THE SPINNING DISKS ILLUSION
BY JOHANNES ZANKER
ROYAL HOLLOWAY, UNIVERSITY OF LONDON, U.K.
2005 FINALIST
In the Spinning Disks Illusion, grayscale gradients in the shape of disks are arranged in concentric circles that seem to spin slowly, instead of appearing completely motionless—which they actually are! The illusion is caused by involuntary eye movements: each eye motion moves the image onto a new population of retinal photoreceptors. If you stare at the red central dot, carefully holding your eyes in place, the illusory motion will cease.
THE ENIGMA ILLUSION
Look at the center of the left-hand image below and notice how the concentric green rings appear to fill with rapid illusory motion, as if millions of tiny cars were driving hell-bent for leather around a track. For almost two hundred years, artists, psychologists, and neuroscientists debated whether this type of striking illusory motion originates in the eye or in the brain; for almost two decades, the controversy centered on the motion perceived in a similar painting, called Enigma, created by Isia Leviant, an artist associated with the Op Art movement. Op Art started in the 1960s with the explicit intent to examine illusory perception. Our colleague Jorge Otero-Millan created this particular image as a reinterpretation of Leviant’s Enigma.
Does the illusion originate in the mind or in the eye? The evidence was conflicting until we found, in collaboration with Xoana Troncoso and Otero-Millan, that the illusory motion is significantly driven by microsaccades: small involuntary eye movements that occur when we fix our eyes on a target.
Some years ago, Susana noticed that the speed of illusory motion in Enigma was not immutable across time, but depended on how precisely she fixed her gaze. If she held her eyes very still while staring carefully at the center of the image, the motion seemed to decrease and would occasionally come to a full stop. Conversely, when she focused her eyes loosely, the movement sped up. Our previous research had shown that strictly focusing your eyes suppresses the production of microsaccades, with dramatic effects on visibility. It followed that microsaccades may drive the perception of Enigma’s illusory motion under normal, or loosely focused, fixation conditions.
To test this idea, we asked volunteers to stare steadily at a small spot at the center of an Enigma-like pattern while we tracked their eye movements. Subjects pressed a button whenever the motion appeared to slow down or stop and released the button whenever the motion sped up. As we predicted, microsaccades increased in frequency just before people saw faster motion, and became sparser just prior to the slowing or halting of the motion. The results, published in 2008, proved for the first time that this type of illusory motion starts in the eye. Otero-Millan’s Enigmatic Eye (right image on opposite page), also a tribute to Enigma, reflects the role of eye movements in the perception of the illusion.
The precise brain mechanisms that cause us to perceive the Enigma Illusion are still unknown. One possibility is that microsaccades—and perhaps other eye movements, too—produce small shifts in the geometric position of the peripheral areas of the image. These shifts may cause repeated contrast reversals that could create the illusion of motion. The neuroscientist Bevil Conway and his colleagues at Harvard Medical School demonstrated that pairs of static stimuli with different contrast levels can generate motion signals in visual cortex neurons. This phenomenon, in combination with eye movements, may explain the perception of illusory motion in many static patterns, including the Enigma Illusion.
THE ROTATING-TILTED-LINES ILLUSION
This illusion, developed by the vision scientists Simone Gori and Kai Hamburger, is a variation on Enigma. To experience the illusion, move your head forward and backward as you fixate in the central area (or, alternatively, hold your head still and move the page). As you approach the image, notice that the radial lines appear to rotate counterclockwise. As you move away from the image, the lines appear to rotate clockwise. Vision scientists have shown that illusory motion activates brain areas that are also activated by real motion. This could help explain why our perception of illusory motion is qualitatively similar to our perception of real motion.
PULSATING HEART
BY GIANNI SARCONE, COURTNEY SMITH, AND MARIE-JO WAEBER
ARCHIMEDES LABORATORY PROJECT, ITALY
2014 FINALIST
This Op Art–inspired illusion produces the sensation of expanding motion from a completely stationary image. Static repetitive patterns with just the right mix of contrasts trick our visual system’s motion-sensitive neurons into signaling movement. Here the parallel arrangement of opposing needle-shaped red and white lines makes us perceive an everexpanding heart. Any other outline delimited in a similar fashion would also appear to pulsate and swell.
THE BLURRY HEART ILLUSION
BY KOHSKE TAKAHASHI, RYOSUKE NIIMI, AND KATSUMI WATANABE
UNIVERSITY OF TOKYO, JAPAN
2010 FINALIST
The Blurry Heart Illusion is simple yet powerful. Shifting your gaze from one cross to the next makes the blurry heart wobble while the heart with sharp contours remains stationary. This illusion works because the blurred edges—when viewed through your peripheral vision—activate motion-detecting neurons as you move your eyes around on the page. Placing a red heart on a blue background may enhance the effect due to the high color contrast between red and blue.
THE ROTATING SNAKES ILLUSION
BY AKIYOSHI KITAOKA
RITSUMEIKAN UNIVERSITY, JAPAN
2005 FINALIST
This illusion is a magnificent example of how we perceive illusory motion from a stationary image. The “snakes” in the pattern appear to rotate as you move your eyes around the figure. In reality, nothing is moving other than your eyes!
If you hold your gaze steadily on one of the “snake” centers, the motion will slow down or even stop. Our research, conducted in collaboration with Jorge Otero-Millan, revealed that the jerky eye motions—such as microsaccades, larger saccades, and even blinks—that people make when looking at an image are among the key elements that produce illusions such as Kitaoka’s Rotating Snakes.
Alex Fraser and Kimerly J. Wilcox discovered this type of illusory motion effect in 1979, when they developed an image showing repetitive spiral arrangements of luminance gradients that appeared to move. Fraser and Wilcox’s illusion was not nearly as effective as Kitaoka’s illusion, but it did spawn a number of related effects that eventually led to the Rotating Snakes. This family of perceptual phenomena is characterized by the periodic placement of colored or grayscale patches of particular brightnesses.
In 2005, Bevil Conway and his colleagues showed that Kitaoka’s illusory layout drives the responses of motion-sensitive neurons in the visual cortex, providing a neural basis for why most people (but not all) perceive motion in the image: we see the snakes rotate because our visual neurons respond as if the snakes were actually in motion.
Why doesn’t this illusion work for everyone? In a 2009 study, Jutta Billino, Kai Hamburger, and Karl Gegenfurtner, of the Justus Liebig University in Giessen, Germany, tested 139 subjects—old and young—with a battery of illusions involving motion, including the Rotating Snakes pattern. They found that older people perceived less illusory rotation than younger subjects, not only in the Rotating Snakes Illusion, but also in the Rotating-Tilted-Lines Illusion, depicted earlier in this chapter.
But the Pinna Illusion, pictured below, works for most observers irrespective of age. As you move your head (or the image) forward and back while you look at the central dot, you will see the inner and outer rings rotate in opposite directions. So whatever causes these various percepts to change with age, it cannot be as simple as a failure to perceive illusory motion. These findings will, we hope, lead to future research and a more nuanced understanding of the mechanisms underlying motion perception, as well as the specific effects of aging on different brain circuits.
FLOATING STAR
BY JOSEPH HAUTMAN / KAIA NAO
2012 FINALIST
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This five-pointed star is static, but many observers experience the powerful illusion that it is rotating clockwise. Created by the artist Joseph Hautman, who moonlights as a graphic designer under the pseudonym “Kaia Nao,” it is a variation on Kitaoka’s Rotating Snakes Illusion. Hautman determined that an irregular pattern, unlike the geometric one Kitaoka used, was particularly effective for achieving illusory motion. Here the dark blue jigsaw pieces have white and black borders against a lightly colored background. As you look around the image, your eye movements stimulate motion-sensitive neurons. These neurons signal motion by virtue of the shifting lightness and darkness boundaries that indicate an object’s contour as it moves through space. Carefully arranged transitions between white, light-colored, black, and dark-colored regions fool the neurons into responding as if they were seeing continual motion in the same direction, rather than stationary edges.
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IMPOSSIBLE ILLUSIONS
In an impossible image, seemingly real objects—or parts of objects—form geometric relations that physically cannot happen. The Dutch artist M. C. Escher, for instance, depicted reversible staircases and perpetually flowing streams. The mathematical physicist Roger Penrose drew his famous impossible triangle, and the visual scientist Dejan Todorovi´c created a golden arch that won him third prize in the 2005 Best Illusion of the Year Contest.
The impossible triangle, also called the Penrose Triangle or the Tribar, was actually first created by the Swedish artist Oscar Reutersvärd in 1934. Twenty years later, Penrose attended a lecture by M. C. Escher and, inspired by what he heard, independently rediscovered the Impossible Triangle. Penrose at the time was unfamiliar with the work of Reutersvärd, Giovanni Piranesi, and other previous discoverers of this confounding shape. He drew the illusion in its now most familiar form and in 1958 published his observations in the British Journal of Psychology, in an article co-authored with his father, Lionel. In 1961, the Penroses sent a copy of the article to Escher, who incorporated the effect into Waterfall, one of his most famous lithographs.
The etchings of water rolling uphill in Escher’s Waterfall illustrate the artist’s remarkable intuition that human perception assembles the whole of an image out of a multitude of little parts. Neuroscientific research has proved Escher right: we now know that the visual system puts together the global perception of a scene from many local relations among object features. As a result, tiny mistakes that are too small to detect locally (and that occur in the real world rarely, if ever) can add up across space to become major mistakes at the global level, and—voilà!—you have an impossible image.
Impossible images challenge our hard-earned perception that the world around us follows certain inviolable rules. They also reveal that, because our brains construct the feeling of an overall item by sewing together multiple local features, we don’t mind that the global picture is impossible, as long as its local characteristics follow the rules of nature.
Some of our contest competitors, such as Kokichi Sugihara, have gone a step further and created real-world 3-D objects that nonetheless appear to be impossible. Unlike Renaissance or classical sculptures, such as Michelangelo’s Pietà or the Winged Victory of Samothrace, which can be perceived by either sight or touch, impossible sculptures can be interpreted (or misinterpreted, as the case may be) only by the visual mind.
IMPOSSIBLE MOTION: MAGNETIC SLOPES
BY KOKICHI SUGIHARA
MEIJI INSTITUTE FOR ADVANCED STUDY OF MATHEMATICAL SCIENCES, JAPAN
2010 FIRST PRIZE
A Japanese miner climbs onto the stage with his helmet light bobbing and a pickax slung over his shoulder. He swings the pick a few times and then kneels to inspect something. He digs at some loose rubble with his hands. Suddenly his face lights up and he turns to the audience with newfound riches held forward. “I have discovered a new supermagnet that attracts wood,” he announces. Okaaaay … A video begins playing, and the audience sees four wooden balls rolling uphill, in open defiance of the laws of gravity. Are they being pulled by a magnet? Not really. The “miner” is the mathematical engineer Kokichi Sugihara, and his magnetlike illusion was the winner of the 2010 Best Illusion of the Year Contest. The trick is revealed when we see Sugihara’s slopes from a different vantage point: the wood balls are actually rolling down the ramps, not up. The slopes are cleverly designed to produce an illusion of antigravity from a specific point of view. Sugihara’s invention exemplifies several of the most popular themes in illusion research and creation today. It uses a trick of perspective that produces perceptual ambiguity. There is more than one way to perceive the “magnetic” slopes, but our visual system makes us prefer one interpretation, based on how we expect physical reality to work. Impossible illusions are a way to fool the brain into revealing its default expectations about the world.
“We are surrounded by many industrial products that are made with right angles, such as desks, boxes, and buildings,” Sugihara explained. When confronted with an image that allows for multiple interpretations, we choose the version that allows us to see rectangular solids. In Sugihara’s illusion, none of the columns that support the ramps are vertical, but we interpret them all as perfectly straight. We also perceive, incorrectly, that the center column is the tallest.
Sugihara discovered this illusion by using a computer program designed to read 3-D line drawings, such as architectural blueprints. He tested the program by feeding it images of impossible objects drawn in the style of Escher. He expected the program to respond with an error message; instead, the software interpreted some of the images as peculiar 3-D solids. Sugihara assumed he had a bug in his code, but soon realized that the software was recognizing objects that only seemed impossible from a certain point of view. Delighted, he set out to construct some of these objects, and later added an element of motion to enhance the illusion. To appreciate the magic fully, you can see the balls moving at the Best Illusion of the Year Contest website.
ELUSIVE ARCH
BY DEJAN TODOROVIC´
UNIVERSITY OF BELGRADE, SERBIA
2005 FINALIST
Is this an image of three shiny oval tubes? Or is it three pairs of alternating ridges and grooves?
The left side of the figure appears to be three tubes, but the right side looks like a corrugated surface. This illusion occurs because our brain interprets the bright streaks on the figure’s surface as either highlights at the peaks and troughs of the tubes or as inflections between the grooves. Determining the direction of the illumination is difficult: it depends on whether we consider the light as falling on a receding or an expanding surface. Trying to determine where the image switches from tubes to grooves is maddening. In fact, there is no transition region: the whole image is both “tubes” and “grooves,” but our brain can only settle on one or the other interpretation at a time. This seemingly simple task short-circuits our neural mechanisms for determining an object’s shape.
IMPOSSIBLE ILLUSORY TRIANGLE
BY CHRISTOPHER TYLER
SMITH-KETTLEWELL EYE RESEARCH INSTITUTE, U.S.A.
2011 FINALIST
Christopher Tyler of the Smith-Kettlewell Institute in San Francisco invented the autostereogram, a type of random dot pattern that allows many people to perceive a 2-D image as if it were in 3-D. Autostereograms are the basis for the famous Magic Eye books that were all the rage in the 1990s. In true academic fashion, of course, Tyler never made a cent off them. (Although he discovered a method for creating autostereograms, he did not patent it.) At the 2011 contest, Tyler began his presentation by showing the Penrose Triangle, the quintessential impossible object introduced at the beginning of this chapter. Tyler also displayed another famous triangle, the one named for the Italian psychologist Gaetano Kanizsa that we also described earlier. The Kanizsa Triangle shows that the brain can create entire objects by filling in missing information. Tyler wondered whether he could integrate the two perceptual traditions. When he laid the outline and inner crossbars of the Penrose Tria
ngle over the three incomplete balls denoting the Kanizsa Triangle, he discovered something remarkable: the brain will fill in the shapes not only of simple figures, but of impossible ones, too. Tyler’s illusion confirms the idea, mentioned in this chapter’s introduction, that our brains construct the feeling of a global 3-D percept by sewing together multiple local percepts. As long as the relations among local features follow nature’s rules, our brains do not seem to mind that the global percept is impossible, or that the local structures contain only the sparsest information.
AND THE WINNER IS …
For many years, the Italian sculptor Guido Moretti donated copies of his Three-Bar Cube and other impossible sculptures as trophies for the Best Illusion of the Year Contest. Depending on your vantage point, the Three-Bar Cube appears to be a Necker cube (the classical illusion named after the Swiss crystallographer Louis Albert Necker), an unspecified solid structure, or an impossible triangle. This specific vantage point is known to scientists as the accidental view, but there is nothing accidental about it. For the observer to perceive each particular shape, the view must be carefully staged and choreographed.
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