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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 Many Faces of Alternating-Sign Matrices [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 I give a survey of different combinatorial forms of alternating-sign matrices, starting with the original form introduced by Mills, Robbins and Rumsey as well as corner-sum matrices, height-function matrices, three-colorings, monotone triangles ...
James Propp
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Domino tilings of the Aztec Diamond [PDF]
, 2015 Imagine you have a cutout from a piece of squared paper and a pile of dominoes, each of which can cover exactly two squares of the squared paper. How many different ways are there to cover the entire paper cutout with dominoes?
Rué Perna, Juan José
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Journal of Graphics, GPU, and Game Tools, 2011 In this article we describe and investigate tiled shading. The tiled techniques, though simple, enable substantial improvements to both deferred and forward shading. Tiled Shading has been previously discussed only in terms of deferred shading (tiled deferred shading).
Olsson, Ola, Assarsson, Ulf
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Remarks on quiver gauge theories from open topological string theory [PDF]
, 2010 We study effective quiver gauge theories arising from a stack of D3-branes on certain Calabi-Yau singularities. Our point of view is a first principle approach via open topological string theory.
Carqueville, N. +3 more
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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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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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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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