H.Vogel’s pattern for sunflower forets.
> import Diagrams.Backend.SVG.CmdLineA representation of Vogel’s model for the floret pattern of a sunflower head. Vogel, H (1979). “A better way to construct the sunflower head”. Mathematical Biosciences 44 (44): 179–189. doi:10.1016/0025-5564(79)90080-4.
> {-# LANGUAGE NoMonomorphismRestriction #-}
> import Diagrams.Prelude
> import Data.Colour.Palette.BrewerSetThe n florets of the sunflower are positioned at radii proportional to the square root of n and rotated by a factor 2.4 radians in accordance with Vogel’s model.
> mkCoords :: Int -> [P2 Double]
> mkCoords n =[coord (fromIntegral i) | i <- [1..n]]
> where
> coord m = p2 $ fromPolar (sqrt m) (2.4 * m)
> fromPolar r theta = (r * cos theta, r * sin theta)The color of each floret is based on it’s radius.
> floret :: Double -> Diagram B
> floret r = circle 0.6 # lw none # fc (colors !! n)
> where
> n = floor (1.4 * sqrt r) `mod` 10
> colors = black : (reverse $ brewerSet YlOrBr 9)> sunflower :: Int -> Diagram B
> sunflower n = frame 4 $ position $ zip (mkCoords n) (florets n)
> where
> florets m = [floret (sqrt (fromIntegral i)) | i <- [1..m]]> example :: Diagram B
> example = frame 4 $ sunflower 2000 # bg black> main = mainWith (example :: Diagram B)