I’ve been wanting to do a new version of my earlier post of The Twisted Stairs.  That’s partly because the way I placed the figures in the original posting, they got in a bit the way of seeing the twist in the lateral flights of stairs. I reckon you can see the twist effect better now, as they transform from stairs seen from below (at the top by the balcony), to stairs seen from above (down at floor level). I wanted to see if I could get it right, because this is an impossible stair effect that maestro M.C.Escher never used. Sometimes his staircases as a whole can be seen either as from above or from below, but they don’t twist from one viewpoint to the other half way up. As I mentioned in the earlier post, I reckon that’s because the twist effect depends on fudging the perspective, and Escher didn’t do fudge. His perspective is almost always miraculously lucid.

Another reason for a new version is that I wanted to produce a high resolution version, suitable for giant 35 x 23 inch posters. As ever, you are welcome to use downloads of the image here for any private purposes, but if you wanted to think about buying a framed print, or giant poster, here’s where to take a look.

There are more technical details on the original post. I borrowed the figures for this new version from Durer, Pieter Brueghel the elder, and Hogarth.

Woops, slight technical glitch with the original post of this, just before Christmas. So this is a re-posting of the third of our animated illusion cartoons, Chicken and Leaf. It may still run jerkily on first run through, should be OK second time around.

You can also view Chicken and Leaf as a
Quicktime Movie

You can also see our this cartoon along with the previous ones in our Animated Illusion Cartoon category.

This cartoon ends with a special effect – a tessellation that transforms in space and in time. Tessellation (or tiling) wizard M.C.Escher was brilliant at these transforming patterns, as in his Metamorphosis prints. I’m sure he’d have done animations of those if he could, but without a computer they’d have taken years. In my animation there are two sequences of transformations, first where the pattern morphs in sync all over the screen – a number of people have done those – and then the one that morphs across the image as well as in time.  I’m not aware anyone else has done one of those.  Please let me know if so, I’d love to see it – and otherwise, I hope if you’re an animator you’ll be provoked into doing a better one than mine.

Eyespots are fascinating. Nature presents all sorts of camouflage and mimicry, but mostly when prey species look like harmful species, or are camouflaged against background, or imitate leaves, or when seahorses look like seaweed (sea dragons). The imitation then is in 3D, like a waxwork. But eyespots are nature’s only example of patterning that becomes a picture. Eyes in real life tend to be quite rounded and beady or bulging, but butterfly eyespots are flat. Yet they can be amazingly convincing, like the ones at the top of this picture of a peacock butterfly, complete with illusionistic highlights.

And apparently birds really are deceived by the eyes.  A study five years ago by Adrian Vallin and colleagues at Stockholm University demonstrated that butterflies with eyespots covered up really are much more likely to be eaten.  Apparently, the Peacock butterfly tends to rest with wings folded, looking a bit like old leaves, but when threatened suddenly spreads its wings to reveal this alarming mask.  It even makes a noise as well.

But when you look at lots of eyespots it gets more puzzling.  For example, the eyespots that are top in this picture look very realistic, but then the ones lower down are a bit of a mess.  Generally, looking through pictures of lots of eyespots, there’s the same spectrum from very illusionistic to very approximate.  Do they all work in the same way?  And then, the most illusionistic eyespots of all are maybe the ones on the underneath of the wings of the owl butterfly.  But birds only see those when the butterfly has its wings folded, so that only one eyespot is visible.  (Or does the owl butterfly lie on its back with its wings open when it’s depressed?).

So when the birds are frightened by eyespots, are they just responding to a stimulus on the retina that’s a bit like the pattern of stimulus from real eyes, so that even appoximate eyespots will do?  If so, why have some eyespots evolved to be so illusionistic?  Maybe the messy spots, like the ones lower down my photo, are transitional forms.  But if the illusionistic eyespots, complete with highlights, are more effective, can we then say that the birds are being deceived by pictures?  I don’t think there’s another example of a non human unequivocally understanding a picture. Reflections in a mirror, yes.  That was established amongst others by by Frans de Waal of the Yerkes primate research centre in Atlanta. But not pictures. Sure, there’s the the story from ancient Greece, of the contest between the painters Zeuxis and Parrhasius, when the painter Xeuxis painted grapes that were so realistic the birds swooped down to try to eat them? But I don’t believe it. I don’t think animals and birds do understand pictures.

Except maybe of eyespots.

Update January 7th 2010!  Turns out I’m wrong about animals – dogs anyway – and pictures!  Read on for the details.

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You’re welcome to download and use for private purposes any of the imagery on the site, except for a very few pictures where I indicate that third party copyright might apply. But if you’d like a giant, 35 x 23 inch poster, full of illusions, you can buy it (along with loads of illusions on bags, T-shirts etc.) from www.Cafepress.co.uk/optoct. I was delighted when I saw the quality of the poster. Each of the illusions is identified with a discreet caption line, so that you’d be able to follow them up on this or other sites.  And of course, lots of these illusions are brand new versions, often with an extra twist of some kind.

Illusions make brilliant gifts.

You’ll also find a poster of the whole of my optical illusion cartoon story.  If you’d like to preview that, read on.

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Here are a couple more variants of the Poggendorff illusion (mog, or moggy, by the way, is a term of endearment for a cat in UK English, but I’m not sure it’ll be familiar if your background is in American English). The symmetry axes of the dog and cat heads are objectively aligned, but to my eye appear displaced in much the way that the (objectively aligned) test line appears to be in classic versions of the illusion (as in pale blue, to the left).

I’ve added the blobs to the dog version, and the pigeons to the cat figure, because I have the impression that they make the illusion a little stronger. However, I haven’t tested that experimentally with these figures.  It’s also interesting to try deleting the images progressively, to see how much can be deleted before the illusion vanishes. Maybe there are conventional Poggendorff figure elements embedded in these figures in a way I haven’t realised.

For example, it’s well established that the illusion can arise when the usual line elements are reduced just to dots, (the dot version that might apply here is Stanley Coren’s – scroll down that link to view it). It would be possible to selectively erase the figures here until just dots were left. But reduced to dots the illusion is very weak, and here it looks quite robust to me.

I think it is the symmetry axes that are taking the place of the usual test lines here.  For me, that makes it that much more likely that the illusion arises because of two dimensional pattern elements.  (However, many specialists don’t agree, and attribute the illusion to attempts by the brain to interpret Poggendorff figures as arrays of lines in depth).

I have a special interest in this illusion, and you’ll find stacks more on it by clicking on the Poggendorff illusion category, in the categories list to the right.  I have ideas about what I think might be going on – but actually, I don’t rate them all that highly. Sometimes in science, when a problem resists progress for a very long time, (over a century in the case of this illusion), so that there are all sorts of ingenious competing explanations, it’s a sign that something is going on that nobody’s even begun to imagine.  I think that could well be the case with Poggendorff.

This is one of the oldest ambiguous images I know. It’s a small clay mask from Mesapotamia, (in modern day Iraq), made about 3750 years ago. It’s the face of the giant Humbaba, but as he might have appeared to a soothsayer, looking into the writhing entrails of a sacrificed animal for purposes of divination. If the face of Humbaba appeared in the entrails, in the way we sometimes see a face in clouds, it was a sign of revolution on the way. This evocation of the experience is in the British Museum, and they have a web page about it. (They even know the soothsayer who made it …).

I’ve written in earlier posts about the way that artists often seem to use perceptual puzzles as a starting point for aesthetic and emotional effects in artworks. This is a particularly fascinating example. It’s a work of art, but it’s also a record of emotional effect arising out of a perceptual puzzle, an ambiguous image, in a quite different kind of activity – divination. If I’ve got it right, quite a lot of fortune telling starts with ambiguous visual discoveries like this, when peering into tea-leaves, or crystal balls. I wonder how deep the common roots of aesthetics and shamanistic experiences go.

One route you can trace is through the entrails. You can’t quite be sure in this image, but when you look at the real thing, so you can look round the edges, the face is made up of one continuous entrail, coiling to and fro. If you can get to the British Museum, it’s in a case in their new Mesapotamia gallery, but you may have to hunt around, it’s not big.

This is a brilliant illusion discovered by Baingio Pinna of the University of Sassari in Italy.  The circles appear to spiral and intersect, but are in fact an orderly set of concentric circles. The illusion is due to the way the orientation of the squares alternates from circle to circle, and that contrast alternates from square to square within each circle. The illusion is related to the movement illusions of Akiyoshi Kitaoka and to twisted cord illusions.

What’s going on is suggested by this next version, with the edges enhanced, plus a bit of blurring.

This image approximates (with false colour) the data transmitted within the brain once the image has been filtered by cell systems early in the visual pathway, including centre-surround cell assemblies (a bit technical, that link). The role of these is to enhance edges, so that bright edges are now emphasised by dark  fringes and vice versa. Note that between the little stacks of alternating light and dark fringes, along the line of the circles, the dark fringes of bright squares align with the dark edges of adjacent squares and vice versa. The scale and spacing of the squares is just right to get that alignment, and as a result the effect enhances the inward turning, spiralling effect due to the orientation of the squares. The fringes combine to give an effect a little like interfering waves. The illusion seems to be bamboozling processes that are usually superbly effective at filtering out the key information about edges and their orientation in the visual field.

However, showing that centre-surround cell outputs could be enhancing the inward turning character of the lines forming the large circles doesn’t explain why the brain integrates the local effects into the perception that the large circles as a whole are spiralling inwards. I guess that’s because, to a much greater extent than we realise, we infer global configurations from what we see just in the central, foveal area of the field of view. That also seems to be the case with impossible 3 dimensional shapes, as in the impossible tribar.

Back in 1987 James Walker and Matthew Shank in the university of Missouri were doing a study of the Bourdon illusion. In some figures they devised for comparisons in their study they noticed a new effect, quite unrelated to their study. The figure upper left is a version of their chance discovery. The centre line is objectively horizontal, but can seem to rise slightly to the right. Walker and Shank tried the effect experimentally, and found it was indeed seen by a majority, but not all of their observers.  (Note for techies:  For a PDF of their article, input 1987 as year, the authors’ names plus Bourdon and contours as keywords on the Psychonomic Society search site).

The effect seems related to the Tolanski illusion, lower left: the gaps in the sloping lines are exactly level with one another, but the right hand one looks a touch higher. Generally, our judgments of horizontal or vertical across empty space between lines with a pronounced slope seem to get just a little rotated in the direction of the slope. The effect is even stronger for me with curved lines (as bottom right) than with straight ones. I’ve even found it in informal experiments with a number of observers as upper right, when vertically positioned target dots appear rotated towards the slope of blurred or broken slanting edges in which they are embedded.

But in my version of the figure, upper left, we can also see the Poggendorff effect at work, (according to me at least). Look at the two outer, nearly horizontal arms. They are exactly aligned, but to my eye the right hand one looks higher than the left hand one. That’s just the result we would get if we deleted the middle three pairs of lines, to end up with opposed obtuse angles, in what is sometimes called an obtuse angle Poggendorff figure.

Do the Tolanski and Pogendorff illusions share a mechanism, or do we see in the top left figure both the rotation of the horizontal line, and the misalignment of the outer arms, arising by chance from different processes in the brain? We can’t yet be sure, but I reckon the same processes are most probably at work, and are to do with projecting orientation and alignment judgments across figures with powerfully competing axial emphasis. The Tolanski and Poggendorff figures present a sort of reciprocal pairing: with Tolanski figures judgments of vertical or horizontal are compromised in a figure with a dominant slant, whereas in classic versions of the Poggendorff illusion judgments of oblique alignment are rotated between vertical or horizontal lines.

This is a version of an illusion discovered by Jacques Ninio.  Imagine that the coloured rectangles are real translucent plastic sheets, different in colour but identical in size.  They are shown in correct perspective, as they would appear if both were sloping away from us at the same angle.  However, the nearer one appears to slope much more than the further one. Ninio shows the effect with a diagram of arches in his book The Science of Illusions, p. 27 and fig 3-7. He explains it as an example of the way that we sometimes seem to compress visual space with distance, so that for example a flight of stairs seen head on looks steeper the further we are from it. It’s a reminder of the way that visual space is far from geometrically regular. The distortions of space must have evolved because they are advantageous in everyday vision. But in the unusual arrangements presented in some optical illusions objects can appear distorted, as in this illusion and in size-constancy effects. With those, space and objects seem to expand with distance, rather than contract as in this illusion.

Like the effects in many illusions, it is the unlikeliness of this configuration of inclined planes that makes it a challenge for the strategies we normally find reliable in making visual sense of the world.  When planes in our field of view are seen in a more usual configuration, aligned with gravitational vertical, we have no problem in correctly judging their inclination in space, even if the planes are inclined in relation to our field of view. Try this picture of some more imaginary planes, this time in the cathedral of Sees, in France.

For another case where the brain struggles with sloping planes, see the post on the wonky dagger and balconies illusions. In those illusions, puzzling sloping planes are shown, but not, as here, at different distances. Instead, the slope in those cases is ambiguous.

This wonderful ornamental canoe prow represents some fabulous creature, looking to the right.  Prows like this appeared on boats used in a cycle of trade around the Trobriand and nearby Islands in the Western Pacific, called the Kula trade.  The wonderfully ornamented canoes were only a small part of the story of this cycle of trading, but an intriguing one: the idea was to contrive a canoe so visually baffling that as your fleet of canoes approached the beach, it left your trading partners too bemused to compete in bartering. (For a more detailed account, if you fancy a bit of fairly heavyweight anthropology, there’s a fascinating essay by Alfred Gell called The Technology of Enchantment, in a book on art and anthropology from 1992).

The canoe prow is in the museum in Liverpool, UK, but to see a whole canoe go to the museum in Adelaide, Australia. It doesn’t have quite such a splendid, baffling prow, but it does show what these fabulous boats were like.

If you’d like to know out why these canoe prows remind me of paper marbling, read on.

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