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Lepton
2008-Aug-23, 08:32 PM
This is a single grid rotating but your vision will detect 5-6 independent rotations.

http://img264.imageshack.us/img264/452/dorgridfastum6.gif

Moose
2008-Aug-23, 09:04 PM
That's pretty neat. If you want to see the full rotation, just blink your eyes repeatedly.

TrAI
2008-Aug-23, 11:04 PM
This is a single grid rotating but your vision will detect 5-6 independent rotations.
...


Hmmm, I am not to good at explaining this kind of stuff, but I'll try: The darker and lighter areas is kind of a moire phenomena, I made an image that I'll append to this post. It consists of three frames combined, and shows the moire effect quite well.

The apparant rotation looks like a temporal aliasing effect, the angular change of the lines becomes higher than the sampling rate of the animation, so you get some areas where there is little difference between each frame, while other parts have more movement. These overlap with the moire effects, and you get the apparently quiet areas framed by more noisy areas, and a reinforcement of the apparent rotation.

Of course, one should expect strange things to happen when one tries to move a rectangular grid in a circular coordinate system that is simulated on a display unit that uses a rectangular coordinate system. :p:D

cjl
2008-Aug-24, 04:41 AM
I would say it's more an artifact of the framerate of the animation than an optical illusion, after looking at it a bit more closely (including individual frames). If you sped up the frame rate or reduced the spin rate, it would look right.

WaxRubiks
2008-Aug-24, 04:50 AM
I wonder if it would work in real life, with a grid on a spinning piece of paper...

To me, it seems like the brain is breaking up the image into sections, and processing them separately, and then knitting them back together. The sections are slightly rounded and seem to move about.

I can even control the sections consciously, so some extent, as I can when I watch the swirls that you get on a untuned TV. But that would probably give me a migraine if I did it for too long.

If you just let your mind do its magic, without control, I bet it could actually help get rid of a migraine...

cjl
2008-Aug-24, 05:25 AM
I doubt it would work with a physical piece of paper, because as I said, I very strongly suspect that it is a framerate artifact of the animation, rather than an actual optical illusion.

ravens_cry
2008-Aug-24, 05:28 AM
Well, someone get a variable speed moter, some tape and some cardboard and graph paper. That way we don't have to suspect anymore. We will know.

WaxRubiks
2008-Aug-24, 06:47 AM
all you need is some graph paper and an old record player.

I might do it myself.

still then there would be the flickering of the light.

HenrikOlsen
2008-Aug-24, 12:43 PM
It's probably helped by the primitive line drawing as well, anti-aliasing should have been a minimum requirement to lessen artifacts

nauthiz
2008-Aug-24, 02:10 PM
At first glance, it looked to me like part of the issue is that the combination of image size, frame rate, and rotation speed is such that the boxes on the periphery are moving by more than their own size between each frame.

I tested it by marking one square on its course through the animation. It's only a bit over 1/2 of the way out from the center, but there are spots where its position in one frame does not overlap with its position in the other frame. It was actually very hard for me to keep track of the square I was marking as I was stepping through the GIF one frame at a time; there was a fair bit of guess-and-check work.

Anyway, marking one box definitely weakened the illusion, and I suspect that decreasing the amount of rotation between frames by about 70% would make it go away entirely.

Unfortunately the filesize is nearly 1MB and there's nowhere I can upload an image that large to share it (nor can I decrease the resolution without 'breaking' it), so y'all will have to trust me on this. ;)

Lepton
2008-Aug-24, 02:21 PM
Unfortunately the filesize is nearly 1MB and there's nowhere I can upload an image that large to share it (nor can I decrease the resolution without 'breaking' it), so y'all will have to trust me on this. ;)

You can upload it to many of the picture hosting sites such as imageshack and then put it here as an image so we don't have to trust you :)

nauthiz
2008-Aug-24, 02:47 PM
imageshack it is. . .

http://img440.imageshack.us/img440/9837/dorgridfastum6markedep9.gif

alexvorn2
2008-Aug-24, 09:38 PM
and what interesting in this?

TrAI
2008-Aug-24, 10:23 PM
all you need is some graph paper and an old record player.

I might do it myself.

still then there would be the flickering of the light.

Hmmm... As I mentioned earlier, I suspect this may be a temporal aliasing effect, so if you mount a grid on a motor, you may have to use a strobe light to see the effect...

01101001
2008-Aug-24, 11:32 PM
Hmmm... As I mentioned earlier, I suspect this may be a temporal aliasing effect, so if you mount a grid on a motor, you may have to use a strobe light to see the effect...

Yeah. I think rotational motion blur would tell the brain right where the center was and remove the ambiguity. (As would a more-faithful-to-reality animation that realistically portrayed motion blur.)

As for descriptions, like: "This is a single grid rotating but your vision will detect 5-6 independent rotations," I disagree that it is a single grid rotating, for it appears to me a crude animated movie partially simulating similar, one that happens to be actually loaded with ambiguity.

It can be illuminating how a brain resolves such ambiguity, and psychologists spend much time investigating similar effects, but asserting what the response's stimulus "really" is not informative.

I don't think this example is really an illusion, where the typical interpretation is contrary to the facts. This one is just vague.

But, I like vague.

hhEb09'1
2008-Aug-24, 11:51 PM
I don't think this example is really an illusion, where the typical interpretation is contrary to the facts. This one is just vague.I'm not sure what you mean here. On my new monitor (today) I sense about two or three dozen independenly rotating "cells". If I look closely and follow individual lines, it's clear that there is a single point about which everything else is rotating (I can hold my cursor above it, and it does not move).

01101001
2008-Aug-25, 12:12 AM
If I look closely and follow individual lines, it's clear that there is a single point about which everything else is rotating.

I mean the animation is inherently ambiguous. It is not one thing or the other. There's no right and wrong.

OK, I wouldn't but it does look like some classify ambiguous visual stimuli as optical illusions of a sort, but they're not the classic type where appearances are different from reality. The latter are more respectful of the meaning of "illusion".

Edit: The opening description is a bit like saying: This Necker Cube (Wikipedia (http://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Necker_cube.svg/180px-Necker_cube.svg.png)) was really a cube with the bottom surface visible to the viewer. If you can (also) see a cube where the top surface is visible, you're not seeing what is really there.

http://upload.wikimedia.org/wikipedia/commons/thumb/e/e7/Necker_cube.svg/180px-Necker_cube.svg.png

nauthiz
2008-Aug-25, 12:26 AM
If you look closely at other areas, it's clear that there's also a single point that everything is rotating around, albeit not a center point that lies on the intersection of grid lines.

I think much of the ambiguity is because of the frame rate. Squares in the outer portion moving something in the neighborhood of two units per frame according to the "global" interpretation, but at the same time if you're looking at one of the corners it's easier to see a separate rotation centered over there because the brain has an easier time working with an interpretation where each square is moving a little bit between frames than with one where each square is teleporting across a relatively large distance between every frame.

hhEb09'1
2008-Aug-25, 12:37 AM
I mean the animation is inherently ambiguous. It is not one thing or the other. There's no right and wrong.I disagree. See below.
If you look closely at other areas, it's clear that there's also a single point that everything is rotating around, albeit not a center point that lies on the intersection of grid lines.I dunno. When I look close, that doesn't seem to be true. Even better, when I pull away from the monitor, the description in the OP (a solid grid rotating about a single central point) seems like the best desciption.

Delvo
2008-Aug-25, 03:24 AM
If I de-focus my eyes, I get periodic, momentary flashes of four lines, one pair vertical and one pair horizontal, running entirely from edge to edge as in tic-tac-to, but slightly closer to the center than they'd be if they divided the image into even thirds/ninths.

Jeff Root
2008-Aug-25, 08:20 AM
Delvo,

That tic-tac-toe pattern is just a flaw in the individual frames with
horizontal and vertical lines. Those odd lines are two pixels wide.

Old Grapejuice Stain,

The grid certainly is one grid rotating as a whole, but the thing which
causes the illusion is that it jumps between frames, exactly the same
as the backward-rotating wagon wheel illusion. Exactly the same
cause, very similar effect. The reason for the difference of course is
that the grid is rectangular while wagon wheel spokes are radial.

I see quite sharp boundaries between adjacent rotating areas. However,
if I follow along the boundary of one rotating area, I see the boundary in
one place, but if I follow the (same) boundary of the immediately adjacent
rotating area, the boundary isn't necessarily in the same place!

I made a slightly spiffier version. I kept the overal dimensions and grid
spacing, but antialiased the lines and made the steps between frames a
bit smaller. I also reduced the number of frames so that the file is about
40% smaller. The original has 50 frames in 7.2-degree steps; mine has
only 15 frames in 6-degree steps, covering 90 degrees of rotation. The
original is 4 times the size it needed to be.

Rotating grid illusion animation (http://www.FreeMars.org/jeff2/grid1.gif)

I haven't noticed so far that the smaller step size reduces the illusion,
though it might.

Edit to add: Uggh. My browser, on my slow computer, adds an "illusion" of
its own. The screen is broken up into sections very much like the illusion
that is supposed to be there. Maybe if I slow the animation down a bit my
browser will be able to keep up. Anyone else have this problem?

I slowed it down a tiny bit but that wasn't enough. I hope I'm the only
one who can't view my animation properly.

-- Jeff, in Minneapolis

hhEb09'1
2008-Aug-25, 08:42 AM
The grid certainly is one grid rotating as a whole, but the thing which
causes the illusion is that it jumps between frames, exactly the same
as the backward-rotating wagon wheel illusion. Exactly the same
cause, very similar effect. The reason for the difference of course is
that the grid is rectangular while wagon wheel spokes are radial.Explain that a little further. I'm interested, and don't quite understand it.
Rotating grid illusion animation (http://www.FreeMars.org/jeff2/grid1.gif")
Cute!


404 ... A response you sometimes get,
404 ... As you surf across the Net.
404's a shorthand way to say, "Too bad,
But the stuff you want is not here to be had."

404 ... If your typing's not precise,
404 ... "Try again" is my advice.
If you clicked a link to get here from another place somewhere,
Could you back up and send email to the author over there?
Say, "The page you linked to isn't, any more ... 404!"

Moose
2008-Aug-25, 02:33 PM
Explain that a little further. I'm interested, and don't quite understand it.Cute!

I think Jeff means the chemical refresh rate of your cone cells is complicit in the grid rotation illusion. I would expect that as well.

Delvo
2008-Aug-25, 03:48 PM
Both 6 and 7.5 would be rather large increments between frames if the goal were to accurately depict the whole pattern's movement.

For a 400x700 image, the biggest circle which can entirely fit into the image would have a diameter of 400 pixels and thus a circumference of 1256.637 pixels. The distance from center to a corner is the hypotenuse of a 200x350 triangle, which is 403.113 pixels, so the smallest circle enclosing the whole thing (with that diagonal being its radius) would have a circumference of 2532.833 pixels. 6 would be a 60th of either circle, and 7.5 would be a 48th of it.

That means that any feature along the edges of the image must move between 26 and 53 pixels per frame-change if we use 7.5 increments, or between 20 and 43 pixels per frame-change if we use 6 increments. Depending on how you look at it, the little squares are 17 or 18 pixels tall and wide, which gives them diagonals of roughly 24 or 25 pixels, so the distance that each square must move near the edges exceeds the squares' length & width in any case and can be over three times as much at worst, and is barely even slightly under the diagonal length at best and more that twice as much at worst.

It's like trying to watch cars on the highway if they instantaneously teleport forward by two or three car lengths at a time, with other identical-looking cars behind them so that car A always has car B behind it but car B teleports into the space between car A's old and new locations. The discontinuity is bound to make you lose track of which cars are which.

I'm tempted to make a version with 1 or smaller increments between frames which rotates at the same rotational speed, but I suspect it will be too much work...

TrAI
2008-Aug-25, 04:12 PM
Explain that a little further. I'm interested, and don't quite understand it.Cute!

Well, it is a well known effect, but can be rather longwinded to explain, but the articles for the wagon wheel effect (http://en.wikipedia.org/wiki/Wagon-wheel_effect)(this is probably similar to the stroboscopic version, the computer screen is redrawn at a certain frequency, the animation is redrawn at some frequency and so on) and temporal aliasing (http://en.wikipedia.org/wiki/Temporal_aliasing) at Wikipedia may help explain the meaning.

Jeff Root
2008-Aug-25, 07:41 PM
Old Grapejuice Stain,

Did you try again later? At first I had a typo in the URL so that FreeMars
couldn't find the GIF. A few minutes later I deleted the original file and
replaced it with one having a slightly slower frame rate. It works better
in my animation program and in my image viewer than it does in IE.

Moose,

Chemical refresh rate of the cone cells isn't really involved. It is just as
Delvo explains, the farther the lines are from the center, the farther they
jump between successive frames. So the jump near the center of the
image is only a couple of pixels -- much less than the size of a square --
while the jump near the edge of the image can be twenty or thirty pixels
or more -- larger than the size of a square. In parts of the image where
the jump is about equal to the size of a square, you identify one square
in one frame with a different square in the next frame. In the wagon
wheel illusion, you identify each spoke in one frame with a different spoke
in the next frame.

-- Jeff, in Minneapolis

Moose
2008-Aug-25, 08:13 PM
In the wagon
wheel illusion, you identify each spoke in one frame with a different spoke
in the next frame.

Yes, and what, exactly, causes the perception of "frames" in the wagon wheel illusion when you see it happen in real life?

If eyes refreshed literally instantly, you wouldn't lose track of the spokes of the wagon wheel, nor would you from a physical rotating grid like the one the image is emulating. I suspect a physical grid would preserve a similar effect, if it were rotating in almost-time with your eyes.

NEOWatcher
2008-Aug-25, 08:14 PM
Both 6 and 7.5 would be rather large increments between frames if the goal were to accurately depict the whole pattern's movement.
...
I'm tempted to make a version with 1 or smaller increments between frames which rotates at the same rotational speed, but I suspect it will be too much work...
I didn't see what the size of the boxes are, but my thinking is that the rotation must be less than that of a half of a box on the outermost edge of the rotation.

Any box that moves to a position in the latter half (an integral number of boxes plus between a half and whole box) will look like it will go backwards.

For instance if we take the hypothetical distances along a radii.
1) 0.19
2) 0.38
3) 0.57
4) 0.76
5) 0.95
6) 1.14
7) 1.33
8) 1.52
boxes at distances of 3 to 5 will appear to move backwards, and then again starting at 8.

Abbadon_2008
2008-Aug-25, 09:10 PM
There should be a 'CAUTION: Viewing The Image Below, Following Mealtime, Can Result in an Involuntary Gastric Purge' sign for this.

I nearly ejected my BLT and cole slaw onto my brand new laptop.

Neverfly
2008-Aug-25, 09:14 PM
There should be a 'CAUTION: Viewing The Image Below, Following Mealtime, Can Result in an Involuntary Gastric Purge' sign for this.

I nearly ejected my BLT and cole slaw onto my brand new laptop.

The world can't think up Warning Labels as fast as folks out there can think up reasons why one should even be necessary...

Jeff Root
2008-Aug-26, 12:13 AM
In the wagon wheel illusion, you identify each spoke in one frame
with a different spoke in the next frame.
Yes, and what, exactly, causes the perception of "frames" in the
wagon wheel illusion when you see it happen in real life?

If eyes refreshed literally instantly, you wouldn't lose track of the
spokes of the wagon wheel, nor would you from a physical rotating
grid like the one the image is emulating. I suspect a physical grid
would preserve a similar effect, if it were rotating in almost-time
with your eyes.
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

Gigabyte
2008-Aug-26, 12:18 AM
I wonder if it would work in real life, with a grid on a spinning piece of paper...

If I still had that old turntable ...

Delvo
2008-Aug-26, 01:51 AM
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.

Jeff Root
2008-Aug-26, 02:12 AM
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

blackbird
2008-Sep-26, 05:27 AM
O'Reilly's illusion is explained at http://unitaryflow.blogspot.com/2008/09/illusion-of-center.html:

http://i361.photobucket.com/albums/oo56/holotronix/RotatingGridCross.gif

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

http://i361.photobucket.com/albums/oo56/holotronix/RotatingGridFixedPoints65.gif

hhEb09'1
2008-Sep-27, 03:34 PM
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 :)