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.
I’m fascinated by the way that spectacular aesthetic effects often seem to involve bamboozling our everyday strategies for making visual sense of the world. This is a beautiful example, a detail of interlace decoration on a 14th century (Western dates) Mamluk Period door in the Louvre from the Al-Maridani mosque in Cairo. (I’ve shown other examples of a role for bamboozled perception in aesthetics in an earlier post, and in the Illusions and Aesthetics category to the right).
As you can begin to see in the image, where I’ve combined the interlace pattern on the door with a schematic analysis of its reflection, the interlace we see in the door is a segment of a rosette pattern that repeats across a wider field. But that’s not obvious at all when you just see the door. The artist has not emphasised the lines of the design, but rather the infills – stars and other little geometric tiles. We’re distracted from grasping the overall geometry by all the assertive, enclosed shapes, with their heavy outlines. And the overall shapes that do jump out for me are the beautiful curves that run from top to bottom of the image, which also distract attention from the hexagonal geometry of the pattern. For more analysis of the pattern and the fabrication of the doors, see below, but first, here’s the whole door.
When the chevron pattern in the movie is in perspective, so that the bars get thinner and closer together with distance, the bars and the fan of bright bands on them appear to stream past us, as if we were travelling along a tunnel. When the bars are all the same size and equally spaced, so that they don’t show perspective depth cues, the fan of bright bands appears to be expanding. The outer bright bands even look as if they are sliding along the bars.
Thanks to Priscilla Heard for the suggestion that the key to the expansion effect is in the absence of perspective cues. If you’d like more on that ….
Go back a couple of centuries and there were no chains of shops or malls. In the high street in the UK you would have found the type of shop you were after by looking out for a sign hanging out. There were signs for pharmacists, tobacconists, pawnbrokers, whatever. Nowadays there’s just one traditional sign still sometimes to be seen – the barber’s pole, as left in the animation.
The barber’s sign shows a famous illusion. The cylinder is rotating horizontally, but the stripes look as if they are rising – which would be impossible, unless you had some long pole sliding through the cylinder.
You can begin to see why in the demo on the right: focus on the vertical slot and the grating seems to be moving vertically (as in the barber’s pole). But focus on the horizontal slot and in a moment the grating may seem to move horizontally. Behind the round hole, for me it tends to look as if moving obliquely.
It’s a demo that depends for a start on a fact I find counter-intuitive: if a grating of oblique lines passes behind a small hole in a mask, (an extensive grating, so that the edges of the grating never appear in the hole), the lines stay objectively the same as they traverse the hole, whether the grating, at the orientation shown in the animation, is moving horizontally to the left, obliquely up and to the left, or vertically upwards, (or conversely, as not shown here, horizontally to the right, obliquely down and to the right, or downwards).
That leaves the brain struggling to guess which way the grating is actually travelling, and being pretty indecisive about it. In the animation, when the mask goes a bit transparent, I find that if I focus on the vertical slot the whole grating tends to appear to move vertically. Focus on the horizontal slot and after a moment the grating moves horizontally. Behind the circular hole, the grating tends for me to move obliquely.
So behind the illusion first of all is an objective fact, that the stimulus the grating presents as it passes behind the slots remains constant even when its true direction of movement changes. But then, why does the grating appear to us to move consistently vertically in a vertical slot, and horizontally in a horizontal slot? The short answer is, nobody is quite sure. For a start, the cell groups which detect movement in the eye only sample small receptive fields, compounding the effects of the mask. So effects of movement across the visual field, even without the mask in this demo, have to be stitched together in the brain. In this illusion, the stitching seems to follow signals from the edges of the slots, where the moving ends of the hatched lines do objectively run along the orientation of the slots. But as ever, not all the effects we see in a careful study follow such a simple rule as that. Just how the brain finally puts it all together is much, much more subtle. If you like getting seriously technical, try this paper by Nick Fisher and Johannes Zanker from 2001.
Some of the best of all illusions in the tradition of rotating heads were designed for advertising in the 1930′s by British artist Rex Whistler – you really have to take a second look to convince yourself the lower faces are just rotations of the upper ones. He was sadly killed in action in World War Two, but the heads were collected in a book of 1979, AHA. He got the idea from some seventeenth century engravings, (reproduced below), which had first appeared in 1671 in a book by polemicist Pierre Berault. The Western, Christian world at that time was riven with hatred between Catholics and Protestants, and these images are an anti catholic salvo, showing a Pope (left pair of roundels below) and a cardinal (right pair of roundels below) transforming into devils with rotation.
I found these details in two editorials about rotating heads for the journal Perception, by perceptual scientist and artist Nick Wade and colleagues. Check them out for lots more info and images. One is from 2003, the other from 2005, and they are the most authoritative source of information on rotating heads generally.
One of my favourite René Magritte paintings is Carte Blanche. I’ve two earlier posts that play on the same effects – an image for Halloween and a classical scene. I’ve always wondered if the effect would be even stronger and stranger in an animation. So here it is.
Usually an area of the visual field within an outline, or more or less bounded by an outline, is either an object or an aperture. (One of my earliest posts on the site is also about that). We are so good at not getting those mixed up in everyday vision that when they get mixed up in a picture, like the Magritte painting or my examples, the effect is strangely disconcerting.
Here’s a dark-on-light, bubble version of The Kanizsa triangle. The triangle is usually shown in white against black circles and lines, and can even look slightly brighter than background, though its edges are only indicated by the gaps in the lines and by the segments missing from the circles. The brain adds the edges and fills in the triangle, as the most probable explanation for what’s missing. The effect was created by Gaetano Kanizsa, as a demonstration of subjective contours, which in turn were first explored a bit over a century ago, as examples of Gestalt theory. Bit of a link for enthusiasts that – ditto the following links – but if technical stuff is for you, there’s a great historical survey of the theory. The theory as then developed is not now accepted, and just how the brain reconstructs the triangle is still debated.
Like many geometric illusions, and like the watercolour illusion (see recent post), the Kanizsa triangle also appears when reversed out as a black shape against bright lines and segments. So here I’ve recruited some soap bubbles as a background to the effect.
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In this wonderful image of the Buddha from Bagan, Myanmar, facial expression changes from stern through smiling to radiant as the figure is viewed from increasing distance. According to my friend Eddy Keon, the highest status members of the temple audience, along with temple officials, would have stood closest to the Buddha and therefore have experienced him at his sternest, whilst his radiance increased with the poverty of the viewer, banished to the back of the crowd.
The figure is the Kassapa Buddha, one of four Buddhas in the Ananda Temple, Bagan, Myanmar. The city was the capital of the ancient Pagan kingdom, built, along with the temple and this figure of the Buddha, eight hundred years ago.
If the way I see this animation is how most people do, the strength of the Poggendorff illusion can depend on our patterns of fixation when looking at it. Adding distracting dots to the figure can attract the eye either obliquely along the parallels or at right angles across them. To my eye, when the oblique track between the acute angles in the figure is labelled with flashing blobs, the strength of the illusion is reduced. When the track at right angles across the parallels is labelled, effect is maximised. The effect doesn’t change instantly for me, but settles down after each track has flashed two or three times. I get the same effect if I switch fixations every second or so between equivalent blobs in still Poggendorff figures. The effect is strongest, as below, when the blobs are in the acute angles when the parallels are vertical, and across parallels when the parallels are horizontal. So in the figure below, the illusion is not far off equal strength for me in the bottom pair of figures, but looks maybe a bit stronger at top left, and has almost vanished at top right.
In the original effect, as seen to left, islands with two-tone outlines seem tinted with the colour of the inner tone, if lighter than the outer, and otherwise appear (as in the lower figure) whiter than the background.
Sure enough, as seen centre, the effect is still there, but a bit weaker, when exactly the same two-tone outlines are placed on black. The upper interiors, which seemed tinted on white, appear (to my eye) blacker than the black background. The lower interior, which looked whiter than background on white, now appears tinted. In other words, on white the haze spreads from the paler outline, when the darker outline encloses it, whereas on black, the haze spreads from the darker outline, and when enclosed by a paler outline.
Consistent with that, to my eye, on the right when the colours of the two-tone outlines are reversed on black, the interior that appeared tinted in the centre lower figure appears blacker than background. The upper figures, with interiors blacker than background in the centre, look tinted to the right.
The effect is strongest for me in the three lower figures, looking across the whole image. (Ignoring the Santa figure, added for seasonal effect). For me the effect also works best slightly larger, so click on the figure to see a larger version.