Twindragon

dragon.hs

{-# LANGUAGE FlexibleContexts, MultiParamTypeClasses  #-}
{-# LANGUAGE NoMonomorphismRestriction, TupleSections #-}
module Main where
import Data.Complex
import Data.List
import Diagrams.Animation
import Diagrams.Backend.Cairo.CmdLine
import Diagrams.Prelude

main :: IO ()
main = do
  let motion = transformed |>> blured :: Animation Cairo R2
  animMain $ motion <> pure (animRect' 30 motion # fc white)

dragon :: Complex Double -> Int -> [Complex Double]
dragon alpha n = map sum $ subsequences [ recip (alpha^^i) | i <- [1..n] ]

plot eps points =
  position [ (origin .+^ r2 (realPart z/eps, imagPart z/eps), dot c) | (z, c) <- points ]
  where
    dot c = circle 1 # lcA c # fcA c

picture = plot 0.007 $ map (,opaque black) $ dragon (negate 1 :+ 1) 10

transformed = tr <$> interval 0 1 <*> picture
  where
    tr t = rotateBy (3/8 * fromRational t + (1 - fromRational t)) . scale (fromRational t*1.41421356 + 1 - fromRational t)

blured = blr <$> backwards (interval 0 0.25)
  where
    pic = dragon (negate 1 :+ 1) 10
    blr t = plot 0.007 (map (,opaque black) pic) <> plot 0.007  (map ((,black `withOpacity` (t*4)).(+1)) pic)