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The one you're not looking at turns clockwise

Look at either the red dot or the yellow dot.  The circles near that dot will turn counterclockwise.  The others turn clockwise!

Or: let your eyes bounce back and forth between the two.

Or: look away from both of them.

Puzzle  1: how does it work?

Puzzle 2: who first made this gif?  I can't find the original source.

#illusions  
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I can't tell for sure because every time I look they seem to change but I think it is something to do with the black and white lines that look like they are moving clockwise. 
Ray Lee
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Off-topic: If you defocus your eyes you can make the two of them add up into one of those 3-d illusions in the center. The color of the central dot shifts between yellow and red somewhat fluidly.
 
It doesn't quite work for me in all the described ways, but looking away from both gives me a strong clockwise impression.

It seems to be that the brain is better at seeing the motion of the black and white lines when not looking directly at the animation, and they seem to be fragments of a clockwise rotation. The colour difference in the centre dots is presumably a red (and yellow) herring?
 
+Ray Lee - yes, that's fun.  When I cross my eyes to make the red and yellow dots merge, the circles around this central dot move counterclockwise... but the circles around the other two dots seem to move clockwise... as if they were gears.  Now my vision is messed up. 
 
i find that if i look at a spot midway between the two colored dots, both sets appear to go counterclockwise.

Also, if i slide my focus down from that midpoint, the rotation for both slows, almost seems to stop at some point, and then goes back the other direction.
 
+Samantha Ho - me too!  But if my eye twitches a bit toward one, the other seems to reverse direction.
 
Well, when I defocus my eyes, I see three dots (the middle being bright orange) and three circles rotating like three gears joined pairwise, the outer two counterclockwise, the middle one clockwise
 
Funny you should ask! I spent a few years on picking apart this particular illusion. It was the topic of my dissertation!
https://digital.lib.washington.edu/researchworks/handle/1773/25444

Here's a broad-strokes summary of my explanation.

* There are two sources of visual motion, the circles themselves, and the gratings contained within each circle. If you look closely, you see that the spots move, but the black and white stripes also move within each spot.
* In the red ring, the stripes move in the same direction as the spots (relative to the overall picture, not relative to the spots.) In the yellow ring, stripes and spots move in opposite directions.
* The stripes and the circles are examples of "first order" and "second order" motion, respectively. In first order motion, a light feature in one frame (like a white stripe) moves to and matches a light feature in the next frame, or a dark spot changes position but still remains a dark spot. Most visual animals (at least as complicated as a fly) detect first order motion motion very well.
* However, if the visual system just matched light stripes to light stripes and dark stripes to dark stripes, you wouldn't see the movement of the spots. To see the spots move, a second mechanism has to detect that regions of high contrast (containing both dark and light parts) is changing its position. And humans have separate mechanisms that detect this more complicated type of motion.
* Your brain devotes a lot more matter to processing imagery right where you are looking, than to images coming out of the corner of your eye. When you view an object out of the corner of your eye, the information that gets through visual cortex has been "compressed," to borrow a computer term. So as you switch from looking directly at the yellow spot to viewing it peripherally, you are switching from an, uncompressed to a compressed view.
* If the compression was analogous to just blurring or pixelation, you'd expect to still see the circles moving, because they are larger than the gratings, and the gratings would blur out first! But the compression is more complicated than blurring.
* As it turns out, the compression the brain uses in peripheral vision accounts for first order motion but not for second order motion! Seen from the corner of your eye, the motion of the black and white gratings makes it through, but the fact that this motion was associated with the spots, and the different movement of the spots, is lost.

I'm not sure who made this gif, but it looks like it was adapted from a version of this illusion that Arthur Shapiro made a few years ago. Dr. Shapiro has also studied this type of illusion. Here's his blog entry from then:
http://www.illusionsciences.com/2008/12/rotating-reversals.html
 
+Robert Byrne wrote: "It seems to be that the brain is better at seeing the motion of the black and white lines when not looking directly at the animation, and they seem to be fragments of a clockwise rotation."

Yes, I think that's it.  I bet our peripheral vision is not so good at seeing the contrast between the moving circles and the colored background, since most of our color vision ability is concentrated near the middle.  The contrast between black and white lines is easier to see with peripheral vision... and they're going clockwise.
 
I've always suspected that the Wopld, operates like this ... doing some completely contrary to my expectations when I'm not looking! ;-)
 
Even worse, it's like the one you're not concentrating on turns clockwise. I'm sure it's because I always follow the left quantum branch.
 
+Peter Meilstrup - cool, I'm glad you happened to be around!

"In the red ring, the stripes move in the same direction as the spots (relative to the overall picture, not relative to the spots.) In the yellow ring, stripes and spots move in opposite directions."

I don't understand this.  First, I don't see a "red ring" or "yellow ring".  There's a red dot and a yellow dot.  Second,  the black-and-white stripes seem to be moving in the opposite direction from the circles they're in, both at left (around the red dot) and at right (around the yellow).
 
+Bill Reed wrote: " I've always suspected that the Wopld, operates like this ... doing some completely contrary to my expectations when I'm not looking! ;-)"

Yes - like how it stuck that "p" in "Wopld".  This is also how lints gets under my bed.  It never happens when I'm watching.
 
+John Baez
Sorry, I have a habit of commenting on the run without proofing! My bad. :-)
 
No, it's just the world subverting you.
 
+John Baez
"[T]he world subverting" me? I don't understand; I' a bit of a Solipsist, and also a Masochist apparently, so who's subverting who? ;-O
 
For me it works as you described. However, if I look at one dot (say, red) and at the same time try to concentrate on one of the striped circles around the yellow dot, I can see dots around the red and that particular circle around yellow going counterclockwise. In this case movement of the other striped circles around the yellow is still much harder to comprehend, but mostly they continue clockwise movement.

It seems that I can spend more processing power also to a single thing outside the main focus, but this makes peripheral vision to work even worse.
 
Consistent with the points about peripheral vision but not yet pointed out: you can make both go clockwise if they're both in peripheral vision. 
 
+David Chudzicki Trying to put both in my peripheral vision, what resulted, for me, was both moving counterclockwise. I attempted to move both into my peripheral vision by moving my head to my left and so the most direct view was in my right eye. Now, I am left eye dominant and so I'm wondering if eye dominance could be part of the explanation?
 
And it seems to me that the background is rotating at a higher speed than the circles. Maybe that leaves a nonzero net speed in the clockwise direction?
 
"Yellow circle" is a sloppy shorthand for "the ring of elements around the yellow disk," and you're right, they are both opposite! The difference is that the stripes around the yellow dot are faster then the ones around the red. I hadn't noticed that in this version, but it's consistent with the part of my thesis I thought I could skip summarizing :)

So: each circle at the center of vision appears to move counterclockwise, with the spots. Put them way out in the periphery like 45 degrees, and you see both clockwise, moving with the stripes (with the right ring faster.) It's at some intermediate distance from the center of vision where you can get the rings turning different directions, depending on how strong the difference is between first and second order motion. (And where that balance is varies a lot from person to person.)

The strange part is that in some situations you can add clockwise first order and clockwise second order motion and get counterclockwise appearance! I have only speculation for why that could be, but it happened for all but one of my observers to some extent. I suspect whoever made this .gif found the same thing and adjusted it to avoid that effect.
 
If you keep them just in peripheral vision and then move your vision a tiny bit closer to one of the dots you can make it seem the spots will collide!
 
After watching this for a while now, the effect has disappeared. Disappointing.
 
While reading the text at the top of this post, I can see that both are turning clockwise, but not when looking directly at them.
 
When I look at one and concentrate on the other, the other still flickers but I can slow its rotation and even stop it rotating.
 
This one is really amazing. works all the time !! :)
 
Okay, here's how it really works.   I've written a program that takes over the camera on your computer, detects which dot you're looking at, and turns the circles accordingly.
 
I commented earlier that after extended observation the effect seemed to have disappeared. Now the effect is back.
 
+Bill Reed - I turned the software back on.
  Just messing with you.
 
If I view it in stereogram mode, everything stopped.
...oh wait, my computer just froze on the refresh.
 
Hrm, they always both turn CCW to me. :(
 
When I look in the middle the left one turns both counter-clockwise on it's near side, AND clockwise on its far side. The right one just goes counter-clockwise. I wonder if this is because I'm right eye dominant (well the brain does the processing).
 
I know this, its a game of brain
 
Rotating dots are like wholes, behind them is circle with stripes which seems as it turns in the opposite direction (it is static in fact). When I focus on the dot in the center, moving dots are perceived correctly, because that is the shape I give myself highest priority. When I focus on periferal surface or other dot, perifery is just surface and so I perceive the striped circle rotating behind the wholes. (here the vision fails for me)
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