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import Control.Monad.State
import Data.List.Split (chunksOf)
import System.Random
import Graphics.Rendering.Chart.Backend.Cairo
import Graphics.Rendering.Chart.Easy
import Data.Colour.Names
import Diagrams.Backend.Postscript
import Diagrams.Prelude
randomWalk :: (RandomGen g) => Int -> Int -> State g [[Double]]
randomWalk d n =
get >>=
(\g ->
let (g1, g2) = split g
in (put g1) >>
(return $
take n $
scanl (\x y -> map (uncurry (+)) $ zip x y) (replicate d 0.0) $
chunksOf d $ randomRs (-0.5, 0.5) g2))
drawWalk :: [[Double]] -> Diagram B
drawWalk w = fromVertices $ (\[x, y] -> p2 (x, y)) <$> w
main = do
g <- newStdGen
let (w10, g2) = runState (randomWalk 2 10) g
let (w1000, g3) = runState (randomWalk 2 1000) g2
let (w100000, g4) = runState (randomWalk 2 100000) g3
renderDia Postscript (PostscriptOptions "02.05.01.eps" (dims2D 500 500) EPS) $
foldr1
Diagrams.Prelude.atop
[lc red $ drawWalk w10, lc blue $ drawWalk w1000, lc green $ drawWalk w100000]
let (e1, g5) = runState (sequence $ replicate 10000 $ randomWalk 2 2) g4
let (e10, g6) = runState (sequence $ replicate 10000 $ randomWalk 2 11) g5
renderDia Postscript (PostscriptOptions "02.05.02.eps" (dims2D 500 500) EPS) $
foldr1
Diagrams.Prelude.atop
[ mconcat $
map
(place (lw Diagrams.Prelude.none $ fc yellow $ ((circle 0.01) :: Diagram B)))
(map (\[x, y] -> p2 (x, y)) (map last e1))
, mconcat $
map
(place (lw Diagrams.Prelude.none $ fc black $ circle 0.01))
(map (\[x, y] -> p2 (x, y)) (map last e10))
]
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