Calendar 2015 - 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