Paradoxical form of filled/empty optical illusion

The filled/empty illusion (Oppel–Kundt) is one of the oldest geometrical-optical illusions, but the determinants of the illusion are not yet sufficiently understood. We studied magnitude of the illusory effect as a function of the height of vertical strokes subdividing a spatial extension of fixed length, using the psychophysical standard–variable matching paradigm. For vertical strokes shorter than, or of the same height as strokes delimiting the standard, the length was over-reproduced consistently with earlier studies of the illusion. However, for vertical strokes three times longer than the delimiters, the illusory effect paradoxically decreased, and attained negative values in two of six subjects. The magnitude of the effect thus depends on the patterning of the space between the delimiters, not merely on the number of subdividing elements.