An anaglyph demonstrating an amusing binocular effect.

by Jack Schwartz

Courant Institute of Mathematical Sciences
New York University

The figure seen below demonstrates an amusing binocular effect. Seen thru red-blue anaglyphic glasses, the section on the left shows two dark nested rectangles against a bright background in the red-filtered image, and a uniform black in the blue-filtered image. On the right we have one outer dark rectangle in the red-filtered image, and a smaller bright rectangle in the blue-filtered image. In anaglyphic view, the usual violent edge-dependency of perceived intensity makes the interior of the greenish rectangle look almost black, as expected. But another less familiar effect may be noted. In anaglyphic view the two rectangles on the left appear flat, as expected. But the outer rectangle on the right seems to be curiously 'akimbo', and, observed closely, is seen to be tilted in 3-D left-to-right (and curiously hard to look at). This binocular effect (i) disappears if either eye is closed, and (ii) reverses its 'tilt' if the anaglyphic glasses are reversed. The behavior is roughly that which would be expected if fusion were developing between the vertical edges of the outer dark rectangle R on the right and the adjacent edge of the bright rectangle it contains. This interpretation is supported by examination of the pair of lines in the middle of the figure, which also shows imperfect fusion and change in depth perception. Compare the right-hand edges of the rectangles on the right which are geometrically similar, but note (blue filter on right eye) that in the rectangles the black right edge seems to be raised, while in the middle lines it is the bright line that seems to be raised.

What gives this anaglyph its unusually befuddling appearance is the fact that the depth-perception mechanism raises the right (or left) edge of the outer right-hand rectangle without normal binocular fusion taking place. This suggests that these two effects are separable, with fusion possibly occurring as the result of a process of active repression of one (or both!) of the monocular images input to binocular vision.

By arraying multiple copies of the basic pattern seen at the right of Figure 1, either repeating their colors or interchanging black and yellow, we can produce an image that goes beyond the capabilities of th visual system when viewed anaglyphically, and is seen as a collection of strangely tilted elements, some of which even disappear from time to time. This is seen in Figure 2.