Plato's Cave: Spline-Like Properties

Spline-Like Properties of the Kanizsa Figure

The smooth bending properties of the illusory edge in the Kanizsa figure suggest an analog relaxation mechanism in the Gestalt tradition in the nature of a wooden spline between clamped endpoints, as shown below, or perhaps a magnetic field between opposite poles of two bar magnets as shown below.

In either of these models the globally smooth curve is not a product of some stored template or analytical algorithm, but rather emerges naturally as a result of local interactions. A dynamic relaxation system can thus be defined to have these properties in response to oriented edge signals. For example, imagine a system which responds to two horizontal edge signals, represented by the shaded barred circles below, with a field-like oriented response as shown below.

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