Breathing Square
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Applet design: Al Seckel  Programing: ET-Labs, Inc.  Breathing Square©1997 IllusionWorks, L.L.C.

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     You will note a rigidly rotating square. Use the control at the bottom to vary the size of the occluding square. What happens to your perception of the square's rigidity?

What's Going On?

     When you first look at the rotating breathing square, you might come to the conclusion that it is not really an illusion at all -- that the change in size is simply due to the change in perceived area as the square rotates behind the occluder. This, however, is not the case.

     The breathing square illusion is due to your visual system's inability to resolve ambiguous information about the rotating square's true direction of movement when it is occluded by an aperture.

     In the breathing square illusion, the spaces between the four occluding squares (1, 2, 3, 4) serve as apertures through which the contours of the underlying square are partially visible.

     As the square rotates, the visible portions of the segments move towards or away from the center horizontally (in spaces 2 and 4) or vertically (in spaces 1 and 3). 

     For example, in the top part (1), there is a motion cue due to the straight lines of the green square between any two occluders. However, integrated over a small time window the square is rotating to the right.

     In addition, you also have the intersection of the square with the borders of the occluding red boxes. Here, the motion is (seemingly) not ambiguous and it moves straight up on the left side and straight down on the right side. Due to the spatial separation of the segments and the overlying squares, your visual system is somewhat handicapped in perfectly integrating the ambiguous motion signals of the four squares together into a rigid motion.  Instead, your visual system perceives the segments as having a strong component of motion towards or away from the center.

     If you decrease the distance between the occluding boxes the up-down motion predominates and the square breathes. If you make the distance very small, the rotatory component predominates. This perceived motion of the segments leads directly to the illusion of the sides bulging out or shrinking in - the "breathing" aspect.

     Implicit in the explanation for this effect is the idea that the motion of the contour can, under some circumstances, be dominated by the motion of the terminators. So, even though there might be enough information in space or time to recover the "correct" motion by integrating the contour motion signals, the local terminator motions seem to overwhelm the motion computation in several cases such as the breathing square illusion. If one reduces the perceptual salience of the terminators, or increases the salience of the contour, the effect can  be expected to diminish. 

      In the Wallach extended-aperture effect (barber pole illusion), for instance,  adding stereo-disparity to indicate that the terminators are non-intrinsic, lessons the effect significantly, as shown by Nakayama and Shimojo.

      Pawan Sinha of MIT tested this hypothesis by creating a sequence where the lines do not translate horizontally or vertically but simply rotates in place. Physically, this corresponds to the rotation of a "non-rigid" square that actually shrinks and grows as its rotates. The percept, however, is that of a perfectly "rigid" square rotating.

     The breathing square illusion was conceived by professor Misha Pavel of the Oregon Graduate Institute.

Entire web site©1997 IllusionWorks, L.L.C.