This animation is part of the demos for:
Bai, D., & Strickland, B. The "double ring illusion": The physical constraint of solidity shapes visual processing.
Explanation
Here, the preference for the 180° interpretation is disrupted (for most observers, the unstable percept is restored).
This is explained by the fact that object solidity can no longer be violated thanks to the gaps.
This also shows that the proximity of the rings cannot explain the effect. The visual system indeed incorporates solidity to guide processing of object motions.
Separated
Overlapping
Gapped
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