scholarly journals Multiscale substitution tilings

2021 ◽  
Author(s):  
Yotam Smilansky ◽  
Yaar Solomon
Keyword(s):  
Substitution Tilings

Highly symmetric random substitution tilings

2008 ◽  
Vol 223 (11-12) ◽  
Author(s):  
Juan Garcia Escudero
Keyword(s):  
Substitution Tilings ◽  
Random Substitution

scholarly journals A dichotomy for bounded displacement equivalence of Delone sets

2021 ◽  
pp. 1-18
Author(s):  
YOTAM SMILANSKY ◽  
YAAR SOLOMON
Keyword(s):  
Compact Space ◽  
Equivalence Classes ◽  
Natural Topology ◽  
Fell Topology ◽  
Local Complexity ◽  
Substitution Tilings ◽  
Local Topology ◽  
Delone Sets

Abstract We prove that in every compact space of Delone sets in ${\mathbb {R}}^d$ , which is minimal with respect to the action by translations, either all Delone sets are uniformly spread or continuously many distinct bounded displacement equivalence classes are represented, none of which contains a lattice. The implied limits are taken with respect to the Chabauty–Fell topology, which is the natural topology on the space of closed subsets of ${\mathbb {R}}^d$ . This topology coincides with the standard local topology in the finite local complexity setting, and it follows that the dichotomy holds for all minimal spaces of Delone sets associated with well-studied constructions such as cut-and-project sets and substitution tilings, whether or not finite local complexity is assumed.

ET0L SYSTEMS FOR COMPOSITE DODECAGONAL QUASICRYSTAL PATTERNS

2001 ◽  
Vol 15 (08) ◽  
pp. 1165-1175 ◽  
Author(s):  
JUAN GARCÍA ESCUDERO
Keyword(s):  
Pisot Number ◽  
Substitution Tilings ◽  
Inflation Factor ◽  
L Systems ◽  
Inflation Rules

Two types of deterministic substitution tilings with 12-fold symmetry and a Pisot number as inflation factor are generated and described in terms of bracketed L-systems. Composition of the inflation rules allows to construct other types of dodecagonal patterns which can be described with the help of ET0L-systems and may be used in order to derive nondeterministic models of quasicrystal structures.

scholarly journals On substitution tilings and Delone sets without finite local complexity

2019 ◽  
Vol 39 (6) ◽  
pp. 3149-3177 ◽  
Author(s):  
Jeong-Yup Lee ◽  
◽  
Boris Solomyak ◽  
◽  
Keyword(s):  
Local Complexity ◽  
Substitution Tilings ◽  
Delone Sets

scholarly journals Fractal dual substitution tilings

2016 ◽  
Vol 3 (3) ◽  
pp. 265-317 ◽  
Author(s):  
Natalie Priebe Frank ◽  
Samuel Webster ◽  
Michael Whittaker
Keyword(s):  
Substitution Tilings

A Computer Search for Planar Substitution Tilings with $$n$$ n -Fold Rotational Symmetry

2015 ◽  
Vol 53 (2) ◽  
pp. 445-465 ◽  
Author(s):  
Franz Gähler ◽  
Eugene E. Kwan ◽  
Gregory R. Maloney
Keyword(s):  
Rotational Symmetry ◽  
Computer Search ◽  
Substitution Tilings

FRACTAL TILINGS FROM SUBSTITUTION TILINGS

Fractals ◽  
2019 ◽  
Vol 27 (02) ◽  
pp. 1950009
Author(s):  
XINCHANG WANG ◽  
PEICHANG OUYANG ◽  
KWOKWAI CHUNG ◽  
XIAOGEN ZHAN ◽  
HUA YI ◽  
...  
Keyword(s):  
Short Paper ◽  
Self Similarity ◽  
Substitution Rule ◽  
Substitution Tiling ◽  
Simple Strategy ◽  
Substitution Tilings

A fractal tiling or [Formula: see text]-tiling is a tiling which possesses self-similarity and the boundary of which is a fractal. By substitution rule of tilings, this short paper presents a very simple strategy to create a great number of [Formula: see text]-tilings. The substitution tiling Equithirds is demonstrated to show how to achieve it in detail. The method can be generalized to every tiling that can be constructed by substitution rule.

scholarly journals MLD relations of pisot substitution tilings

2010 ◽  
Vol 226 ◽  
pp. 012020
Author(s):  
Franz Gahler
Keyword(s):  
Substitution Tilings

scholarly journals On substitution tilings of the plane with n-fold rotational symmetry

2015 ◽  
Vol Vol. 17 no. 1 (Discrete Algorithms) ◽  
Author(s):  
Gregory R. Maloney
Keyword(s):  
Rotational Symmetry ◽  
Substitution Tiling ◽  
Computer Assistance ◽  
Discrete Algorithms ◽  
Special Cases ◽  
International Audience ◽  
Substitution Tilings

Discrete Algorithms International audience A method is described for constructing, with computer assistance, planar substitution tilings that have n-fold rotational symmetry. This method uses as prototiles the set of rhombs with angles that are integer multiples of pi/n, and includes various special cases that have already been constructed by hand for low values of n. An example constructed by this method for n = 11 is exhibited; this is the first substitution tiling with elevenfold symmetry appearing in the literature.

scholarly journals Diffraction of block substitution tilings

2018 ◽  
Author(s):  
Uwe Grimm ◽  
Michael Baake
Keyword(s):  
Substitution Tilings
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