The paradoxical Checker Shadow illusion


On the left is Edward Adelson’s famous Checker Shadow Illusion, published in 1995.  Square B looks much darker than D.  However they are actually the same uniform grey, as can be seen by comparison with the bar overlaying them in the middle image.

What’s going on?  The brain has strategies for keeping the relationships between the tones and colours of objects in a scene – for example between the light and dark rectangles here – consistent, in spite of big variations in illumination in different parts of the scene.  The shadow of the cylinder gives the variation in illumination in this scene.

That makes the middle picture visually paradoxical.  C looks much lighter than A, and yet we can see that it is the same tone as D and the overlaying grey bar, and therefore B as well.  But B looks the same tone as A, even though A looks, paradoxically, darker than C.

To my eye, the paradox is even more mysterious in the right hand version.  At first glance, A, B, C and D all look to me the same tone – and yet if I concentrate just on A and C, C tends still to look lighter.

The key is that Adelson’s illusion only works when we see objects as part of a three-dimensional scene, complete with illumination.  The introduction of the grey bar in the middle image breaks the spell, for the squares it overlays.  In the right hand image, the left hand side looks three dimensional, and shows the illusion.  But the two squares sticking out to the right no longer seem so much a part of the scene, and we see them in their true colours.  It is remarkable that there can be such variations in appearance in different parts of the visual field, and from moment to moment with shifts in attention.

For Adelson’s own, more technical (and authoritative) explanation, go to:  and click on Research



Never-ending Penguin Stair

This is a variation on M.C.Escher’s 1960 lithograph Ascending and Descending.  At first we see the staircase leading into the distance, and ending in mid-air, but then at about 15 seconds in, the furthest point of the staircase  lines up with the nearest point.  At the same time the perspective cues that made the distant platform a bit smaller, and a bit paler, than the nearest platform vanish so that they appear the same size.  Our brains then assume that they connect up, even though the result is a stair that could not exist in real 3D space. From 20 seconds in, the penguins entering from the right are always heading towards us in an endless loop, but never get any nearer.

This post is an update on a much earlier one, from 2008.

The Breathing Golden Snail Illusion

The snail appears to inflate, and yet its shape does not really change at all.  Nor does the lighting change.  All that changes is the character of the surface of the shell.  It transforms from very shiny to completely matt and unreflective. Surfaces don’t change like that in the real world, but it’s easily achieved in 3D animation software, such as Blender, which I use.

But why should that make the shell seem to inflate?  The size of the shell is just as well specified when shiny as when matt.  I think it may have to do with the movement of the blurry shadow edge as it sweeps outward towards the edges of the shell.   We transmit blurry, so-called low spatial frequency, soft edges along different brain pathways from the ones that transmit the sharp, so-called high spatial frequency edges, which we see in highly reflective surfaces.  Soft edges indicate the overall roundness of objects.  And soft edges moving symmetrically over a surface towards the object edges would probably only appear, in the real world, in the case of an expansion.  However, the effect  also depends in a way I don’t understand on the shape of the object.  Not any old shape gives the expansion effect with the same treatment – I ended up with this one by trial and error.

This is an opportunity to say how terrific the Blender package is.  It’s free for anyone to download and use and the developers and the Blender community have done a really fantastic job in making it available to anyone, anywhere with internet access.  It takes a bit of learning (I don’t begin to do it justice) but it’s now comparable to high end professional animation software.

Celebrating Magritte

(Post updated at 31/8/19). This is a 3D movie, which I showed recently at a vision science meeting, (ECVP in Leuven, Belgium).  You will only be able to view the movie in 3D if you have learned how to fuse the two images into one without a viewer, by so-called cross-eyed viewing.  If you don’t have the technique and want to learn it, one of the best Youtube guides is this Youtube tutorial.  (But best to give the technique a miss if you have any eye adjustment problems).

Alternatively, if you have a pair of red/cyan movie glasses, view this next version (ideally full-screen – the larger the better):


The movies are based on one of René Magritte’s most haunting paintings, Carte Blanche, or The Blank Cheque, which you can see at:

Magritte  brilliantly baffles our expectations about spatial organisation, just by bringing into the foreground, in front of the horse and rider, one strip of landscape background, and one tree-trunk.  I wanted to see how the effect would work as a fly-by, 3D animation.

That required a change of motif.  For the animated version the central motif must not touch the ground.  So instead of the horse and rider in the original painting, I chose another Magritte theme: a floating pipe.

The 3D versions set up a competition, between two processes usually in perfect agreement:  on the one hand our judgments of depth based on binocular disparity – the slightly different viewpoint of each eye;  and on the other hand depth arrangements indicated by the occlusion (or masking) of more distant objects by nearer ones.

Different observers see the result in different ways.  Most commonly, when the pipe is interrupted because a tree trunk or background appears in front of it, the different parts of the pipe seem to be at different distances from us.  It can even seem to weave in and out of the tree-trunks, and they can bend around it.  It seems that the occlusion (masking) cues are winning out over the disparity cues.

An ambiguous heads Indian mural

Photos © Michaela Butter

The elephant and the horse share an eye!  You can see the eye as belonging either to the elephant and its trunk, or to the head of the horse caught between the elephant’s tusks. It’s an optical illusion of a kind unusual in Indian painting.  It was brilliantly spotted by my friends Michaela and Eddy Keon, visiting the palace in the beautiful, not so well known Rajasthani hill town, of Bundi.

The painting is in a style developed by the unknown artists who decorated the palace at Bundi with glorious murals in the seventeenth century.  Bundi painting is one of a number of local styles of Rajasthani painting, developed, mostly by artists decorating palaces, separately from the better known contemporary Mughal styles.

A prize surprise

A few weeks back, with collaborators Priscilla Heard and Christopher Tyler, I won second prize with this movie in the annual Best Visual Illusion of the Year Contest.  I think we were lucky!  As ever the competition showcased some fascinating, quite new illusions, and this year’s were a particularly strong bunch.

Extra – July 2019 – Earlier this year we published a paper analysing the illusion  in the online, open access journal i-Perception.

Last year the competition organisers published a beautiful book, showing some of the illusions that won prizes in the years since the competition started in 2005.  You can see details on this site.


A Funny Turn

It may take a bit of practice, but you’ll be able to see the silhouette dinosaur rotating either way around.  One way round, it’s  rotating just like the top right hand of the four coloured dinos.  To see it rotate the other way round, start with the head facing left.  Then try imagining that the head is getting nearer to you as it goes lower.  Once you’ve seen the rotation go both ways, it tends to change spontaneously from one to the other.

I’m not great at imagining 3D shapes moving in space. When I set this up, I assumed that when the silhouette rotates the way around that doesn’t match the top right hand coloured dinosaur, it  will instead match one of the two left hand dinos, but half a rotation out of step.  The top left one is just a mirror reflection of the top right coloured one, and the lower left one a time-reversed version of it.  But I wasn’t sure which of the those left hand dinos it would match.  (The lower right coloured dino is a reflection plus a time-reversal of the top right one.  That switches the rotation twice – back to matching the way around the top right dino goes).

But the silhouette dino, when seen as rotating opposed to the top right dino, isn’t like either of the left hand versions!  In those, the head is always nearest to us when it’s at its highest, and furthest from us when it is lower down.  With the silhouette view clockwise, it’s the other way round:  the head is nearest to us when its low down.  I think it’s an impossible view, invented by the brain.  There’s no way I can get the real dino to give me that view.  (Actually – full disclosure – I didn’t film a real dinosaur.  It’s a model).

I haven’t quite puzzled out why the views work like this.

Extra:  18/2/20

I found the explanation in a chapter in the wonderful Oxford Compendium of Visual Illusions,  Nicolaus F. Troye “The Kayahara silhouette illusion” pp 582-585.

The key is that the sihouette version image is not just rotationally ambiguous (it rotates clockwise or anti-clockwise), even as a static image it’s also depth ambiguous.  So the silhouette above can either appear just like the upper left dino in the picture, head nearest to us, or a bit like the lower centre dino, head furthest away.  Both ambiguities – rotation and depth – can only flip at the same time.

But note that the silhouette and the picture of the dino with head more distant are not quite the same.  That’s because the dino extends so far into depth that it shows perspective effects.  First, with reversal our viewpoint slightly changs.  But more strikingly, when we see the silhouette dino with its head furthest from us, the head looks far too large.  That’s because of the size constancy effect – we tend perceptually to enlarge the size of more distant objects.  So here, when the head is seen as more distant, it also appears far too large, and the tail, conversely, too small.

That also applies with the moving version, when the silhouette dino is seen as revolving anti-clockwise:  its head seems to shrink as it rotates towards us, and to expand as it rotates away.


Twisted Wall

Here is a vivid real world illusion, spotted and photographed by my friend Eddy Keon:  it’s a brand new wall in Nottingham, UK, and it’s perfectly vertical, but with these shadows, it looks twisted.

The twist seems to be due just to the way the edges of the shadows running down the wall lean over more and more as the eye travels from left to right across the photo.  It’s a kind of crazy perspective effect!

Watch your step!

 We’ve posted on illusions in architecture before, but they’ve been historic ones, in Roman mosaic floors and in so-called trompe-l’oeil ceilings.  Here’s a brilliant recent example, (2015) from Jamie Fobert Architects, for London’s luxury shopping Burlington Arcade.  The arcade was opened in 1819, when modern shopping was just beginning to be a boom activity.  For a description of the new floor project by the architects, click on

A friend just told me there are also eye-popping illusion floors in some of the bedrooms of the imaginatively named Seaside Park hotel in Leipzig.

A Shrink and Swell Illusion

We  just got into the final top ten entries in the annual Best Visual Illusion of the Year contest.  We didn’t get in the top three, (in fact, we seem to have come last … ) but it’s great to have made the top ten.  The movie here is a different version of our competition entry.

The illusion is that the objectively static sides of a V-shaped window appear either to expand or to contract horizontally. Figures within the window, expanded at the top and squashed at the bottom into the V-shape, rise or fall at constant speed.

At the end of this version, we show that we’ve actually found three fairly different ways of producing this illusion.  We found them by studying the reflections seen in novelty illusion rings called Witch Rings as they rotate.  We posted about using animations to imitate effects seen in the reflections, in 2013, and then in 2015 and 2016.  But now we think the illusion we’ve found in our animations, though an interesting discovery, only makes a small contribution to the very vivid illusion seen in the rings in the real world – the secret of the rings remains mysterious!

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Illusions and visual special effects – explanations and tutorials