Koffka's effect is mediated by figure thickness at the joining region

Three-quarters of a century ago Gestalt psychologist Kurt Koffka described a remarkable effect: when a contiguous gray ring is placed on a background half one shade of gray, half another, the ring appears homogeneous. However, if the ring is divided, the two halves of the ring appear different shades of gray, the half of the ring on the darker background appearing lighter than the half of the ring on the lighter background. The Gestalt principle of continuity is used to explain this effect. But what microscopic principles might be mediating this effect? Recently we found sufficiently thin rings (annuli) appear heterogeneous even when geometrically continuous. Here, using crescent-shaped figures instead of the circular annuli used for the traditional Koffka effect, we show that this effect of thickness of the ring is mediated by the thickness at the boundary of the region where the halves of the figure are joined.