Results 1 to 10 of about 33,813 (262)

Fractal Tilings Based on Successive Adjacent Substitution Rule

Complexity, 2018
A fractal tiling or f-tiling is a tiling which possesses self-similarity and the boundary of which is a fractal. f-tilings have complicated structures and strong visual appeal. However, so far, the discovered f-tilings are very limited since constructing
Peichang Ouyang, Xiaosong Tang, Kwokwai Chung, Tao Yu   +3 more
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Symmetries of Monocoronal Tilings [PDF]

Discrete Mathematics & Theoretical Computer Science, 2015
The vertex corona of a vertex of some tiling is the vertex together with the adjacent tiles. A tiling where all vertex coronae are congruent is called monocoronal.
Dirk Frettlöh, Alexey Garber
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Constructing and Visualizing Uniform Tilings

Computers, 2023
This paper describes a system which takes user input of a pattern of regular polygons around one vertex and attempts to construct a uniform tiling with the same pattern at every vertex by adding one polygon at a time.
Nelson Max
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Highly symmetric aperiodic structures -INVITED [PDF]

EPJ Web of Conferences, 2021
The symmetries of periodic structures are severely constrained by the crystallographic restriction. In particular, in two and three spatial dimensions, only rotational axes of order 1, 2, 3, 4 or 6 are possible.
Grimm Uwe
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An n-Dimensional Generalization of the Rhombus Tiling [PDF]

Discrete Mathematics & Theoretical Computer Science, 2001
Several classic tilings, including rhombuses and dominoes, possess height functions which allow us to 1) prove ergodicity and polynomial mixing times for Markov chains based on local moves, 2) use coupling from the past to sample perfectly random tilings,
Joakim Linde, Cristopher Moore, Mats G. Nordahl   +2 more
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The Crossing Number of The Hexagonal Graph H3,n

Discussiones Mathematicae Graph Theory, 2019
In [C. Thomassen, Tilings of the torus and the Klein bottle and vertex-transitive graphs on a fixed surface, Trans. Amer. Math. Soc. 323 (1991) 605–635], Thomassen described completely all (except finitely many) regular tilings of the torus S1 and the ...
Wang Jing, Ouyang Zhangdong, Huang Yuanqiu   +2 more
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Recursive tilings and space-filling curves with little fragmentation

Journal of Computational Geometry, 2011
This paper defines the Arrwwid number of a recursive tiling (or space-filling curve) as the smallest number a such that any ball Q can be covered by a tiles (or curve fragments) with total volume O(volume(Q)).
Herman Haverkort
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Tilings in topological spaces

International Journal of Mathematics and Mathematical Sciences, 1999
A tiling of a topological space X is a covering of X by sets (called tiles) which are the closures of their pairwise-disjoint interiors. Tilings of ℝ2 have received considerable attention (see [2] for a wealth of interesting examples and results as well ...
F. G. Arenas
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Wildest SL2-tilings

Examples and Counterexamples
Tame SL2-tilings are related to Farey graph and friezes; much less is known about wild (not tame) SL2-tilings. In this note, we demonstrate SL2-tilings that are maximally wild: we prove that the maximum wild density of an integer SL2-tiling is 25 and ...
Andrei Zabolotskii
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The Estimating of the Number of Lattice Tilings of a Plane by a Given Area Centrosymmetrical Polyomino

Моделирование и анализ информационных систем, 2015
We study a problem about the number of lattice plane tilings by the given area centrosymmetrical polyominoes. A polyomino is a connected plane geomatric figure formed by joiining a finite number of unit squares edge to edge.
A. V. Shutov, E. V. Kolomeykina
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