hénon attractor

French astronomer Michel Hénon reported on this strange, fractal attractor in 1976. Since then, it has been among the most studied examples of chaotic dynamical systems.

	{-# LANGUAGE NoMonomorphismRestriction #-}
	import Graphics.UI.SDL as SDL
	(xRes, yRes) = (1366, 768)
	(a, b) = (1.4, 0.3)
	main = withInit [InitVideo] $ do
	w <- setVideoMode xRes yRes 32 [NoFrame]
	s <- createRGBSurface [] 1 1 32 0 0 0 0
	fillRect s Nothing $ Pixel 0xFFFFFF
	enableEvent SDLMouseMotion False
	setCaption "Hénon" "Hénon"
	render w s henon
	SDL.flip w
	run w
	run w = do
	e <- pollEvent
	delay 64
	case e of
	KeyUp (Keysym SDLK_ESCAPE _ _) -> return ()
	_ -> run w
	render w s = mapM_ draw
	where
	rect (x,y) = Just $ Rect (round x) (round y) 1 1
	g (x,y) = (500*x + xRes / 2, 900*y + yRes / 2)
	draw (x,y) = blitSurface s Nothing w $ rect $ g (x,y)
	henon = take 99999 $ filter g $ iterate f (0,0)
	where
	f (x,y) = (1 - a*x^2 + y, b*x)
	g (x,y) = -1.5 < x && x < 1.5 && -0.45 < y && y < 0.45

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