)
  let xs = map (\xc -> (fromIntegral xc)*(xmax-xmin)/(fromIntegral xstep) + xmin) [0..(xstep-1)] :: [Double]
  let ys = map (\yc -> (fromIntegral yc)*(ymax-ymin)/(fromIntegral ystep) + ymin) [0..(ystep-1)] :: [Double]

  mapM_ putStrLn $ rows xs ys iters