Category Archives: Impossible worlds (inc. staircases)

Pictures using graphic tricks to present spaces and objects that could not exist in the everyday world

Roger Shepard’s Arc de Triomphe revisited

Arc de Triomphe illusion

In 1990 the psychologist and artist Roger Shepard published a cartoon version of this effect, captioned “I stand corrected”, in his book Mindsights (page 91).  I wanted to try a photo processed version of it and here’s my second attempt.  When I tried before, back in 2008, I somehow couldn’t get my mind round what Shepard had done, and produced an even more twisted version.

M.C.Escher’s lithograph Belvedere from 1958 is famous variant on the theme.  Subsequent investigators have presented animated 3D versions of it that help explain the effect.

My new version is based on a late nineteenth century Photochrom postcard.  They were made by a beautiful process that added colour lithographically to black and white photos.  You can see the original in a collection of gorgeous period cards of views from all over the world in the USA Library of Congress.

Gustave Verbeek

Gustave Verbeek cartoon

About a hundred years ago one of the most popular newspaper comic-strip artists in America was Gustave Verbeek.  He contrived whole pages of pictures telling cartoon stories, which showed one sequence of scenes when viewed one way up, and the following set when turned upside down.  His best known adventures were those of Lady Lovekins and Old Man Muffaroo, each of them, as in the scenes above, always the inverse of the other.  His stories are so crazy and his drawings so imaginative that it can take a moment to realise one scene really is the exact inverse of the other.   His imagery is surrealist – long before surrealism emerged with artists like Salvador Dali in the establishment art world.

His cartoons have recently been reprinted (not cheap!)

Verbeek was developing an earlier tradition of rotating heads illusions, in which a head has one identity one way up, and another upside down.  See my first earlier post of that, with an animation, and another example with Santa turning into playwrite Henrick Ibsen

The Twisted Stairs (version 2)

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.

Bad Day in the Art Museum

Art gallery

Interesting things can happen when you have pictures within pictures. Not so much, for example, with an everyday photo of an art gallery, if all the pictures are behaving well and staying in their frames. But sometimes it’s not possible to tell when the picture of a picture ends, and the picture of the real world begins. Here’s an example, in which the paintings in an art gallery are definitely not behaving how paintings should.

M.C.Escher did some brilliant pictures in which the boundary between the real world and the graphic world breaks down in the same way. The most famous is his print Drawing Hands of 1948, but you’ll find lots of others. Amongst contemporary artists, Rob Gonsalves has done some really clever paintings, such as Unfinished Puzzle. It’s the kind of issue that interested Picasso and Braque too, in their cubist paintings. In one by Braque you can see a cubist palette hanging on an illusionistic nail.

Here’s another famous example, a painting from a bit over a century ago, by Pere Borrell del Caso.  It’s called Escaping Criticism. I guess the artist felt hard done by at the hands of critics, and did this as a demonstration of virtuosity.  (I believe the original painting is in the Banco de Espana Madrid   –  Spain’s national bank).

Escaping criticism by Borrell del Caso

The guys climbing back into a painting in my image are borrowed from a copy of Michelangelo’s lost study for the Battle of Cascino. The shipwreck is from a 200 year old painting by English Romantic painter J.M.W.Turner in the art museum Tate Britain in London, of a bad day in the English Channel.

Scrambled space


One of surrealist painter Rene Magritte’s cleverest paintings, Carte Blanche, is of a rider in a wood, but all mixed up with the trees. I had a shot at playing with the same effects in the earlier Halloween post.  This time, I’ve tweaked up the complication with an impossible figure/ground reversal half-way up the columns, (in the manner of the impossible fork illusion – see our earlier post Outlines, objects and apertures).

A while back I tried out a similar figure/ground scenewarp in one of the picture pairs for an optical illusion cartoon story, Opticaloctopus.

The twisted castle

This is another transformation based on one in my illusion cartoon story.  I did it to see whether I could devise an adventure, set in graphic world, with transformations that are forbidden in our everyday world as the events that take the story forward.  Most of the transformations, like this one, offer an escape route for a character being pursued.  Not very imaginative.  I did also have animation in mind, and working out this particular 3D morph would be no joke.  It’s based on the four sided version of the famous impossible triangle, with added extensions for the towers, as above.  For the classic impossible tribar, see my earlier post on Escher’s Waterfall Explained.  For impossible figures with four sides and more, check out Gershon Elber’s site.   

Convex/concave spacewarp

convex concave space illusion

This is about the simplest of all spatial transformations.  In the top picture, the mice are at risk from the cats.  In the bottom picture, the stairs have vanished, and as the eye travels along the picture from the left, a concave terrace turns into a convex, step shape.  There’s now a protective inside/out space-warp between the cats and the mice.  I adapted the scene from one I devised for my optical illusion cartoon story.  If you wanted to experiment with scenes based on this transformation, the essential scheme is as to the left here. Note that there must be no tonal contrast across the middle line, just in the middle of the image.

Topologically, I suppose the shape is just a saddle shape, as to the right, so it could exist as a rectangular, 3 dimensional shape, but it would be such an improbable one, and seen from such an unlikely angle, that it looks like an illusion.  For a fiendishly clever picture on the theme of inside out transformations, see M.C.Escher’s print Convex/Concave.  (Try that title in Google images, or find it on the official Escher website).

Outlines, objects and apertures

Impossible shape illusion


This stag may look OK at first glance (well, you know, sort of…), but hang on, has he got three antlers, as at the top of the picture, or only two, as down by his ears?  Following on from the last post, it’s another example of what happens when apertures or gaps in the visual scene – like the segment of starry night in the last post – become objects. But with the stag it’s even weirder, because the middle antler, for example, starts out at the top OK, but by the time it gets down to the stag’s head, it’s become background.  Want to know more?  Read on!

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Halloween magic

Occlusion illusion

Here’s a scene for Halloween.  In our everyday view of the world, the orderly way in which one thing blocks our view of another is something we can depend on to orientate ourselves in the world around us.  These witches are breaking the rules.  The lower ones appear and disappear at puzzling locations, and the witch lower right even vanishes behind a segment of starry sky.  It’s as if the segment of sky had become an object in the visual field, instead of an aperture – an oddly weird effect, for me.

I got the idea from a wonderful painting by Rene Magritte, Carte Blanche.  If you go to for that link, you’ll just need to scroll down a couple of pictures – you’re looking for a painting of a lady on a horse in a wood.

Oh, and I borrowed the musclemen from the 450 year old illustrations to the pioneering anatomical studies of Andreas Vesalius. 

A New(?) Ever Receding Staircase

Here’s a new kind of never-ending stair (I think).  It’s like the famous never-ending staircase seen from above by M.C.Escher, called Ascending and Descending.  However, in this new staircase instead of figures doomed to go downstairs for ever we have penguins destined to walk away from us forever.  It’s based on the geometry of the object in my post on paradoxical size-constancy.

New Penguin Stair

Here’s an animated version:

Like Escher’s famous impossible staircase, (and also as with the impossible tribar), the effect depends on our seeing a scene from a viewpoint from which points that would be at different distances from us seem to connect up. Here’s a view in more usual perspective of one configuration that would give rise to the ever receding staircase above. The trick depends not just on getting the alignment just right, but also on suppressing the usual perspective cues.  Size diminution with distance is the most important one.  The other is aerial perspective, in which contrast flattens out and colours get bluer with distance. I’ve put them both back below.


For more on staircases like Escher’s famous picture Ascending and Descending …..

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