> import Diagrams.Backend.SVG.CmdLine
This is a transcription in Haskell of "Hex Variation" by William Kolmyjec.
The algorithm itself is inspired by [the version of Steve Berrick](http://recodeproject.com/artwork/v3n4hex-variation), from the
[Recode project](http://recodeproject.com).
> {-# LANGUAGE NoMonomorphismRestriction #-}
>
> import Diagrams.Prelude
> import System.Random
We first define the parameters of the tile, which is hexagonal. The side of a
hexagon is the radius of its circumscribed circle, here taken as 1.
The apothem is the distance from the center to the side:
> h = sqrt(3)/2
We define the difference between the radius and the apothem:
> h' = cos(pi/3)
We then define a tile. The hexagon is not actually shown but inside are two
arcs, along with a vertical line. To see the tiling, you can add an hexagon in
the list below:
> hexagon' :: Diagram B
> hexagon' = mconcat [arc1 # translateX (-1)
> , vrule (2*h)
> , arc1 # rotateBy (1/2) # translateX 1
> ]
> where
> arc1 = arc' 0.5 (xDir # rotate (-pi/3 @@ rad)) (2*pi/3 @@ rad)
In the final tiling, the tiles will be rotated randomly with angles in $\{0,
\frac{2 \pi}{3}, \frac{4 \pi}{3} \}$.
> rotateHexagon' :: Int -> Diagram B
> rotateHexagon' n = hexagon' # rotate (n'*2*pi/3 @@ rad)
> where
> n' = fromIntegral n
The tiling is created from a list of centers, defined here:
> centerPosition :: Int -> Int -> (Double, Double)
> centerPosition x y
> | (x `mod` 2 == 0) = ((2-h')*x', 2*y'*h)
> | otherwise = ((2-h')*x', (2*y'-1)*h)
> where
> x' = fromIntegral x
> y' = fromIntegral y
The function generating random angles with a fixed seed:
> generateAngles :: [Int]
> generateAngles = randomRs (0, 2) (mkStdGen 31)
Finally, the tiling is created here:
> hexVariation :: Diagram B
> hexVariation = position (zip (map p2 pos) (map rotateHexagon' angles))
> where
> pos = [(centerPosition x y) | x <- [0..nb-1], y <- [0..nb-1]]
> angles = take ((nb+1)*(nb+1)) $ generateAngles
The envelope of our tiling is `nb*1.5*side + 0.5*side` in width and `nb*2*h+h` in
height. We remove the "corners" to avoid "holes" at the borders of the figure
and define the new width and height:
> width' = nb*1.5 - 0.5
> height' = nb*2*h - h
Which are used to "clip" the figure here:
> nb = 12
> example :: Diagram B
> example = hexVariation # center # rectEnvelope x0 u0 # rotateBy (1/4)
> where
> x0 = p2 (-width'/2, -height'/2)
> u0 = r2 (width', height')
> main = mainWith (example :: Diagram B)