Dragon Curve ASCII

dragon.hs

{-
  Plotting the dragon curve
  =========================
       Console Version

  http://en.wikipedia.org/wiki/Lindenmayer_system
-}

import Control.Monad
import Control.Arrow
import Data.List
import qualified Data.Set as S

-- Should be 90 degrees, but just playing with it to see what happenes
angle = pi/2.2

data Direction = X | Y | F | P | N deriving (Show, Eq)

dims = (95,33)

-- Magic number: Itteration of the Lindenmayer transform
main = render dims $ normalise ((fromIntegral *** fromIntegral) dims) $ points $ dragon 12

render :: (Int, Int) -> [(Int,Int)] -> IO ()
render (w,h) l =
  forM_ [0..h] $ \y -> do
    forM_ [0..w] $ \x -> putStr $ if S.member (x,y) s then "X" else " "
    putStrLn ""
  where s = S.fromList l

normalise :: (Float,Float) -> [(Float,Float)] -> [(Int,Int)]
normalise (w,h) l = map ((\x -> round (x * w / maxx)) *** (\y -> round (y * h / maxy))) l'
  where
    minx = minimum $ map fst l
    miny = minimum $ map snd l
    l'   = map (subtract minx *** subtract miny) l
    maxx = maximum $ map fst l'
    maxy = maximum $ map snd l'

points :: [Direction] -> [(Float,Float)]
points l = snd $ foldl' foo (0,[(0,0)]) l
  where
    foo :: (Float,[(Float,Float)]) -> Direction -> (Float,[(Float,Float)])
    foo (a, xs)           P  = (a + angle, xs)
    foo (a, xs)           N  = (a - angle, xs)
    foo (a, xs@((x,y):_)) F  = (a, (x + cos a, y + sin a):xs)
    foo i _                  = i

dragon :: Int -> [Direction]
dragon n = filter (`elem` [F,P,N]) (dragons !! n)

dragons = iterate (concatMap substitute) [F,X]

substitute X = [X,P,Y,F,P]
substitute Y = [N,F,X,N,Y]
substitute x = [x]

{-
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XXXXX XXX    XXXXXXXXXXX XXXXXXXXX          XXXX   XXXXXXXXXX
   XXXXXX      XX XXXXXXXXXXXXXXXX           XXX   XXXXXXXXXX
                XXXXXXXXXXXXXXX XX                 XXXXXXXXX
             XXXXXXXXXXXXXXXXXXXXX   XXXX      XXXXXXXXXXX
             XXXXXXXXXXXXXXXXXXXX  XXXXXX X  XXXXXXXXXXXXXXX
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                XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
              XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX XXXX XXXX
             XXXXXXXXXXXXX       XXXXXXXXXXXXX
             XXXXXXXXXXXXXXXXXX  XXXXXXXXXXXXXXXXXX
               XX XXXXXXXXXXXXX    XXX XXXXXXXXXXXX
                  XXXXXXXXXXXXX        XXXXXXXXXXXX
                    XXX  XXX            XXX  XXX
-}