I’ve not been posting much because I’ve been struggling with a mammoth revision of my technical site on the Poggendorff illusion.  But now that’s done, here’s a post on another Poggendorff puzzle.

In earlier posts I’ve shown examples of competition between illusions, and included a demo of a paradox when the Poggendorff and Muller-Lyer illusions go head to head.  Bottom left above I’ve shown that last demo again – not so pretty, but I think a clearer demo.  Thanks to the Muller-Lyer illusion the outward pointing arrowheads appear closer together than the inward pointing ones, when objectively the arrow points are identical distances apart (note the reference lines in the middle of the figure).  But at the same time, at the left end of the figure, the arms of the same arrowheads, objectively aligned, would have had to move further apart, not nearer, in order to produce the effect of misalignment that we see.  So the two illusions seem to coexist in total opposition to one another, without a qualm. I’ve repeated the arrowheads to the lower right, to show that, at least as I see it, their appearance is just the same as when embedded in the Poggendorff figure.

But then the top figures show that both these illusions can be inhibited, when set in competition with other illusions.  Top left the Poggendorff illusion is normal to the left, but cancelled to the right (or is it even reversed?) when the test arms are illusorily rotated by the addition of some Cafe Wall characteristics. And top right, there’s much less difference (again to my eye) between the illusorily lengthened and shortened elements of the Muller Lyer illusion when we see them in the context of a Ponzo illusion (a scene in apparent depth) than as we see them isolated below the Ponzo scene.  In the Ponzo scene, the size-constancy effect is increasing the size of the smaller Muller-Lyer element.

So why are the Poggendorff and Muller-Lyer illusions sometimes inhibited when set in competition with other illusions, when at other times they co-exist with rivals in glorious paradox?  Any ideas?

You’re going to have to hurry, but if you can get to the Royal Cornwall Museum in Truro, England, before July 3rd, you can see this brilliant sculpture of a dog by British sculptor David Kemp, in his exhibition The Botallack Hoard.  It’s one of the dogs in his piece The Hounds of Geevor, and if you don’t make the show, you can see them anytime in bronze in the centre of the nearby town of Redruth.  Truro and Redruth are in Cornwall, which if you look at a map of England is the pointy bit in the bottom left hand corner.  David lives pretty much as far down the bottom corner as you can go, and I think he’s one of the very best sculptors anywhere working, amongst other interests, on ambiguous images, on which I’ve posted several times before.  He works with every kind of what some people might call junk, but he discovers in it ideas that I find very funny and very beautiful.  If you’d like more information on David Kemp, see his brilliant website.

Here’s another of David’s sculptures, of three musicians, along with more detail of one of them.

This is a detail from British artist William Hogarth‘s print made in 1754, to demonstrate mistakes in perspective.  For example, the sheep lower left get larger with distance, not smaller, and the woman top right is leaning out of a window offering a light to a man in the distance.

However I’m really showing it because a brilliant new animated demo of perspective anomaly, by Kouchiki Sugihara, has just won the first prize in the international Best Illusion of the Year Contest.  Don’t miss it, the ten best entries are shown, and there is some brilliant new stuff.

Coming back to Hogarth, his print was way before its time.  It was over a hundred years later, late in the nineteenth century, that illusion and puzzle picture books became common.  Then artists took up the challenge, Magritte and Escher for example.

Want to see the whole of Hogarth’s print?

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Here is a new animation in our series of animated illusion cartoons, Waiting for Shining Person.  (As with our earlier cartoons, It may run jerkily on first run-through.  It should be fine thereafter.)

Compression for Flash has slightly reduced the effect. If possible, view Waiting for Shining Person as a
Quicktime Movie

The illusion it features is the glare effect.

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.