HUMAN PERCEPTION SEEMS TO TRY to impose order on disorder. This month I shall discuss two illusions that are based on this tendency. The first illusion is an array of random dots that, viewed in a certain way, seem to form concentric circles. The other illusion is seen in the patterns and motions on a television screen that is tuned to a channel over which no signal is being transmitted. The random "snow" that covers the screen can apparently be ordered by the visual process.

I first became interested in random-dot displays last year when I got a letter from A. G. Klein of the University of Melbourne. With his letter came a transparency of randomly arranged dots, some less than a millimeter across and others several millimeters. Klein had made the transparency by sprinkling graphite powder on a sheet of paper and then running the paper through a 3M transparency producer. He also enclosed with his letter a photocopy of the transparency.

Following instructions from Klein, I aligned the transparency on the copy and then slightly rotated the transparency about a point near the center. Suddenly the random array of dots turned into concentric circles centered on the point of rotation. The circles were not complete, but the illusion that they were there was compelling. The question is why my visual system thus imposed order on disorder.

One can make similar transparencies of random dots in other ways. One way is to dip an old toothbrush into paint and then spray the paint onto a surface by running a finger over the bristles. You could spray the paint onto paper and make a transparency on a machine, or you could deposit the paint directly on a sheet of plastic. Alternatively you could insert two sheets of carbon paper between a sheet of regular paper and a sheet of acetate. Lay the sheets of carbon paper so that they are back to back. Then hit the four layered sheets repeatedly with the bristles of a wire brush. The points of impact will appear as identical dots on both the regular paper and the acetate. Photographs of sandpaper will also work, according to D. M. MacKay of the University of Keele in England, who in 1964 reported that illusions of circles and spirals can be seen in both positive and negative photographs of sandpaper. Regardless of the technique, a slight rotation of the two identical patterns after an initial alignment gives rise to the illusion of concentric circles.

Leon Glass of the University of Rochester has investigated this illusion for 10 years. In 1969 he described some of the

simple observations one can make with the random-dot patterns and speculated about the aspect of the perceptual system responsible for the illusion. In 1973 Glass and Rafael Perez published the results of a variety of experiments with the random-dot patterns. They made the patterns with a pseudorandom-number generator that is available in the computer language Fortran. Next a computer chose the positions of the dots, which were then inscribed with a Calcomp plotter. The plots were redrawn by hand and converted into transparencies.

In some experiments the patterns on the paper and those on the transparencies were the same size, so that the alignment of the two was precise. In other experiments one of the two was reduced, so that the alignment was close only in a small area. If the two patterns were at the same scale, Glass and Perez observed the same types of illusions I have described. If the patterns were not at the same scale, two types of illusion were possible. One resulted if the experimenter aligned the dots in one small area and was careful not to rotate the transparency with respect to the paper. Then the superposed patterns gave the appearance of an explosion. A slight rotation of the transparency with respect to the paper transformed the explosion into a form that resembled a spiral galaxy.

Glass and Perez noted that if only a small section of the superposed patterns was visible, the illusion of circles, explosions or spirals either was less apparent or was absent. The illusions depend on a correlation by the observer of the appropriate pairs of dots in the patterns (the ones that would coincide if the patterns were at the same scale and were exactly aligned). When the patterns are rotated, those pairs are separated. The observer apparently takes in the entire display, correlating the separated pairs. The correlation somehow suggests the illusion. If the field of view is limited to a small section of the pattern, however, the observer either cannot correlate the pairs as well or the number of correlations is insufficient to give rise to the illusion.

In another set of experiments Glass and Perez made transparent negatives of a pattern in such a way as to create white dots on a black background. The patterns in the two transparencies were the same except that one was rotated with respect to the other. The transparencies were placed in a stereoscopic projector, and the observer viewed both of them simultaneously. The intensity of the light from each transparency could be independently controlled by a pair of crossed polarizing filters, one pair in front of each transparency. For example, if the experimenter wanted to decrease the amount of light coming from the right-hand transparency, he rotated one polarizing filter of the pair in front of that transparency.

In one of the experiments identical but rotated transparencies were viewed. As the intensity of light from one of the transparencies was decreased the circles appeared to rotate. For example, suppose transparency was initially rotated clockwise with respect to transparency P. Decreasing the intensity of the light from P' then resulted in a counterclockwise rotation of the illusionary circles.

When the experimenters worked with a pair of transparencies that normally showed an apparent explosion, an adjustment of the intensity of the light from one of the transparencies gave the illusion that the size of the pattern had changed. If the intensity of the light from the transparency with the larger of the two patterns was decreased, the pattern seemed to shrink.

Glass and Perez also experimented with colored filters inserted in the path of the light coming from each transparency. In this way they could give a different color to each of the displays of random dots. The illusions of circles and other patterns remained. Moreover, if the intensity of one of the patterns was varied, the apparent motion (rotation, contraction or expansion) was again present.

When I play with the transparency and its copy that Klein sent me, I first align the two as carefully as I can. At a chosen point on the transparency I press the tip of a pencil and gradually rotate

or was absent. The illusions depend on a correlation by the observer of the appropriate pairs of dots in the patterns (the ones that would coincide if the patterns were at the same scale and were exactly aligned). When the patterns are rotated, those pairs are separated. The observer apparently takes in the entire display, correlating the separated pairs. The correlation somehow suggests the illusion. If the field of view is limited to a small section of the pattern, however, the observer either cannot correlate the pairs as well or the number of correlations is insufficient to give rise to the illusion.

In another set of experiments Glass and Perez made transparent negatives of a pattern in such a way as to create white dots on a black background. The patterns in the two transparencies were the same except that one was rotated with respect to the other. The transparencies were placed in a stereoscopic projector, and the observer viewed both of them simultaneously. The intensity of the light from each transparency could be independently controlled by a pair of crossed polarizing filters, one pair in front of each transparency. For example, if the experimenter wanted to decrease the amount of light coming from the right-hand transparency, he rotated one polarizing filter of the pair in front of that transparency.

In one of the experiments identical but rotated transparencies were viewed. As the intensity of light from one of the transparencies was decreased the circles appeared to rotate. For example, suppose transparency was initially rotated clockwise with respect to transparency P. Decreasing the intensity of the light from P' then resulted in a counterclockwise rotation of the illusionary circles.

When the experimenters worked with a pair of transparencies that normally showed an apparent explosion, an adjustment of the intensity of the light from one of the transparencies gave the illusion that the size of the pattern had changed. If the intensity of the light from the transparency with the larger of the two patterns was decreased, the pattern seemed to shrink.

Glass and Perez also experimented with colored filters inserted in the path of the light coming from each transparency. In this way they could give a different color to each of the displays of random dots. The illusions of circles and other patterns remained. Moreover, if the intensity of one of the patterns was varied, the apparent motion (rotation, contraction or expansion) was again present.

When I play with the transparency and its copy that Klein sent me, I first align the two as carefully as I can. At a chosen point on the transparency I press the tip of a pencil and gradually rotate the transparency until the illusion of the circles begins at a large radius from the center of rotation. The illusion requires the separation of correlated dots, which begins at a large radius sooner than it does closer to the pivot point. Further rotation separates the dots closer to the pivot point and so brings the illusion inward to the center of rotation. Eventually the rotation is large enough to destroy the illusion. Then I see only a relatively dense array of random dots.

The smaller dots were more effective in producing the illusion, probably because the larger dots needed a good deal of rotation to achieve the proper amount of separation. By then many of the smaller dots were no longer contributing to the illusion. A pair of dots made their best contribution when they were separated by a distance that was a few times their diameter. In the relatively dense areas of the pattern the illusion was weak because the proper amount of separation between correlated dots usually meant that other dots were near enough to cause confusion.

I could adjust the direction of the circling in the illusion by pushing with my thumbs at the lower end of the transparency. A push upward with my right thumb generated circles with their center lying to the left, a push upward with my left thumb generated circles with their center to the right. In an intermediate adjustment I could make the lines in the illusion straight instead of curved. Rapidly sliding the transparency around on the copy led to an additional illusion: a white wave sweeping around the page The white area appeared in the region where the dots were aligned and so gave no illusion of circular lines. The rest of the page had curved lines of some kind As I slid the transparency the area of alignment moved over the page and therefore so did the white area.

I tried to produce the illusion of circles by turning the transparency over and aligning a few of its dots with dots on its copy. The alignment was poor, of course, except for a few dots that happened to be about the same size and in approximately the right places. When I rotated the transparency out of this inadequate alignment, no illusion appeared. As I would have guessed, the illusion requires more than just a few dots. Apparently much of the page must be in near alignment with its copy. As Glass and Perez determined, the illusion stems from a "global" examination of the dot display, not from an examination of just a few dots.

In the same vein I can investigate how little of the display must be viewed in order to maintain the illusion. I first adjust the transparency and its copy in order to produce the best illusion of circles. Then I cover the transparency with a sheet of paper in which I have cut a square hole. By using different sizes for the hole I can see different amounts of the pattern. If the area of my view is only a few times wider than the average dot size, the illusion is weak or absent. If the area of my view is increased to about 20 times the dot size, the illusion can be discerned. I seem to observe the full illusion when the area of my view is at least 50 times the dot size.

When I lift the transparency slightly from the photocopied page, the illusion changes from concentric circles to either an explosion or a spiral. Glass and Perez created illusions of this kind by super-posing patterns that were identical except for scaling. In effect I achieve the same thing because the transparency is closer to me than the page and so appears to be slightly larger than the page.

I can also get the explosion illusion by holding the transparency close to a mirror and then viewing both the transparency

and its mirror image with one eye. An assortment of circles, spirals and explosions can be made by warping the transparency when it is placed over the photocopied page. For example, if I align the transparency and the photo copy and then distort the transparency, about halfway up the page I can force it into a "hill" that extends from the page. The result is that the lower end of the display has circles, the middle has either spirals or explosions and the top has large circles.

In addition to doing your own experiments with rotations in random-dot displays you may want to try your hand at producing art from the geometric patterns the illusions give. If you construct a relatively large random-dot display and warp the transparent sheet appropriately, you can make an illusion that changes with different perspectives. The circles and spirals vary as you move past the display. Probably someone has already done this in "op art," although I do not know who.

A different kind of random-noise display can be seen if you tune your television set to a channel to which no signal is being transmitted. The screen is filled with random snow picked up by the antenna. The display is one not of random dots but of randomly fluctuating intensities of light on the screen. Although the entire screen is fluctuating in intensity, the fluctuations in any small area of it !t have greater contrast than the fluctuations of the entire screen. One therefore has the impression that white dots are darting about the screen.

In 1961 MacKay reported several curious illusions that could be seen in the television snow. If you stare at the screen, you will probably find that in the center of your field of view the snowstorm is far more intense than it is away from the center. The effect is enhanced if you stare with one eye instead of two. MacKay noted that this region of enhanced agitation is associated with the foveal area of the field of view. The fovea is the part of the retina that affords the sharpest vision, because it has the closest packing of photoreceptors.

MacKay also pointed out that contrary to what one might think a screen viewed with one eye seems brighter and more densely packed with snow than the same screen viewed with both eyes. Moreover, with binocular viewing the apparent spots on the screen seem to be more persistent and their motion seems to have an oilier quality. If the screen's intensity is reduced, its appearance eventually becomes about the same for both kinds of viewing. At low intensities the screen appears to show discrete spots of light darting about and much of the frenzied quality of the movement is missing.

If a finger, a loop of wire, a black circle or some other such object is held in front of the screen, the spots appear to adhere to it, creating an illusion of a boundary layer at the contours of the object. One can even create an illusion of directed flow by choosing an appropriately shaped object. If a black circular loop is moved about in front of the screen, the spots of light appear to move with it, as if they had been lassoed. A moving finger seems to be pursued by a swarm of particles.

Earlier (in 1957) MacKay had demonstrated that a grid placed on such a screen can help the viewer to organize the random visual noise into a partly coherent pattern. When he placed a pattern of radial lines on the screen, the white spots on the screen appeared to move perpendicularly to the lines and so seemed to be swirling around the center of the grid. The swirling could be either clockwise or counterclockwise; at times areas of the display appeared to be turning in opposite directions. If MacKay rotated the grid, the pattern in the snow appeared to turn in the opposite sense. When he placed a grid of concentric circles on the screen, the dots again seemed to move in a stream that was perpendicular to the lines, but this time they flowed radially outward from the center of the grid pattern. The pattern in the snow also rotated slowly about the center of the grid. In some of MacKay's later experiments he found that putting a ring on the screen gave the illusion of snow drifting slowly around the ring.

I made similar observations with my own television screen and a set of moiré transparencies from the Edmund Scientific Company (101 East Gloucester Pike, Barrington, N.J. 08007). In the package of transparencies (Series A) the best effects came with patterns No. 4 and No. 5 placed on the television screen. No. 4 consists of a small central circle surrounded by radial lines; No. 5 consists of many closely ruled concentric circles.

When I held No. 4 on the screen, the center of the pattern forced the snow into frenzied activity and the radial lines made it spiral around either clockwise or counterclockwise. I could switch the apparent sense of rotation almost at will. To enhance the effects I adjusted the set's controls for brightness and contrast. My results were best when the brightness control was turned completely down and the contrast control was at its midpoint, but only experimentation will determine the optimum conditions for other television sets. The white dots appeared to be on a slightly curved surface lying just behind the plane of the glass of the screen. The various features of the illusions were present with both monocular and binocular viewing.

When I held the pattern close to one eye and shut the other eye, the illusion became extremely lively, particularly when

I was able to reverse the flow or set up counterflows simultaneously. The flow near the edge of the screen seemed to be less active. If I lowered the intensity until the screen was almost dark, the organization of the dots decreased until they resembled small bugs randomly darting about the grid system.

Pattern No. 5 organized the snow into pulsations, as if the center of the pattern were either the source or the sink of radial lines. This "emission hole" effect was notably intense when I held the transparency close to my eye. Again the organization disappeared when lowered the intensity of the light on the -screen from its peak level. When the intensity was highest, I had the strong impression that ripples were flowing over the screen; they looked much like the ripples produced by a pebble tossed into a pond.

By slightly displacing one transparency of pattern No. 4 in laying it over a copy of the same pattern, I was able to create two areas of swirling. With two copies of pattern No. 5 I made two emission holes. When I carefully aligned the transparencies and then misaligned them, I could superpose the normal moiré patterns (seen when two identical patterns are superposed and also slightly misaligned) on the organization of the screen noise. One of my transparencies had black lines, the other red; The result of superposing the two transparencies was that red lines were added on the organized flow of the snow.

No one is sure why the visual process organizes the snow when an appropriate pattern is placed on the television screen. MacKay has suggested that the interaction of contour-sensing elements in the visual process may bring about the organization, but exactly how they do it is not known. Perhaps the elements in the visual network that sense the contours of the superposed pattern may then be insensitive to motion along the contours. As a result the observer would see only the motion perpendicular to the contours. Alternatively couplings of contour-sensitive elements may enhance the sensitivity of the visual system to motion perpendicular to the contours. It is not known which explanation is correct, but recent work by MacKay, H. J. M. Gerrits and H. P. Stassen has shown that if the superposed pattern is stabilized on the retina (by means of a suction cup attached to the eye), the pattern fades and the illusion of organization in the snow diminishes. (Stabilizing any pattern on the retina causes it to fade from perception.) Therefore perceiving the pattern is necessary for the illusion.

In 1974 R. I. MacDonald of Carleton University in Ottawa independently reported an observation about snow on a television set that was similar to one of MacKay's observations. MacDonald noted that when he stared at the snow first with both eyes and then with one eye, the snow appeared to move slower and the spots seemed to be smaller. He was able to reproduce the same effect with the random noise generated by a laser beam transmitted through a pair of ground-glass plates. As one of the plates was moved around in the light from the other plate, the light was projected onto a screen and examined by an observer.

MacDonald also checked to see if this effect depended on the correlation of the eyes when both eyes were used. An observer viewed the screen with two cardboard tubes directed so that each eye saw a different section of the screen. The observer then closed one eye. The effect was again present, implying that it does not depend on the correlation between the eyes when the screen is seen binocularly. You could check this result with the snow on a television screen by similarly employing cardboard tubes.

As a last experiment I tried defocusing my eyes while watching the snow on my television screen. When I gently pressed the lower portion of my eye, the screen noise became significantly more vigorous and appeared to flow up and down. I assume that the pressure altered the shape of my eye and therefore prevented it from properly focusing the image of the screen onto my retina, but why this impaired focusing increased the intensity of the noise I do not know.

Bibliography

VISUAL EFFECTS OF NON-REDUNDANT STIMULATION. D. M. MacKay in Nature, Vol. 192, No. 4804, pages 739-740; November 25, 1961.

CENTRAL ADAPTATION IN MECHANISMS OF FORM VISION. D. M. MacKay in Nature, Vol. 203, No. 4948; August 29, 1964.

MOIRÉ EFFECT FROM RANDOM DOTS. Leon Glass in Nature, Vol. 223, No 5206, pages 578-580; August 9,1969.

PERCEPTION OF RANDOM DOT INTERFERENCE PATTERNS. Leon Glass and Rafael Perez in Nature, Vol. 246, No. 5432, pages 360-362; December 7, 1973.

KINETIC CYCLOPEAN EFFECT. R. I. MacDonald in Nature, Vol.249, No.5453, page 192; May 10, 1974.

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