A family of aperiodic tiling with infinitely many orientations

A family of aperiodic tiling with infinitely many orientations

To date, most tilings of the Euclidean plane have the property that their tiles appear in finitely many orientations (TFMO), and well-developed theories in the study of aperiodic tilings and tiling spaces assume the property TFMO. This paper provides examples of aperiodic tilings whose tiles occur i...

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Bibliographic Details
Main Authors: Say-Awen, April Lynne D., Frettlöh, Dirk, De Las Peñas, Ma. Louise Antonette N.
Format: text
Published: Animo Repository 2018
Subjects:
Aperiodic tilings
Tiling spaces
Mathematics
Online Access:https://animorepository.dlsu.edu.ph/faculty_research/5937
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Institution: De La Salle University
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Summary:To date, most tilings of the Euclidean plane have the property that their tiles appear in finitely many orientations (TFMO), and well-developed theories in the study of aperiodic tilings and tiling spaces assume the property TFMO. This paper provides examples of aperiodic tilings whose tiles occur in infinitely many orientations. The prototile sets of these tilings include triangle prototiles with irrational angles.

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