At first, she was spinning clockwise and then when I started to read the text, she switched over to counter-clockwise and now I can’t get her to go clockwise again.

I must have mutant eyes, because the animation in the OP does absolutely nothing for me. I’ve stared at it with my glasses off and on, with the lights on or off, and there’s just…nothing. The best I can get is a vague sort of after image of it, but nothing else. Definitely no illusions of movement or size change. Now I feel all left out.
Really?
Not to sound like an absolute idiot but:
Did you stare at the center? I find that staring, not looking hard, at the center works best. You do have to wait about 20-30 seconds.
A lit room is *much *better.
What’s supposed to happen is things around you will become distorted and they will move in a wavelike motion. It is noticeable, but I have not managed to hold this effect for more than 7 seconds.
So it might be brief(er) for you.
Au contraire!
I went to your link and kinda blew past the instructions, so I watched the pattern for several minutes thinking, “This is it?” Then I remembered the part about looking at it and then looking away.
Whoa! Trippy!
Thanks for posting the link.
This is the same thing, but its on youtube, and the pattern of movement varies slightly, follow the video instructions.
If this does not work for you, then it simply won’t. Some people can’t see certain optical illusions.
There is NO scary moment in this moment, I’m not a jerk.
Hope this one works for ya’, its silly fun:
Oh and FYI, if you can manage to wait a full minute or more, the effect will be more intense, but will not last much more, maybe 2 seconds more max.
The first link does nothing for me. I see some gray and white lines twirling and a black and white striped box up top wavering, but that’s it.
What is it supposed to do? I looked at the black and white box for 20 seconds and then looked away at the wall in my computer room. Nothing.
I clicked on “get trippy” and while that is some animation, it didn’t make me hallucinate either.

I absolutely dig the OP’s link. I was a bit skeptical, looked at the opposite blank wall, thought "hmm… a bit of color. . .’ and then looked at a framed picture on the close wall and thought “oh, hell, I’m back in college!” It’s very much like the “the walls are breathing” effect one gets eating certain chemicals.
Stare at the center of this image (the ***middle ***part where everything merges into a sqaure) for 20 seconds or more, just look at the middle.
Keep looking.
Once its over, stare at the walls or at any surface and move your head around, you will see things twist and enlarge and shrink afterwards.
Have the room well lit.
If not try the Youtube link I posted, it might be better.
Tell me if this helps.
I’m a lefty, and any time I see this illusion, she always goes clockwise first.
If I concentrate long and hard, I can flip her. Now, using a modified version of Whynot’s trick, I can flip her instantly. (instead of focusing on her foot, I focus on the shadow of her foot to flip her.
Okay People, last trippy link, this one is made with circles not with squares and may be more intense for some of you:
Whoa.
My teddy bear is breathing!
This is the only way I can get it to switch back and forth, almost like her foot were the hand of a watch the hand of a clock.
And in case anyone is still keeping score, she was moving counter-clockwise for me first.
Anyone?
Woah. I just stared at it for about a minute, then looked up at the framed photo above my monitor. Bits of it enlarge and shrink in a weird pulsating way. Cool! 
It absolutely worked for me, and reminded me a lot of the visual effects I sometimes got after dropping acid back in the day.
Kind of like watching more distant objects with a bonfire between you and them, like rising heated air was making the image waver.
Oh, and I agree, just keep watching dead center of the animation and then pull your eyes aside to something else in the room.
I saw the dancer moving Counter-Clockwise at first.
I was finally able to get her to switch by completely shielding the rest of her body with my hand and focusing just on the pivot foot.
Whatever way I saw her going last is the way I see her if I close the page and load it back up.
For the record a co-worker saw me staring stupidly at the computer and asked what was going on… so I told her. She was able to make her switch fairly easily, while I was still having problems with it. (Just to get out there as evidence that I and a co-worker were able to see the spinning girl in different directions while looking at the same illusion. She- in fact, able to get her to spin while I could only see it in one direction.)
Frustrated Wonderer- your hallucination links give me headaches… and yet I can not look away