Calendar 2015 - Lung

Lung

Interlocking space filling curves - in the limit the perimeter between adjacent blocks becomes infinite, like a perfect lung for transferring oxygen from air to blood and carbon dioxide in the other direction. Made with the Haskell Diagrams library:

{-# LANGUAGE TypeFamilies, FlexibleContexts #-}
import Diagrams.Prelude hiding (E)
import Diagrams.Backend.SVG.CmdLine (defaultMain)
import Control.Monad.State (state, evalState)
import Data.Colour.SRGB (sRGB24)

data H = N | E | S | W

data T = L | R

step L = [L,R,L]
step R = [L,R,R,R,L]

seed = [R,R,R,R]

levels = iterate (concatMap step) seed

heading N L = W
heading E L = N
heading S L = E
heading W L = S
heading N R = E
heading E R = S
heading S R = W
heading W R = N

angle N =  90 @@ deg
angle E =  0 @@ deg
angle S = -90 @@ deg
angle W =  180 @@ deg

draw d h = (arcD d a a', h')
  where
    a = angleDir $ angle h
    a' = case d of
            L ->  90 @@ deg
            R -> -90 @@ deg
    h' = heading h d

arcD L a b = arc a b
arcD R a b = scale (-1) $ arcCW a (rotate b a)

draws = mconcat . (`evalState` E) . mapM (state . draw)

base
  = draws (levels !! level)
  # closeTrail
  # pathFromTrail
  # translate (r2 (-1, 0))
  # stroke

left
  = base
middle
  = base
  # scale (sqrt 0.5)
  # rotate (45 @@ deg)
  # translateX (2 ^ (level + 1))
right
  = base
  # scale 0.5
  # translateX (2 ^ level * 3)
  # translateY (2 ^ level)
four
  = base
  # scale (sqrt 0.125)
  # rotate (45 @@ deg)
  # translateX (3 * 2 ^ level)
  # translateY (2 ^ (level + 1))

lung
  = (left # fc r <> middle # fc y <> right # fc g <> four # fc b)
  # rotate ((atan 5 :: Double) @@ rad)
  # centerXY
  # pad 1.01
  # lc black
  # lw 0.1
  # bg white
  # rotate (-90 @@ deg)

y = sRGB24 0xff 0xdf 0x80
r = sRGB24 0xff 0x88 0xaa
b = sRGB24 0xaa 0xaa 0xff
g = sRGB24 0x88 0xff 0xaa

level = 4

main = defaultMain lung

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