There were at least two threads in General Science discussing this.
I gave what I am satisfied is the correct explanation in one of them.

I have only ever seen actual turning wagon wheels or the illusion
on TV, in which the illusion is caused by the strobing frames of the
TV picture, in exactly the same way that it is produced by strobing
frames of the animations in this thread.

I have seen the effect in "real life" that I think you are talking about
on car hubcaps and a ceiling fan. It is essentially the same as the
wagon wheel illusion, but the strobing is provided by reflections from
shiny parts of the rotating objects. This was made clear by looking
at the slowly-rotating ceiling fan under the right lighting conditions.

If the rotating object is shiny and has repeating shapes around its
circumference, like spokes on a wheel or blades on a fan, light from
one direction, such as direct sunlight or a lamp, can be reflected off
a portion of that shape each time it is in the same position relative
to the light source and your eye. If you, the rotating object, or the
light source are moving linearly relative to the other two, the position
of the rotating part which reflects the light to your eye will change.
That can make the rotation appear to be backward.

I watched a ceiling fan when sunlight was shining on a narrow sidewalk
just outside the windows of the room with the fan. The sunlight was
reflected from the sidewalk through the window onto the underside
of the fan blades. When the blades were in the right position, a line
of sunlight was then reflected to my eyes from the shiny surfaces of
the blades. This appeared as a relatively bright flash. The rest of
the time, the blades were only dimly lit by the ambient light in the
room. As long as I stayed in one position, the light was reflected
from the blades every time they were in the same position. Let's say
it was when the blades passed through the 2-o'clock position. If I
moved over a ways, I would see the flash in the 3-o'clock position.
If I walked past the fan, I would see the position of the reflection
rotate forward or back, just like the wagon wheel illusion.

-- Jeff, in Minneapolis

__________________
http://www.FreeMars.org/jeff/

"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"

"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves

If I still had that old turntable ...

__________________
smile, and the Universe smiles with you

This is different from the wagon wheel or car wheel in that the wheel's motion is actually smoothly continuous, and other factors chop it up into distinct moments at certain intervals, whereas in the animated image, the actual motion is already inherently chopped up into distinct moments at certain intervals, so no other sources of interferences are necessary to explain why it would look that way.

I did make an animation that proceeds 1° at a time, but that turned out to be the easy part. GIMP is mysteriously insisting on a slow frame rate, so I can't get the rotation speed to be as fast as the rotation speeds of prior examples here. And because so much of the image changes in consecutive frames, the file is over 4 MB anyway, and I don't have a website to host it on. So it won't be posted here unless somebody wants me to email it to him/her and is able to increase the frame rate and host it elsewhere.

Delvo,

The point is of your first paragraph is not apparent. A strobe mechanism
needs to be present, but it doesn't matter what the mechanism is.

I can see the effect just by looking at two consecutive frames. I don't
need the full-circle animation.

-- Jeff, in Minneapolis

__________________
http://www.FreeMars.org/jeff/

"I find astronomy very interesting, but I wouldn't if I thought we
were just going to sit here and look." -- "Van Rijn"

"The other planets? Well, they just happen to be there, but the
point of rockets is to explore them!" -- Kai Yeves

O'Reilly's illusion is explained at http://unitaryflow.blogspot.com/2008...of-center.html:



where you can also find a rotating grid with two centers:

Cute. He says it is based upon the number 65, which figures in 8 pythagorean triples as the hypotenuse. Actually, it figures in 4, but I can see what he means. However, I think he also uses 65² = 0² + 65², or vice versa