gumowski-mira attractor

Here's an unusual chaotic attractor: the web doesn't seem to have much information on this one, except that it was invented to model particle trajectories in physics. A google image search for 'mira fractals' does turn up some pretty results though.

The system seems to give interesting results only when b is close to one. It behaves less chaotically when b > 1 is fixed, so you can actually animate it - click the thumbnail to see.

	import Control.Arrow ((***))
	import Graphics.UI.SDL as SDL
	(xres, yres) = (200, 200)
	main = withInit [InitVideo] $ do
	w <- setVideoMode xres yres 32 [NoFrame]
	enableEvent SDLMouseMotion False
	setCaption "Gumowski-Mira" "Gumowski-Mira"
	loop w p pss
	where
	p = (xres `div` 2, yres `div` 2)
	pss = map points [0.31, 0.3101.. 0.316]
	loop w p pss = do
	render w p $ map (round *** round) $ head pss
	e <- pollEvent
	case e of
	KeyUp (Keysym SDLK_ESCAPE _ _) -> return ()
	_ -> loop w p $ tail pss
	render w (x,y) ps = do
	s <- createRGBSurface [SWSurface] 2 2 32 0 0 0 0
	fillRect w (Just $ Rect 0 0 xres yres) (Pixel 0)
	mapM_ (draw s 0xFFFFFF . rect . center) ps
	SDL.flip w
	where
	center = ((xres - x) +) *** (+ (yres - y))
	rect (x,y) = Just $ Rect x y 1 1
	draw s c p = do fillRect s Nothing $ Pixel c
	blitSurface s Nothing w p
	points a = take 650000 . map (h *** h) $ iterate f (12, 0)
	where
	f (x,y) = let x' = b*y + g x in (x', -x + g x')
	g x = a*x + (2 * (1 - a) * x^2) / (1 + x^2)
	(b,h) = (1.005, (* 4))

view raw gumowski-mira.hs hosted with ❤ by GitHub