This is a brilliant illusion discovered by Baingio Pinna of the University of Sassari in Italy.  The circles appear to spiral and intersect, but are in fact an orderly set of concentric circles. The illusion is due to the way the orientation of the squares alternates from circle to circle, and that contrast alternates from square to square within each circle. The illusion is related to the movement illusions of Akiyoshi Kitaoka and to twisted cord illusions.

What’s going on is suggested by this next version, with the edges enhanced, plus a bit of blurring.

This image approximates (with false colour) the data transmitted within the brain once the image has been filtered by cell systems early in the visual pathway, including centre-surround cell assemblies (a bit technical, that link). The role of these is to enhance edges, so that bright edges are now emphasised by dark  fringes and vice versa. Note that between the little stacks of alternating light and dark fringes, along the line of the circles, the dark fringes of bright squares align with the dark edges of adjacent squares and vice versa. The scale and spacing of the squares is just right to get that alignment, and as a result the effect enhances the inward turning, spiralling effect due to the orientation of the squares. The fringes combine to give an effect a little like interfering waves. The illusion seems to be bamboozling processes that are usually superbly effective at filtering out the key information about edges and their orientation in the visual field.

However, showing that centre-surround cell outputs could be enhancing the inward turning character of the lines forming the large circles doesn’t explain why the brain integrates the local effects into the perception that the large circles as a whole are spiralling inwards. I guess that’s because, to a much greater extent than we realise, we infer global configurations from what we see just in the central, foveal area of the field of view. That also seems to be the case with impossible 3 dimensional shapes, as in the impossible tribar.

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.   

Size constancy is the term for our tendency to see distant objects as larger than they are. So the far end of a shape with parallel sides looks wider than the near end. (See the earlier post on The Wonky Window). It seems to be such a basic feature of vision that it can give rise to amazing effects.  In the photo, first note note that the “sculpture” is impossible! All four blocks are receding from us, so they could only connect up in real space as a bendy snake. Instead they join up in an impossible, ever-receding, endless loop.  (See the earlier post on M.C.Escher’s Waterfall for how that kind of impossible figure works). Here the endless loop leads to a paradox, thanks to size constancy. The distant end of each block seems wider than the near end, and yet at the same time seems to be exactly the same size as the apparently smaller, near end of the next block. Measure the sides of the blocks and you’ll find them parallel. It’s one of many demonstrations that perceptual space is not always geometrically consistent, (or it can be non-Euclidean, as the specialists put it).

I located my impossible sculpture in a deeply receding space because that makes the effect just a bit stronger.

Update January 2010: How could I have overlooked this?  The stripes I’ve added to these blocks will be enhancing the effect of divergence by adding the chevron illusion to the size-constancy effect.  The chevron illusion was first reported 500 years ago, by French writer Montaigne, as related in Jaques Ninio’s book on illusions, page 15.  The chevron effect is a special case of the illusion later re-discovered a bit over a century ago as the Zollner illusion.  Some specialists would say both effects depend on the brain’s attempts to make sense of figures as shapes in space.  I suspect that’s true of the size-constancy effect, but that the chevron effect is 2D, pattern driven.  That seems supported by the observation that whilst in the picture above the chevron and size-constancy effects are acting in consort, they can also oppose one another, reducing the effect of divergence.

Read on for more on size-constancy.

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Here’s a demonstration of one of M.C.Escher’s famous pictures, the Waterfall. (Just put Escher Waterfall into Google Images to see his version).

First of all, you need to understand how a famous “impossible figure” called the tribar produces its effect.

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