Monthly Archives: January 2010

Geometric illusions, Impossible worlds (inc. staircases), Optical Illusions

The Twisted Stairs (version 2)

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The Twisted Stairs - version 2

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.

Animated Illusion Cartoons, Optical Illusions, Tessellations

Animated Illusion Cartoons – re-posting of Chicken and Leaf

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.

These cartoons are meant to work just like movie versions of a three- or four-frame cartoon in a newspaper – each one presents a situation that ends with a punch-line.  The cast of characters are all illusion figures of different kinds, but each cartoon depends on a particular illusion effect.

The main illusion effects to watch out for in this movie are tessellations, and especially the final transformation, which transforms across the image at the same time as it transforms locally:

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.

I’m fascinated by the effect that the movie ends with – 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, but of course couldn’t do animations.  I’m sure he’d have done the animations 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.

Ambiguous images, Optical Illusions

Eyespots

Eyespots on a Peacock Butterfly

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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