Well, on the downside, I run Linux, so I can't run windows code native. On the upside, I can't run windows viruses native... so I ran it. Also, my virusscanner gave it a clean bill, and it looks like a legit site, but... make your own call. As for the illusion itself, I had to try it several times to get the effect. When you say "stare" you need to be more specific. You can't just keep your eyes not moving and pointed at it. You have to have it in focus and also not be too close... the majority of the image needs to be in your forward (non-peripheral) vision. Also, for me, it took a lot longer than 30 seconds to get a noticable effect when I looked away.
The reason is that your eyes have a built-in mechanism to prevent just such a thing. Since sometimes people have imperfections in their eye or retina (everyone has the nerve dark-spot) your brain adapts so that percieved imput doesn't show such static things. Of course, if you stare without your eyes moving for long enough, those same adaptions can actually make objects in the real world disappear from your perception. To prevent that, your eyes have tiny muscles that do nothing but basically "tap" your eye from time to time, making your view shift just slightly, thus preventing your brain from editing out anything that's not part of your eye (which wouldn't "move" even when your eye twitches.) Concious effort can overcome those twitches though... It's easier in a darker room too. I've actually had a window with the blinds closed, and the faint light from outside casts a soft glow on it. If I stared at it long enough, the window would vanish entirely, and the whole room would feel perfectly cave-dark, even though my eyes were open, and there's actually enough light to see anything in the room. Soon as I blinked or moved my view in the slightest, everything instantly came back. This effect seems to utilize the same mechanism. The spiral basically looks like it's "rippling waves" from a center. So while your brain can't edit the whole thing to nothing (it's moving) it can still adjust average values. That effect lasts a few seconds when you look away, and your brain is still doing the adaptation trying to cancel out the "ripples" but now the thing you're looking at has none, so your brain actually creates them in inverse.