Planar Rosa: a family of quasiperiodic substitution discrete plane tilings with 2n-fold rotational symmetry

被引：0

作者：

Kari, Jarkko ^{[1
]}

Lutfalla, Victor H. ^{[2
,3
,4
]}

机构：

[1] Univ Turku, Turku, Finland

[2] Univ Publ, Paris, France

[3] Univ Paris 13, LIPN, UMR CNRS 7030, Villetaneuse, France

[4] Aix Marseille Univ, LIS, UMR CNRS 7020, Marseille, France

来源：

NATURAL COMPUTING | 2023年 / 22卷 / 03期

关键词：

Tilings; Substitution; Quasiperiodic; Discrete Planes; RULES;

D O I：

10.1007/s11047-022-09929-8

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

We present Planar Rosa, a family of rhombus tilings with a 2n-fold rotational symmetry that are generated by a primitive substitution and that are also discrete plane tilings, meaning that they are obtained as a projection of a higher dimensional discrete plane. The discrete plane condition is a relaxed version of the cut-and-project condition. We also prove that the Sub Rosa substitution tilings with 2n-fold rotational symmetry defined by Kari and Rissanen do not satisfy even the weaker discrete plane condition. We prove these results for all even n > 4. This completes our previously published results for odd values of n.

引用

页码：539 / 561

页数：23

共 8 条

[1] Planar Rosa: a family of quasiperiodic substitution discrete plane tilings with 2n-fold rotational symmetry
Jarkko Kari
Victor H. Lutfalla
Natural Computing, 2023, 22 : 539 - 561
[2] Substitution Discrete Plane Tilings with 2n-Fold Rotational Symmetry for Odd n
Kari, Jarkko
Lutfalla, Victor H.
DISCRETE & COMPUTATIONAL GEOMETRY, 2023, 69 (02) : 349 - 398
[3] Substitution Discrete Plane Tilings with 2n-Fold Rotational Symmetry for Odd n
Jarkko Kari
Victor H. Lutfalla
Discrete & Computational Geometry, 2023, 69 : 349 - 398
[4] Sub Rosa, A System of Quasiperiodic Rhombic Substitution Tilings with n-Fold Rotational Symmetry
Jarkko Kari
Markus Rissanen
Discrete & Computational Geometry, 2016, 55 : 972 - 996
[5] Sub Rosa, A System of Quasiperiodic Rhombic Substitution Tilings with n-Fold Rotational Symmetry
Kari, Jarkko
Rissanen, Markus
DISCRETE & COMPUTATIONAL GEOMETRY, 2016, 55 (04) : 972 - 996
[6] A Computer Search for Planar Substitution Tilings with n-Fold Rotational Symmetry
Gaehler, Franz
Kwan, Eugene E.
Maloney, Gregory R.
DISCRETE & COMPUTATIONAL GEOMETRY, 2015, 53 (02) : 445 - 465
[7] Substitution tilings with dense tile orientations and n-fold rotational symmetry
Frettloeh, D.
Say-awen, A. L. D.
De Las Penas, M. L. A. N.
INDAGATIONES MATHEMATICAE-NEW SERIES, 2017, 28 (01): : 120 - 131
[8] A Computer Search for Planar Substitution Tilings with n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n$$\end{document}-Fold Rotational Symmetry
Franz Gähler
Eugene E. Kwan
Gregory R. Maloney
Discrete & Computational Geometry, 2015, 53 (2) : 445 - 465

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