The half-Zöllner illusion

The Zollner figure contains stacks of short parallel segments oriented obliquely to the direction of the stack. Adjacent parallel stacks of opposite polarity seem to diverge where their top segments form an arrowhead. To probe whether or not the opposite polarities are necessary to the illusion, three 'half-Zollner' configurations were designed, containing stacks of a single polarity. The 'orientation profile' of these configurations was studied, that is, the way the strength of the perceived illusion varies with the orientation of the stacks. The subjects had to align two stacks or align stacks with target segments situated at a slight distance from them. All three half-Zollner configurations produced errors that could be assimilated to global-orientation misjudgments. These errors were of opposite sign for the two types of stacks and varied with the orientation of the stacks as in the standard Zollner illusion. A further study was conducted in which the effect of several configurational parameters was explored for a single observer. The standard Zollner illusion increases with the separation of the stacks. The illusion is also increased when the orientations of the segments in different stacks are orthogonal, independently of the particular longitudinal orientations of the stacks. When the ends of the short segments are curved so that at their endpoints they become precisely perpendicular to the axis of the stacks, the standard and half-Zollner illusions are reduced, but not abolished. Therefore, they cannot be entirely accounted for by a mechanism of alignment of illusory contours generated at these endpoints. The results are consistent with the existence of a single common mechanism at work in both the standard and the half-Zollner illusion. It is suggested that the illusion itself is not a rotation of the stacks but either a shear deformation in which the segments of a stack slide with respect to one another, or an expansion of the stacks orthogonally to the segments.