Are Maximally Unbalanced Hilbert-Style Square-Filling Curve Motifs a Drawing Medium?
Douglas M. McKenna

Proceedings of Bridges 2023: Mathematics, Art, Music, Architecture, Culture
Pages 91–98
Regular Papers

Abstract

Hilbert-style, square-filling curve motifs build Hamiltonian cycles on toroidal grid-graphs. Order-n motif paths are equivalent to two-dimensional n-ary Gray codes, which can be characterized by their balance: the disparity between the vertical and horizontal counts of the line segments used. We report on an experiment using maximally—but oppositely—unbalanced Hilbert-style motifs, both dual and zipping, as binary-valued “pixels” in a low resolution image. The images are subtly perceptible, more so when in motion vertically or horizontally on a computer screen.

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