Here’s a movie of a brilliant, double spiral novelty illusion ring.  It’s available to buy from Grand Illusions, and on that link you can also see another movie of the illusory effect.  As the ring is rotated, it seems to expand when rotated one way, and contract when rotated the other way.

It just may be the kind of ring described in one of the oldest reports of an illusion to have come down to us – a description by the French commentator Montaigne, written nearly five hundred years ago.  In an essay called An Apology for Raymond Sebond he describes …

….those rings which are engraved with feathers of the kind described in heraldry as endless feathers – no eye can discern their width, or defend itself from the impression that from one side they appear to enlarge, and on the other to diminish, even when you turn the ring around your finger.  Meanwhile if you measure them they appear to have constant width, without variation …..

However, there’s another illusion, which is more likely to be the basis for the effect Montaigne describes.  It’s the Zollner illusion, the illusion that gives rise to the wavy wall effects described in our previous post.  As pointed out by Jacques Ninio in his 2001 book The Science of Illusions (page 15), a design on a ring like the one below looks wider at the top than the bottom, but is objectively the same width all the way along.

All the same, Montaigne’s description of rotating the ring makes me wonder which illusion was involved.  So I’m on the hunt for surviving mediaeval rings that might decide the issue. And meanwhile, though there are theories about how the Zollner effect arises, no researcher as far as I know has an explanation for the effect shown in the novelty ring available from Grand Illusions (and other suppliers).  I reckon it’s to do with the way that the highlights expand or contract with rotation, but then seem to carry the outline of the object with them.  This is a puzzle which I will be coming back to.

Who owns the body?   Judith does to start with, but then Holofernes does, and finally, it’s ambiguous.

Here’s a new addition to our series of ambiguous improved artworks.  Apologies this time are due to Rubens.  I got the idea for these illusions from a print by Picasso.

For a downloadable still of the end of our animation …

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Do you see an effect of depth as if looking into a tunnel in the right hand spinning pattern?  It’s a new depth illusion published by Hiroyuki Ito last year.  It’s not all that strong in my example,  but it’s certainly there to my eye, and it gets stronger if you can increase the size of the animation (or try just looking at the animation from much nearer the screen than usual).  I also find the effect is stronger if I fixate the pattern (still in the right hand image) about half way between the outer edge of the disk and the edge of the central disk.

When you look out of the window of a rapidly moving train, objects near the rail track flash across your field of view in a moment, but landmarks on the horizon trundle past slowly.  In between, there’s a steady gradation, with objects moving across the field of view more and more slowly with distance.  It’s not so hard to animate a texture pattern with similar characteristics, moving across the field of view.  For example, texture elements near the bottom of the image might travel rapidly from left to right, whilst elements higher up the image  track across ever more slowly with increasing height.  An animation like that will give a vivid illusion of depth towards the top of the image.

But nobody realised you can also get an effect of depth with pattern elements rotating around the line of sight.  It might be expected, because normally, when a textured disk rotates, texture near the edge rotates fastest, and texture near the middle slowest, rather as with the usual velocity distribution of moving scene elements. However, when the texture is on a disk, so that elements half way up the disk travel just half as fast as elements near the edge, experience tells us we are simply seeing rotation, and so we see the disk as flat, as to the left above.

Hiroyuki Ito had the idea that if the moving texture on a disk was made to spiral, so that the texture near the edge was going much faster in relation to texture near the centre than it does on a simply rotating disk, we might see an illusion of depth.  And so we do.

Specialists with access to a library subscribing to the journal Perception can consult the full text of Hiroyuki Ito’s article.  It’s a great journal, but unfortunately, without access to that kind of (usually university) library, getting the full text will cost you a crazy amount.  It’s a shame academic journals exclude the tiny number of non-professional readers who’d be interested with that kind of deterrent.  However, I’m not sure I haven’t found a free workaround – if it works, I’ll post.

I was in a Picasso show recently and noticed the head of a portrait sculpture apparently turning to follow me as I walked past.  More on the Picasso later, the movie above is my reconstruction of the effect, using the head of the emperor Augustus (I think).  It’s not done by animation.  You can set up a static image of your own head at home, and it will apparently turn to follow you as you walk past, not just with the eyes, but with the whole face.  Just imagine what a comfort that could be for your partner – to have your head always keeping an eye on things whenever you can’t be home yourself.

All you need is to print out a photo of yourself, between a three quarter and a full face view, and then fasten it into a concave shape.  I made my concave shape out of a cheap food container, made of some kind of not too hard polymer, so that I could cut it.  As you can see below, I just added a little convex wing at one edge, so that the shape is not all concave, but a bit serpentine.  When I fixed the trimmed photo in the shape, that makes the face concave, but the ear convex.  I reckon the effect works better overall like that, but you might get better results with a bit of experiment.

The real life version will work best if you view it with only one eye as you pass by, or see it from a distance.  That’s because to see the illusion your brain has to overcome the cues telling it the photo is concave, so that you see the face the way the brain insists all faces ought to be, convex.  But then the perspective transformation of the image as you move past is all wrong for a convex shape, and the face only makes sense if seen as rotating.  The effect is related to the Ames Window, and the hollow face illusion.  There’s also a really good YouTube demo using a dragon head.  (Actually, I’ve only just discovered that, and it’s better than my demo, but don’t tell anyone).

I think Picasso may have been the first person to discover this effect, in 1954.

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To view this illusion, you’ll need the knack of viewing 3D picture pairs without special spectacles, or a viewer – that is, by viewing them cross-eyed. If you haven’t got that trick, and want to try, start with one of our earlier posts on 3D.

If you do have the knack of viewing 3D pictures cross-eyed OK, what you should see in this demo is that, when the room space appears in 3D, the pendulum seems to be swinging in a circle. It’s MEANT to be a web-based demo of a famous pendulum effect you can fairly easily rig up in real life. It’s called Pulfrich’s pendulum, after researcher Carl Pulfrich, who published it in 1922. Here’s how it should work in real life.

You hang up a pendulum, say two meters long, but so that it can only swing from side to side – it must not be free to swing backwards and forwards at all. (Details below on a low-tech way of doing that). You place a reference object under the pendulum, (I use a candle stick), so that the swinging pendulum just misses it, right at the mid-point of the swing. Then you view the swinging pendulum head on, but with a dark filter over one eye. All being well, you should see a really vivid illusion: the pendulum appears to swing not just from side to side, but in a circle. So it seems to swing alternately in front of, and then behind, the centre point marked by the reference object.

The effect, in a real life demo, seems to arise because the brain takes longer to process the filtered, darker signal coming via one eye. The position of the pendulum at each moment therefore appears slightly different in each eye. The effect mimics the signal that would reach the brain if the distance of the pendulum from the eye was varying cyclically. The brain therefore infers that the pendulum is most probably swinging in a circle.

So why is my on-screen version here a fake? Read on to find out.

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Just about our first post was a tessellation tutorial. It was quite comprehensive, but a bit heavy going. I’ve been wanting to post an animated demo, because I reckon that seeing that first would make the tutorial much easier to follow. So the animation is below, but first, a reminder of the basics:

A tessellation is a pattern like the one above. The cells of the pattern fit together like jig-saw pieces, with no gaps and no overlaps. You can’t make a pattern like that out of just any old shape. It only works with shapes whose edges can be snipped into pairs of segments with special properties. The two segments in each pair must be indentical, except that they may be either reflections of one another, or rotated in relation to one another, like the hands of an old-fashioned clock. Confused already? Just watch this animation, showing the evolution of the pattern above, and you’ll see how it all works.

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This is a variant on one of the famous demonstrations devised by USA born Adelbert Ames II, the Ames Window.  Watch the name Adelbert rotate, and it just goes around clockwise.  So does its shadow.  But then watch the name Ames II rotate.  At a certain point, it changes direction, and starts to rotate anti-clockwise. At that point, I find I can see the shadow of Ames II go around either way.

The change in direction appears because what’s rotating is not the name Ames II as it would usually appear on a page, but a perspective view of it. It’s receding into the distance with the A end nearer to us, and large, and the II end further away, and smaller. But that means that as the name rotates, at a certain point the smaller end starts to get nearer to us, and the larger end further away. That’s so contrary to anything that ever happens in everyday vision that our brains won’t accept it.  The instant the smaller end of the name tries to swing past the point at which it would be nearer to us than than the large end, the rotation appears to reverse.  The reversal looks a bit odd, but that’s a price our brains seem happy to pay, if it keeps the large and small ends of the name looking like they’re where they should be.

If my attention is on the Ames II bit of the image, in my periphery strange things also start to happen to the Adelbert bit.  When Ames II changes direction it seems to pull Adelbert around with it.  That’s OK for the first quarter turn, when the letters of Adelbert are seen as if from the back. But once they swing round to a front view, there’s a conflict and I’m not quite sure which way it’s turning.

The demo is just about the opposite of the earlier post with the figure of Mercury rotating.  In that demo, the rotation of the silhouette is ambiguous.  There’s nothing ambiguous about the Ames demo:  the lettering enforces one direction of rotation at any point, even if the result requires an about turn.

There’s a brilliant online demo of the window version with a commentary , and also with a visually baffling added feature, by psychologist Richard Gregory.

Does Mercury look like he’s rotating clockwise or anti-clockwise?  That may depend on whether you look at the left hand figure, or the silhouette.  That right hand silhouette figure can appear to rotate either way round.  Some viewers find that it flips from clockwise to anti-clockwise spontaneously, but others may find it hard to make it flip from one rotation to the other at all.  If it doesn’t change easily for you, try waiting till the outstretched arm is pointing top left, and then try to imagine the hand coming towards you (for an anti-clockwise turn) or moving away from you (for a clockwise one).

When the silhouette figure turns clockwise, it’s rotation mirrors the red figure.  When it flips anti-clockwise, the two figures appear to go round the same way, but with the silhouette figure rotating half a turn out of sync with the red figure. I find the change fascinating, like the figures are doing some kind of old style dance, but two different ways.

The rotation of the right hand figure is ambiguous because in silhouette it presents exactly the same image whichever way it turns. Add the reflections and shadows of the red figure and it can only be going one way around.

I made the individual frames for the animation by taking successive still photos all around a reproduction of the original sculpture.  (The original was made by Italian sculptor Giambologna just over four hundred years ago, and is in a museum called the Bargello in Florence, Italy).

Does the ball sometimes seem to be bouncing, and moving nearer and further away?  Look again just at the track of the ball and you’ll see that all it ever does is to move diagonally from one corner of the board to the other. The spatial effects, and even the way the ball seems to accelerate at points, are all down to the moving shadow. When the shadow sticks to the ball, the ball seems to just move across the surface and into the distance. That’s remarkable, because the ball should appear smaller with distance, but in fact the image of the ball here doesn’t change. The shadow cue is so strong it over-rides the problem. As the shadow drops to the foot of the image, the ball appears higher in the space, but nearer to us. Once again, the effects appear even though the ball does change at all in size, as it should according to the rules of perspective – though some viewers might see an illusion of size-change, compensating for the anomalous lack of real size change.

I’ve tried to base my animation demo pretty closely on one described by Daniel Kersten and colleagues in 1997, in their celebrated original publication of this effect. 

The Dutch tessellation whizz M.C.Escher was fascinated by transformations from one tessellation to another, for example in his series of prints Metamorphosis. I’m sure he would have explored animated versions if it had been practical in the 1940′s. So I’ve borrowed a couple of his motifs and animated them. I showed an animated transformation in an earlier post, but that was between two designs that shared the same kind of symmetry. (See the earlier tessellation tutorial for how these tessellations work. If you like technical detail, my earlier animation was of two motifs based on Heesch tessellation no. 11). Sticking to just that one kind of tessellation meant that the corners of each cell of the design had to remain stationary, and only the edges of the cells transformed. This new transformation is a bit different, because it’s not just a transformation from one motif to another, but between two different kinds of symmetry pattern – Heesch nos 17 and 18 in the tutorial – and the corners of the cells of the pattern are not fixed.

In the earlier transforming animation, the design transformed in space, across the image, as well as transforming in time. If I’ve got it right, (I’m not 100% sure about this), that kind of time plus space transformation is not possible in an animation if the corners of the cells of the tessellation change position, as in my new tessellation above. So in this new animation, there’s no change from cell to cell across the design, and all the cells transform together.

I’m fascinated by the artistic possibilities of these kinds of animation, and one aspect of it is to do with what you might call the dance rhythms of the animation. Here’s a variation on the new animation, speeded up and with an added wave that gives a quite different kind of pulse to the design.

These animations are bit monochrome for the moment – colour is on the way, but I’m on a steep learning curve with file sizes, compression etc.