*updated 7/10*

The following is an interesting example of Temporal Aliasing I discovered while working in 3d software.

A large grid seen rotating at a certain speed will appear to group itself into smaller grids, spinning independently.

In this example, we see a central grid, and 3 or 4 orbiting it. To prove it’s one grid, stand back from your monitor.

The illusion/effect has been picked apart by several sources, some intelligent professors and many more angry students have contacted me about it. MIT‘s Fredo Durand gives probably the easiest to understand explaination:

You are trying to capture a motion that is too fast for the framerate you’re using. In the case of a spinning wheel, what happens is that the wheel might turn, for example, 350 degrees between two frames but your eyes interpret it as -10 degrees. A similar thing happens with your grid. At the periphery, the lines move by more than one grid cell between two frames and the resulting visible motion is “snapped” to the smallest possible motion. The correct way to prevent such artifacts is to make sure that the shutter of the camera is open during the full interval between two frames, so that motion that is too fast gets blurred.

Further detail by Professor Berthold Horn (also from MIT):

“Perhaps an illustration of how we seem to interpret rotational
motion as taking place about points near the center of the field of view,
if possible, or so it seems to me. As I move my gaze around,
I tend to pick up apparent rotations about points near the center
of the current view (where temporal aliasing permits).

Reminds me of an apparent higher ability to detect symmetries in
patterns when the axis of symmetry passes near the center
of the field of view, or the center of symmetry is near the center of
the field of view.

Could it be that circuitry for detecting symmetries is expensive and
would need to be replicated for different centers of symmetry?
Which might suggest that there is good circuitry for “central” symmetries.
Others are found or at least verified by shifting the gaze…
Perhaps something similar applies to rotational motion.  Although,
we’re very good at picking up rotational motion from peripheral vision…”

Mathematician Cristi Stoica made this amazing one which has 2 centres.

and this, which has 4 centres…

he writes:

If we rotate the grid at each step with an angle of 360/n, the center is the only point containing all the time vertices of the grid (except, of course, the case when n=1, 2 or 4, when no rotation is viewed). But if we are good enough at math, we can modify the animation such that we obtain more than one fixed point….

The animation above is based on some properties of the number 65. This number plays the role of the hypotenuse in eight Pythagorean triples:
65²=16²+63²=25²+60²=33²+56²=39²+52²=52²+39²=56²+33²=60²+25²=63²+16².

Also:

Interesting discussions at reddit, abc science, bad astronomy

Japanese page with flash applications

Variations made by someone named Theeth (here and here)

seanaltogether created these interactive flash rotating grids: here and here

My original images:

Here there appear to be about 5 or 6 grids.

at a lower frame-rate it looks almost like liquid.