Results 21 to 30 of about 33,997 (183)
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 +3 more
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The Electronic Journal of Combinatorics, 1996 Given a list $1\times 1, 1\times a, 1\times b, \dots, 1\times c$ of rectangles, with $a,b,\dots,c$ non-negative, when can $1\times{t}$ be tiled by positive and negative copies of rectangles which are similar (uniform scaling) to those in the list? We prove that such a tiling exists iff $t$ is in the field $Q(a,b,\dots,c)$.
Kevin Keating, Jonathan L. King
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European Journal of Combinatorics, 2021 25 pages, 5 figures; to appear in European Journal of ...
Jan Hladký, Ping Hu, Diana Piguet
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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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Hard Tiling Problems with Simple Tiles [PDF]
Discrete & Computational Geometry, 2001 It is well-known that the question of whether a given finite region can be tiled with a given set of tiles is NP-complete. We show that the same is true for the right tromino and square tetromino on the square lattice, or for the right tromino alone. In the process, we show that Monotone 1-in-3 Satisfiability is NP-complete for planar cubic graphs.
Cristopher Moore, J. M. Robson
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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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Spherical Tiling by 12 Congruent Pentagons [PDF]
, 2012 The tilings of the 2-dimensional sphere by congruent triangles have been extensively studied, and the edge-to-edge tilings have been completely classified. However, not much is known about the tilings by other congruent polygons.
Gao, Honghao, Shi, Nan, Yan, Min
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Journal of Symbolic Logic, 2001 AbstractWe study the minimal complexity of tilings of a plane with a given tile set. We note that every tile set admits either no tiling or some tiling withKolmogorov complexity of its (n×n)-squares. We construct tile sets for which this bound is tight: all (n×n)-squares in all tilings have complexity Ω(n).
Bruno Durand 0001 +2 more
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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 +2 more
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