{- Heighway dragon.  See http://en.wikipedia.org/wiki/Dragon_curve. -}
module Main where

import Graphics.Rendering.Diagrams
import Control.Monad.State
import Data.Maybe

dragonStr :: Int -> String
dragonStr 0 = "FX"
dragonStr n = concatMap rules $ dragonStr (n-1)
  where rules 'X' = "X+YF+"
        rules 'Y' = "-FX-Y"
        rules c = [c]

strToPath :: String -> Path
strToPath s = pathFromVectors . catMaybes $ evalState c (0,-1)
  where c        = mapM exec s
        exec 'F' = Just `fmap` get
        exec '-' = modify left >> return Nothing
        exec '+' = modify right >> return Nothing
        exec _   = return Nothing
        left (x,y)  = (-y,x)
        right (x,y) = (y,-x)

dragon :: Int -> Diagram
dragon = lc red . curved 0.8 . strToPath . dragonStr

main = renderAs PNG "dragon.png" (Height 500) (dragon 14)