Ambiguous images, Optical Illusions

A wonky dagger illusion

Wonky dagger illusion

There’s something amiss with this dagger, for sure. For a start, the blade’s a bit short. More important, you can’t be sure just from the picture where the blade is pointing. That’s because one and the same perspective view can arise from more than one three-dimensional configuration, out there in the world.  This dagger is particularly hard to interpret.  It could be pointing downwards, with one edge of the blade longer than the other, like the blade in the top left pair of little images, of the dagger seen head on and from the side. Or the edges of the blade could be the same lengths, so we must have a steep perspective view of it leaning sideways, as in the top right hand pair of views. Look at the big image for a few moments, and I think you’ll be able to see it both ways.

Both configurations present exactly the same view in perspective, and both are about equally likely. (Well, maybe equally unlikely with this dagger would be nearer the mark). It’s a variant on an illusion which presents another clash of improbable alternatives – but one that tricks us into going for what may seem the least likely choice.  We could call it the wonky flower box illusion.

wonky flower box illusion

Do the flower boxes in this scene look like they’re rectangular, if seen from above, but sloping downwards? But what if they stick straight ahead out from wall, like well-behaved flower boxes should, but are trapezoid, seen from above, (as diagrammed to the right)? Trouble is, once again the perspective view will be the same either way. What’s curious is that in this case, most observers opt for the downward sloping view of rectangular boxes, unlikely though that would be in the real world.  Trapezoid plan boxes just seem too unlikely. It’s a version of the preference for right angles that leads us to accept incredible distortions of size in the Ames Room illusion.  If technical stuff is for you, here’s a serious analysis of the window box effect (though with balconies rather than window boxes doing the weird sloping stuff).  And if you just can’t get enough of that sort of thing, here’s a report of the same illusion in a church (also a bit on the technical side).

Geometric illusions, Optical Illusions, The Poggendorff Illusion

Padoxical illusions

morinaga's illusion

This is Morinaga’s paradox – two illusions in one, but two illusions that contradict one another. First note the vertical alignment of the arrow points. Don’t the tips of the inward pointing arrowheads, top and bottom, appear to be located just a little further inwards than the tips of the middle, outward pointing arrowheads? That could only be right if the horizontal space between the tips of the (top and bottom) inward pointing arrowheads was slightly less than the space between the tips of the (middle) outward pointing ones. But that’s not how it looks. The inward pointing arrowheads look further apart than the outward pointing ones.

In reality both judgments, of vertical alignment and of the horizontal gaps, are illusions.  The tips of the arrows are perfectly aligned vertically, and the horizontal gaps between the three sets of arrowheads are all exactly the same. That last effect is a version of the Muller-Lyer illusion.

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Impossible worlds (inc. staircases), Optical Illusions

Scrambled space

sqtemp1

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.

Optical Illusions

Pixelated faces

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Who’s this?

pixilated celebrity

 Yes, it’s Shakespeare!   Back in 1973 researchers Leon Harmon and Bela Julesz produced their famous Lincoln Illusion.  They demonstrated effects when an famous image of a face, such as Abraham Lincoln’s, is pixelated quite coarsely.  We can still recognise it easily if the pixelated version is either blurred (as to the right here – it’s a blurred version of the pixelated image, not of the original), or reduced in size, as if seen from a distance. Just three years after the original Scientific American article that made the effect widely known, Salvador Dali based a picture on the Lincoln image. (Michael Bach’s site shoes the original Lincoln image, the Dali picture and a clever interactive demo).

Note the tiny Shakespeare perched in the very bottom right corner of the left hand, pixelated image above.  It’s just the pixelated image reduced.  If you move away from the screen a few feet, you’ll find that the two large images of Shakespeare come to look more and more alike.  It’s odd how even small details of the face seem to appear.  If you want to try it with faces you know, I think it works best with about seventeen pixels along the longest dimension of the picture.  It does work best with an iconic, image – a photo everyone knows – rather than just a face you know.

So who have we here?

Pixelated celebs

I think you’ll have got those, but otherwise (and for more stuff) …

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Ambiguous images, illusions and aesthetics

Mosaic illusions

Mosaic floor at Casale

 

Here’s another example of the way illusion effects have been used in decorative art designs. (For examples in earlier posts, check out the category Illusions and Aesthetics, to the right). This mosaic is one of many from the Villa Romana del Casale, in the middle of Sicily, Southern Italy. Only the floors of this Roman villa are left. They are about 1700 years old, and are the largest expanses of mosaic floor surviving from the ancient classical mediterranean world.

The illusion comes in because different shapes in the design tend to pop out from one moment to the next. For example, in the pictures below I’ve selected out a star and a string of lozenges in the picture on the left, and then a hexagon shape in the picture on the right. Note that the hexagon interlocks with the star beside it with no gaps between them or overlaps, but when we select one, the other kind of vanishes, not only in these demo pictures, but even in the big picture at the start of the post. It’s a figure/ground effect, as in the faces/vase illusion, but without the dramatic light/dark contrast of faces and vase.

Mosaic floor demo
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Illusion demos with animations, Tessellations

Tessellation Animation

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The Dutch tessellation whizz M.C.Escher was fascinated by transformations from one tessellation to another, for example in his series of prints Metamorphosis. I’m sure he would have explored animated versions if it had been practical in the 1940’s. So I’ve borrowed a couple of his motifs and animated them. I showed an animated transformation in an earlier post, but that was between two designs that shared the same kind of symmetry. (See the earlier tessellation tutorial for how these tessellations work. If you like technical detail, my earlier animation was of two motifs based on Heesch tessellation no. 11). Sticking to just that one kind of tessellation meant that the corners of each cell of the design had to remain stationary, and only the edges of the cells transformed. This new transformation is a bit different, because it’s not just a transformation from one motif to another, but between two different kinds of symmetry pattern – Heesch nos 17 and 18 in the tutorial – and the corners of the cells of the pattern are not fixed.

In the earlier transforming animation, the design transformed in space, across the image, as well as transforming in time. If I’ve got it right, (I’m not 100% sure about this), that kind of time plus space transformation is not possible in an animation if the corners of the cells of the tessellation change position, as in my new tessellation above. So in this new animation, there’s no change from cell to cell across the design, and all the cells transform together.

I’m fascinated by the artistic possibilities of these kinds of animation, and one aspect of it is to do with what you might call the dance rhythms of the animation. Here’s a variation on the new animation, speeded up and with an added wave that gives a quite different kind of pulse to the design.

These animations are bit monochrome for the moment – colour is on the way, but I’m on a steep learning curve with file sizes, compression etc.

Geometric illusions, Optical Illusions

Zöllner versus the Twisted Cord

This effect is a bit size sensitive.  It works for me with the diamond about 13 cms or 5 inches wide on my screen, and also a bit larger, but not much smaller.  I think resolution will need to be good too.  All being well, It should show one illusion being overcome by another. All the bars are parallel, but they look wonky. In the top set of four, for example, do the middle pair of bars look just a little further apart near the centre line of the image than towards the upper right edge?  The flanking pairs of bars (still just looking at the top set of bars) look to me closer together at the mid-line than at the upper edge. In other words, that upper right set of bars look like they’ve rotated just a touch, opposed to the orientation of the blurry stripes behind them. (That’s the Zöllner illusion). Now check out the lower set of four bars.  For me, they look like they’ve rotated in just the same direction – but that’s odd, because I’ve mirror reflected the stripes behind them, so that the stripes have changed direction. So those lower bars appear to have rotated so that they end up slightly more aligned with the stripes behind them.

How so?  You’ve guessed, it’s to do with those thin white stripes I’ve added to the lower set of bars. They turn the bars into another illusion of orientation, the twisted cord illusion.  The way I’ve done it, that sets the two illusions in competition, and as a result you’d expect the four lower wonky bars to end up looking about just about parallel. That’s about what happens, for example, when the Zöllner illusion goes head to head with the size-constancy illusion.  But instead, the twisted cord can overcome the Zöllner illusion. Now, that’s very interesting ……

 

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Soap bubble pictures

Funky Wind Turbine

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Like my other soap bubble pictures, this one is fantasy rather than illusion, and the only miracle going on is thanks to Photoshop.  The wind turbine is in Cornwall, as far as you can go in the pointy bottom left hand corner of England without falling off the end.  The bubbles start out as real ones, and see my earlier post for how I photograph those.  (Also for how other photographers have done it).  For more of my bubble pictures, click on soap bubble pictures in the categories list to the right.

There is a perceptual point to this bubble picture though.  When you look at it, do you find that you can almost imagine what it would feel like to be the wind turbine, making this serpentine gesture?  A bit as if you were about to whack a football into a goal with your head, maybe?  That wouldn’t be such a surprise if this was a picture of a human being.  One of the most interesting discoveries of recent years has been of “mirror neurones” in the brains of primates.  These are brain circuits, associated with real movements or gestures, but which fire off without consequent movement when we merely observe someone else making a gesture.  But it’s curious that we can have the same kind of experience when we see a picture of a wind turbine, merely behaving like a person.

Geometric illusions, Optical Illusions, Size-constancy effects

Bressanelli and Massironi’s new illusion

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Here’s another illusion only recently reported, by Daniella Bresanelli and Manfredo Massironi of the Universities of Padua and Verona.  Look at the three shapes, and most people seem to see the bottom one as thinnest, judging width at right angles to the long edges, the middle one as a bit fatter, and the top one as widest of all (still judging width at right angles to the long edges).  In fact, they’re all the same width, and the two bottom shapes are also identical, just rotated in relation to one another.

What’s going on?  If you devour technical articles like snacks, see Bressanelli and Massironi’s paper.  Otherwise …

 

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Illusions and visual special effects – explanations and tutorials