Finding 3D Lattice Paths Exhibiting Knotted Optical Illusions
Anton Bakker and Tom Verhoeff

Proceedings of Bridges 2025: Mathematics and the Arts
Pages 523–526
Short Papers

Abstract

Human perception of three-dimensional shapes is hindered by the fact that we can only see one projection of such a shape at a time. When projections from different perspectives seem to be irreconcilable, we call this an optical illusion. The artistic use of optical illusions can teach the viewer the dangers of making judgments based on a single viewpoint. This lesson is valuable not only for judging spatial shapes, but for many aspects of life in general. We describe the techniques that we have developed to help find lattice paths in 3D space that exhibit knotted optical illusions, and illustrate this with a number of artworks.

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