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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