On the Frequency Module of the Hull of a Primitive Substitution Tiling

Understanding the properties of tilings is of increasing relevance to the study of aperiodic tilings and tiling spaces. This work considers the statistical properties of the hull of a primitive substitution tiling, where the hull is the family of all substitution tilings with respect to the substitu...

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Main Authors:	Say-Awen, April Lynne D, Frettlöh, Dirk, De Las Peñas, Ma. Louise Antonette N
Format:	text
Published:	Archīum Ateneo 2022
Subjects:	frequency module primitive substitution tilings aperiodic tilings quasicrystals Mathematics
Online Access:	https://archium.ateneo.edu/mathematics-faculty-pubs/185 https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1190&context=mathematics-faculty-pubs
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Institution:	Ateneo De Manila University

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spelling	ph-ateneo-arc.mathematics-faculty-pubs-11902022-03-17T07:59:52Z On the Frequency Module of the Hull of a Primitive Substitution Tiling Say-Awen, April Lynne D Frettlöh, Dirk De Las Peñas, Ma. Louise Antonette N Understanding the properties of tilings is of increasing relevance to the study of aperiodic tilings and tiling spaces. This work considers the statistical properties of the hull of a primitive substitution tiling, where the hull is the family of all substitution tilings with respect to the substitution. A method is presented on how to arrive at the frequency module of the hull of a primitive substitution tiling (the minimal -module, where is the set of integers) containing the absolute frequency of each of its patches. The method involves deriving the tiling's edge types and vertex stars; in the process, a new substitution is introduced on a reconstructed set of prototiles. 2022-01-01T08:00:00Z text application/pdf https://archium.ateneo.edu/mathematics-faculty-pubs/185 https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1190&context=mathematics-faculty-pubs Mathematics Faculty Publications Archīum Ateneo frequency module primitive substitution tilings aperiodic tilings quasicrystals Mathematics
institution	Ateneo De Manila University
building	Ateneo De Manila University Library
continent	Asia
country	Philippines Philippines
content_provider	Ateneo De Manila University Library
collection	archium.Ateneo Institutional Repository
topic	frequency module primitive substitution tilings aperiodic tilings quasicrystals Mathematics
spellingShingle	frequency module primitive substitution tilings aperiodic tilings quasicrystals Mathematics Say-Awen, April Lynne D Frettlöh, Dirk De Las Peñas, Ma. Louise Antonette N On the Frequency Module of the Hull of a Primitive Substitution Tiling
description	Understanding the properties of tilings is of increasing relevance to the study of aperiodic tilings and tiling spaces. This work considers the statistical properties of the hull of a primitive substitution tiling, where the hull is the family of all substitution tilings with respect to the substitution. A method is presented on how to arrive at the frequency module of the hull of a primitive substitution tiling (the minimal -module, where is the set of integers) containing the absolute frequency of each of its patches. The method involves deriving the tiling's edge types and vertex stars; in the process, a new substitution is introduced on a reconstructed set of prototiles.
format	text
author	Say-Awen, April Lynne D Frettlöh, Dirk De Las Peñas, Ma. Louise Antonette N
author_facet	Say-Awen, April Lynne D Frettlöh, Dirk De Las Peñas, Ma. Louise Antonette N
author_sort	Say-Awen, April Lynne D
title	On the Frequency Module of the Hull of a Primitive Substitution Tiling
title_short	On the Frequency Module of the Hull of a Primitive Substitution Tiling
title_full	On the Frequency Module of the Hull of a Primitive Substitution Tiling
title_fullStr	On the Frequency Module of the Hull of a Primitive Substitution Tiling
title_full_unstemmed	On the Frequency Module of the Hull of a Primitive Substitution Tiling
title_sort	on the frequency module of the hull of a primitive substitution tiling
publisher	Archīum Ateneo
publishDate	2022
url	https://archium.ateneo.edu/mathematics-faculty-pubs/185 https://archium.ateneo.edu/cgi/viewcontent.cgi?article=1190&context=mathematics-faculty-pubs
_version_	1728621299513688064

On the Frequency Module of the Hull of a Primitive Substitution Tiling

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