Periodic Strips from Aperiodic Tiles

Year: 2024 Authors: Craig S. Kaplan

Core claim

Under mild conditions, any tile set that tiles the plane admits periodic strips of arbitrary width, even when the tiles themselves are aperiodic.

Topics

periodic strips, aperiodic tilings, frieze symmetry, decorative design

Domains

tiling theory, symmetry groups, substitution tilings, aperiodic order, pattern design, frieze decoration, cylinder wrapping, fabric and wallpaper

Methods

constructive examples, local reflection symmetry, tiling patch analysis, informal existence argument

Media

kites and darts, Penrose rhombs, cylindrical objects, printed friezes

Source status

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