A sinusoidal curve appears as a zigzag. The explanation requires no new mechanisms — just two known V1 properties working together.
The curvature blindness illusion (Takahashi, 2017): draw a smooth sinusoidal curve with alternating light and dark segments. Under certain conditions, the smooth curve is perceived as a series of straight-line segments meeting at sharp corners. The curvature is physically present but perceptually absent. Previous explanations invoked high-level processing or learning effects. None derived the illusion from known neural architecture.
Menke (arXiv:2603.09765) shows that two well-characterized properties of primary visual cortex (V1) are jointly sufficient. First: polarity-selective simple cells with same-polarity lateral connections break the contour at each contrast reversal point. Where a dark segment meets a light segment, the contour representation is interrupted, and the interruption creates a perceived corner. Second: at moderate contrast, the active orientation channel in V1 narrows — fewer neurons respond per segment — so no single channel spans the full curvature range of each segment. The segments are straightened because the orientation bandwidth is too narrow to represent the curve between corners.
Neither mechanism alone produces the illusion. Polarity breaks alone would create corners but wouldn't straighten the segments between them. Narrow orientation channels alone would reduce perceived curvature but wouldn't create corners. The illusion is the conjunction.
The model has no free parameters beyond what is already measured in V1 physiology. The illusion is not a failure of perception or an artifact of learning — it is a correct prediction of known cortical architecture operating on a specific stimulus. The curve looks like a zigzag because the visual system is doing exactly what it's built to do.
Menke, "Curvature Blindness from Polarity Breaks and Orientation Channel Fragmentation in V1," arXiv:2603.09765 (2026).