Tessellations are patterns whose repeat motifs fit together like jig-saw pieces, with no gaps and no repeats.  For an introduction, see our earlier animation. They can be abstract patterns, but the most intriguing are the ones devised by tessellation maestro M.C.Escher in the middle of the last century, which show representational motifs, such as animals, as tessellating patterns.

Designing abstract patterns that tessellate successfully is just a matter of getting the hang of some rules.  Discovering representational motifs that tessellate is much, much harder.  There are no procedures, or none that I know anyway.  It’s all trial and error, mostly error for me, and really hard!  Escher was brilliant at it.  My efforts are pretty feeble.

But fortunately, you can at least include representational motifs within your tessellations with a little trickery.  The pattern above, based on Leonardo’s famous Vitruvian Man, is an example.  The secret is to use segments of the outline of the representational motif for part of the outline of the tessellating pattern cell.

You do need to be up to speed with making abstract tessellations, and also pretty expert with Photoshop or an equivalent graphics package.  But if you’ve reached that point, or are just curious, here are stages in the development of the pattern shown above….

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Hybrid portraits superimpose one portrait on top of another, so that one appears with close viewing, and the other emerges with more distant viewing. Or with reduced image size. Or just by taking off your specs, if you are just a little way away and are seriously short-sighted. Whatever works for you, here Charlie Chaplin becomes Queen Victoria. The “top” image is filtered to reduce it so that it resembles an outline drawing, and then made partially transparent (and some viewers might need reading glasses to see it). The ‘back” image is blurred (and may only become apparent when viewed from two or  more meters).

The technique was invented by Aude Oliva, Antonio Torralba and Philippe G. Schyns, and presented in 2006 at the huge annual Siggraph (electronic graphics) conference.  Putting it technically, Charlie here appears with all but his high spatial frequencies filtered out, whilst her late Majesty has had all but her low spatial frequencies filtered away.

But don’t be deterred by the jargon.  If you’d like to try your own hybrid portraits, you can do the filtering very easily if you have a full version of Photoshop to play with, (so long as you’ve got the hang of working with layers).   This is how it works in Photoshop CS2 for Mac.  For the high spatial frequency (outlines) image, with an image file open and the image you want to filter selected, go to filter in the menus at the top of the screen, select other.. (at the very bottom of the list of options) and then high pass.. Then play around! You’ll see how you can transform the image with a slider. For the low spatial frequency (blurry) image, start in a new layer, and once again with the image to filter selected, go to filter again, but this time select blur, and then in the options that open up Gaussian Blur. Once again, then just play around with the slider to explore effects. Then you need to make the top image transparent. Make sure the Layers window is visible (click on layers in the Windows menu at the top of the screen if not). Next make sure the layer holding the top image is selected. Now you can adjust the transparency (they call it opacity) at top right in the layers window.

That’s the easy bit. Once the image pair are more or less presenting the effect OK, adjusting the degree of filtering of the images, their contrast, and then the transparency of the ‘top’ image to find the demon tweak that gives maximum effect will drive you crazy! There is a colossal range of possible combinations.

For some great movies of the effect, try this (MIT) site.

Here’s another picture to add to our category of soap bubble imagery.  For details about how I photograph the bubbles, see entries in the soap bubble category.

I hadn’t noticed before that there are some great movies of bubbles on Youtube, such as this model of Jupiter’s turbulence, or this movie of a bubble bursting. There are some really astonishing still photos of bursting bubbles in this report from the Mail Online site.  They’re by Richard Heeks, who’s currently studying for a literature PhD at Exeter University in the UK.

I was fascinated to see those, because back in October 2008 I posted an image of a bursting bubble as a visual metaphor for the financial crisis then at its height.  But not having Richard Heeks’s stunning skill and patience as a photographer, I faked up (pretty obviously I hope) a graphic of a bubble burst in Photoshop.  Not remotely like the real thing, as it turns out.

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.

This is an installation called Zig-Zag Corridor by Czech artist Petr Kvicala, in the Dox art centre in Prague, Czech Republic.  He’s an artist who produces dazzling patterned effects.  In this one, beautiful diagonals meander through the patterns, although the linework is entirely made up of a continuous sequence of horizontal and vertical segments.

However, as my friend Alex noticed, when he featured the installation on his site devoted to stunning photos of architecture in a district of Prague, Vrsovice Photo Diary, there’s another effect here as well:  in places the walls seem to bow outwards in the middle, and the right wall doesn’t look flat at all.  That’s because of an illusion that arises whenever long lines intersect or abut an array of parallel or systematically varying obliques, as to the right above.  The apparently bowed long lines are objectively straight.  It’s called the Hering illusion, first scientifically reported by Ewald Hering in 1861. It’s a special case of the more general Zollner illusion, published by the astronomer and mystic Johann Karl Friedrich Zollner a year earlier.

I don’t know whether the artist introduced these effects by accident (and they probably appear more strongly in photos than in the real installation).  But it’s very, very easy for these illusions to sneak unintended into designs - as I let them do, when I failed to realise their contribution to a quite different effect in an earlier post.

Can you read the message encoded in the image?  A few months back I posted about embedding hidden messages in images. Since then I’ve come across a much better way of doing it, using the lettering in the image above.  Lettering? What lettering?  You may not even have been able to spot the lettering yet. I’m not sure who invented it, but it’s brilliant – I just copied the style of lettering from another demo, on the wonderful website of Michael Bach.  It’s clever because to read the message we have not only to achieve a figure/ground reversal, but also because the distracting objects in the picture are seen as if from above (the default view the brain expects), whilst the hidden lettering is seen from below.  So we have to switch two modes of viewing, figure and ground, and also view from above and view from below.  And then I’ve added scene cues to make it even harder.

However there is a way of revealing the message easily – just blur the image, as in the version below.  Without all the distracting detail in the sharp edges in the scene, all that’s required is a figure/ground reversal, and recognisable letters become the most salient features in the image for the brain.

In my first post on this question, I showed a straightforward exchange between the words Truth and Lies with reversal of figure and ground.  I wanted to tweak that, to add the additional reversal between letters seen from above and from below.  To see that ….

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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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Top left is one of the simplest of all illusions.  The yellow dot is just half way up the vertical height of the triangle, but looks decidedly nearer to the apex. The effect was reported over a century ago, and has been named for its original researchers the “Thiery-Wundt illusion” by recent experimenters Ross Day and Andrew Kimm.  A consensus in recent years has been that we are hard-wired to home in on the “centre of gravity” of the triangle, the point at which three lines bisecting the three angles would meet.  The centre of gravity is a bit lower down than the half-way point of the vertical height of the triangle.  So maybe, the theory goes, we tend to take the centre of gravity as a default central reference point, and so we see the vertical centre point as if shifted a bit towards the apex.  But that can’t be the whole story, researchers Day and Kimm point out, because the effect is still there when the figure is reduced to just one oblique angle side, as centre top in the figure.  In fact, in their experiments, the effect was measured as even stronger that way. So the illusion may look simple, but more than a hundred years after its debut, we’re still basically guessing what’s going on.

Whatever is afoot, it’s probably also involved in the Mueller-Lyer illusion, in which the gap between two inward pointing arrowheads looks larger than an identical gap between two outward pointing ones.  I’ve shown that in 3D in the figure, for viewers who have the knack of so-called “cross-eyed” 3D viewing, without a viewer.  (If that’s new to you, and you want to get the knack, search on Google or try this site – though give it a miss if you have vision problems). But you can see the Mueller-Lyer effect perfectly well in 2D, and for a full discussion of the two illusions, Thiery-Wundt and Mueller-Lyer, if you have access to a research library, see Day and Kimm’s original research paper.  Or for just a bit more ….

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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.

Here’s a new item for our category of soap bubble pictures.  The movie shows a science-centre-style demo, not of a bubble, but of a soap sheet.  It’s a way of showing patterns like the ones that appear on bubbles, but streaming down a huge sheet.  The quality of the movie is not great, so here’s a still photo that shows the effect.

I think this was originally a Victorian demonstration, but I don’t have chapter and verse for that.  It’s a demo you sometimes see in hands-on Science Centres, but often it’s not set up so that you can really see the colours.  For that there has to be a black background to the sheet, and a translucent screen, at an angle of forty five degrees to the sheet, brightly illuminating it.

I’m fascinated by patterns like these.  Just setting patterns in motion, as in many screen savers, doesn’t seem to me to produce effects that are as beautiful.  I don’t think it’s just the colours.  If we could characterise what makes these patterns special, might we then open up a whole new world of visual expression, using computer animation?  Or would we just end up with a small repertoire of pretty effects?

Fancy trying to set up your own soap sheet?  It’s not so hard.

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