Relevant bibliographies by topics / Hyperbolic tilings

Academic literature on the topic 'Hyperbolic tilings'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Hyperbolic tilings"

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Margenstern, Maurice. "An Application of Iterative Pushdown Automata to Contour Words of Balls and Truncated Balls in Hyperbolic Tessellations." ISRN Algebra 2012 (March 29, 2012): 1–14. http://dx.doi.org/10.5402/2012/742310.

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We give an application of iterated pushdown automata to contour words of balls and two other domains in infinitely many tilings of the hyperbolic plane. We also give a similar application for the tiling of the hyperbolic 3D space and for the tiling of the hyperbolic 4D space as well.
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Taganap, Eduard C., and Ma Louise Antonette N. De Las Peñas. "Hyperbolic isocoronal tilings." Journal of Mathematics and the Arts 12, no. 2-3 (June 26, 2018): 96–110. http://dx.doi.org/10.1080/17513472.2018.1466432.

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Qiu, Chongyang, Xinfei Li, Jianhua Pang, and Peichang Ouyang. "Visualization of Escher-like Spiral Patterns in Hyperbolic Space." Symmetry 14, no. 1 (January 11, 2022): 134. http://dx.doi.org/10.3390/sym14010134.

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Spirals, tilings, and hyperbolic geometry are important mathematical topics with outstanding aesthetic elements. Nonetheless, research on their aesthetic visualization is extremely limited. In this paper, we give a simple method for creating Escher-like hyperbolic spiral patterns. To this end, we first present a fast algorithm to construct Euclidean spiral tilings with cyclic symmetry. Then, based on a one-to-one mapping between Euclidean and hyperbolic spaces, we establish two simple approaches for constructing spiral tilings in hyperbolic models. Finally, we use wallpaper templates to render such tilings, which results in the desired Escher-like hyperbolic spiral patterns. The method proposed is able to generate a great variety of visually appealing patterns.
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Levy, Silvio. "Automatic Generation of Hyperbolic Tilings." Leonardo 25, no. 3/4 (1992): 349. http://dx.doi.org/10.2307/1575861.

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Lück, Reinhard. "Quasiperiodic tilings in hyperbolic space." Journal of Physics: Conference Series 1458 (January 2020): 012009. http://dx.doi.org/10.1088/1742-6596/1458/1/012009.

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Lück, R., and D. Frettlöh. "Hyperbolic Icosahedral Tilings by Buckyballs." Acta Physica Polonica A 126, no. 2 (August 2014): 524–26. http://dx.doi.org/10.12693/aphyspola.126.524.

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Margenstern, Maurice, and K. G. Subramamian. "Hyperbolic tilings and formal language theory." Electronic Proceedings in Theoretical Computer Science 128 (September 4, 2013): 126–36. http://dx.doi.org/10.4204/eptcs.128.18.

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de Las Peñas, Ma Louise Antonette N., Rene P. Felix, Beaunonie R. Gozo, and Glenn R. Laigo. "Semi-perfect colourings of hyperbolic tilings." Philosophical Magazine 91, no. 19-21 (November 4, 2010): 2700–2708. http://dx.doi.org/10.1080/14786435.2010.524901.

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Oyono-Oyono, Hervé, and Samuel Petite. "C∗-algebras of Penrose hyperbolic tilings." Journal of Geometry and Physics 61, no. 2 (February 2011): 400–424. http://dx.doi.org/10.1016/j.geomphys.2010.09.019.

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Margenstern, Maurice. "Fibonacci words, hyperbolic tilings and grossone." Communications in Nonlinear Science and Numerical Simulation 21, no. 1-3 (April 2015): 3–11. http://dx.doi.org/10.1016/j.cnsns.2014.07.032.

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Dissertations / Theses on the topic "Hyperbolic tilings"

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Kolbe, Benedikt Maximilian [Verfasser], Myfanwy [Akademischer Betreuer] Evans, John [Akademischer Betreuer] Sullivan, Myfanwy [Gutachter] Evans, John [Gutachter] Sullivan, and Jean-Marc [Gutachter] Schlenker. "Structures in three-dimensional Euclidean space from hyperbolic tilings / Benedikt Maximilian Kolbe ; Gutachter: Myfanwy Evans, John Sullivan, Jean-Marc Schlenker ; Myfanwy Evans, John Sullivan." Berlin : Technische Universität Berlin, 2020. http://d-nb.info/1217326049/34.

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Praggastis, Brenda L. "Markov partitions for hyperbolic toral automorphisms /." Thesis, Connect to this title online; UW restricted, 1992. http://hdl.handle.net/1773/5773.

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Pelzer, Blake Patrick. "An octahedral tiling on the ideal boundary of the complex hyperbolic plane." College Park, Md. : University of Maryland, 2006. http://hdl.handle.net/1903/3854.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2006.
Thesis research directed by: Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Leskow, Lucila Helena Allan 1972. "Tesselações hiperbólicas aplicadas a codificação de geodésicas e códigos de fonte." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/261081.

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Orientador: Reginaldo Palazzo Junior
Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação
Made available in DSpace on 2018-08-18T16:51:18Z (GMT). No. of bitstreams: 1 Leskow_LucilaHelenaAllan_D.pdf: 2583405 bytes, checksum: 3161d9deabaa60a8965a9e3d20ff36aa (MD5) Previous issue date: 2011
Resumo: Neste trabalho apresentamos como contribuição um novo conjunto de tesselações do plano hiperbólico construídas a partir de uma tesselação bem conhecida, a tesselação de Farey. Nestas tesselações a região de Dirichlet é formada por polígonos hiperbólicos de n lados, com n > 3. Explorando as características dessas tesselações, apresentamos alguns tipos possíveis de aplicações. Inicialmente, estudando a relação existente entre a teoria das frações contínuas e a tesselação de Farey, propomos um novo método de codificação de geodésicas. A inovação deste método está no fato de ser possível realizar a codificação de uma geodésica pertencente a PSL(2,Z) em qualquer uma das tesselações ou seja, para qualquer valor de n com n > 3. Neste método mostramos como é possível associar as sequências cortantes de uma geodésica em cada tesselação à decomposição em frações contínuas do ponto atrator desta. Ainda explorando as características dessas novas tesselações, propomos dois tipos de aplicação em teoria de codificação de fontes discretas. Desenvolvendo dois novos códigos para compactação de fontes (um código de árvore e um código de bloco), estes dois métodos podem ser vistos como a generalização dos métodos de Elias e Tunstall para o caso hiperbólico
Abstract: In this work we present as contribution a new set of tessellations of the hyperbolic plane, built from a well known tessellation, the Farey tessellation. In this set of tessellations the Dirichlet region is made of hyperbolic polygons with n sides where n > 3. While studying these tessellations and theirs properties, we found some possible applications. In the first one, while exploring the relationship between the continued fractions theory and the Farey tessellation we propose a new method for coding geodesics. Using this method, it is possible to obtain a relationship between the cutting sequence of a geodesic belonging to PSL(2,Z) in each tessellation and the continued fraction decomposition of its attractor point. Exploring the characteristics of these tessellations we also propose two types of applications regarding the discrete memoryless source coding theory, a fixed-to-variable code and a variable length-to-fixed code. These methods can be seen as a generalized version of the Elias and Tunstall methods for the hyperbolic case
Doutorado
Telecomunicações e Telemática
Doutor em Engenharia Elétrica
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Alves, Alessandro Ferreira. "Análise dos emparelhamentos de arestas de polígonos hiperbólicos para a construção de constelações de sinais geometricamente uniformes." [s.n.], 2011. http://repositorio.unicamp.br/jspui/handle/REPOSIP/261080.

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Orientador: Reginaldo Palazzo Junior
Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação
Made available in DSpace on 2018-08-19T09:31:01Z (GMT). No. of bitstreams: 1 Alves_AlessandroFerreira_D.pdf: 1080224 bytes, checksum: 0748952c3176e9548151bec7e6d9c71d (MD5) Previous issue date: 2011
Resumo: Para projetarmos um sistema de comunicação digital em espaços hiperbólicos é necessário estabelecer um procedimento sistemático de construção de reticulados como elemento base para a construção de constelações de sinais. De outra forma, em codificação de canal é de fundamental importância a caracterização das estruturas algébrica e geométrica associadas a canais discretos sem memória. Neste trabalho, apresentamos a caracterização geométrica de superfícies a partir dos possíveis emparelhamentos das arestas do polígono fundamental hiperbólico com 3 ? n ? 8 lados associado 'a superfície. Esse tratamento geométrico apresenta propriedades importantes na determinação dos reticulados hiperbólicos a serem utilizados no processo de construção de constelações de sinais, a partir de grupos fuchsianos aritméticos e da superfície de Riemann associada. Além disso, apresentamos como exemplo o desenvolvimento algébrico para a determinação dos geradores do grupo fuchsiano 'gama'8 associado ao polígono hiperbólico 'P IND. 8'
Abstract: In order to design a digital communication system in hyperbolic spaces is necessary to establish a systematic procedure of constructing lattices as the basic element for the construction of the signal constellations. On the other hand, in channel coding is of fundamental importance to characterize the geometric and algebraic structures associated with discrete memoryless channels. In this work, we present a geometric characterization of surfaces from the edges of the possible pairings of fundamental hyperbolic polygon with 3 ? n ? 8 sides associated with the surface. This treatment has geometric properties important in determining the hyperbolic lattices to be used in the construction of sets of signals derived from arithmetic Fuchsian groups and the associated Riemann surface
Doutorado
Telecomunicações e Telemática
Doutor em Engenharia Elétrica
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Grewar, Murdock Geoffrey. "Tilings to Nets: a Journey through Hyperbolic Space." Thesis, 2016. http://hdl.handle.net/1885/159630.

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Evans, Myfanwy Ella. "Three-dimensional entanglement: knots, knits and nets." Phd thesis, 2011. http://hdl.handle.net/1885/9502.

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Three-dimensional entanglement, including knots, periodic arrays of woven filaments (weavings) and periodic arrays of interpenetrating networks (nets), forms an integral part of the analysis of structure within the natural sciences. This thesis constructs a catalogue of 3-periodic entanglements via a scaffold of Triply-Periodic Minimal Surfaces (TPMS). The two-dimensional Hyperbolic plane can be wrapped over a TPMS in much the same way as the two-dimensional Euclidean plane can be wrapped over a cylinder. Thus vertices and edges of free tilings of the Hyperbolic plane, which are tilings by tiles of infinite size, can be wrapped over a TPMS to represent vertices and edges of an array in three-dimensional Euclidean space. In doing this, we harness the simplicity of a two-dimensional surface as compared with 3D space to build our catalogue. We numerically tighten these entangled flexible knits and nets to an ideal conformation that minimises the ratio of edge (or filament) length to diameter. To enable the tightening of periodic entanglements which may contain vertices, we extend the Shrink-On-No-Overlaps algorithm, a simple and fast algorithm for tightening finite knots and links. The ideal geometry of 3-periodic weavings found through the tightening process exposes an interesting physical property: Dilatancy. The cooperative straightening of the filaments with a fixed diameter induces an expansion of the material accompanied with an increase in the free volume of the material. Further, we predict a dilatant rod packing as the structure of the keratin matrix in the corneocytes of mammalian skin, where the dilatant property of the matrix allows the skin to maintain structural integrity while experiencing a large expansion during the uptake of water.
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Wieler, Susana. "Symbolic and geometric representations of unimodular Pisot substitutions." Thesis, 2007. http://hdl.handle.net/1828/131.

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We review the construction of three Smale spaces associated to a unimodular Pisot substitution on d letters: a subshift of finite type (SFT), a substitution tiling space, and a hyperbolic toral automorphism on the Euclidean d-torus. By considering an SFT whose elements are biinfinite, rather than infinite, paths in the graph associated to the substitution, we modify a well-known map to obtain a factor map between our SFT and the hyperbolic toral automorphism on the d-torus given by the incidence matrix of the substitution. We prove that if the tiling substitution forces its border, then this factor map is the composition of an s-resolving factor map from the SFT to a one-dimensional substitution tiling space and a u-resolving factor map from the tiling space to the d-torus.
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Books on the topic "Hyperbolic tilings"

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Krajčevski, Mile. Tilings of the plane and hyperbolic groups. 1994.

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Krajcevski, Mile. Tilings of the Plane, Hyperbolic Groups and Small Cancellation Conditions. American Mathematical Society, 2001.

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Book chapters on the topic "Hyperbolic tilings"

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Hyde, S., and S. Ramsden. "Chemical frameworks and hyperbolic tilings." In Discrete Mathematical Chemistry, 203–24. Providence, Rhode Island: American Mathematical Society, 2000. http://dx.doi.org/10.1090/dimacs/051/15.

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Margenstern, Maurice. "Cellular Automata and Combinatoric Tilings in Hyperbolic Spaces. A Survey." In Discrete Mathematics and Theoretical Computer Science, 48–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/3-540-45066-1_4.

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Margenstern, Maurice. "Possible Applications of Navigation Tools in Tilings of Hyperbolic Spaces." In Lecture Notes in Electrical Engineering, 217–29. Dordrecht: Springer Netherlands, 2011. http://dx.doi.org/10.1007/978-94-007-0286-8_18.

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Margenstern, Maurice. "An Algorithmic Approach to Tilings of Hyperbolic Spaces: 10 Years Later." In Membrane Computing, 37–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-18123-8_6.

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Kolbe, Benedikt, and Vanessa Robins. "Tile-Transitive Tilings of the Euclidean and Hyperbolic Planes by Ribbons." In Association for Women in Mathematics Series, 77–98. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-95519-9_4.

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Margenstern, Maurice. "Constructing Iterated Exponentials in Tilings of the Euclidean and of the Hyperbolic Plane." In From Parallel to Emergent Computing, 285–314. Boca Raton, Florida : CRC Press, [2019] | Produced in celebration of the 25th anniversary of the International Journal of Parallel, Emergent, and Distributed Systems.: CRC Press, 2019. http://dx.doi.org/10.1201/9781315167084-14.

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Quasthoff, Uwe. "Hyperbolic Tilings." In The Pattern Book: Fractals, Art, and Nature, 339–41. WORLD SCIENTIFIC, 1995. http://dx.doi.org/10.1142/9789812832061_0129.

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"Golden tilings (in collaboration with J.P. Almeida and A. Portela)." In Fine Structures of Hyperbolic Diffeomorphisms, 161–82. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-540-87525-3_13.

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"Right-Angled Hexagon Tilings of the Hyperbolic Plane." In What's Next?, 206–14. Princeton University Press, 2019. http://dx.doi.org/10.1515/9780691185897-009.

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Kenyon, Richard. "Right-Angled Hexagon Tilings of the Hyperbolic Plane." In What's Next?, 206–14. Princeton University Press, 2020. http://dx.doi.org/10.2307/j.ctvthhdvv.11.

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Conference papers on the topic "Hyperbolic tilings"

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Delfosse, Nicolas, and Gilles Zemor. "Quantum erasure-correcting codes and percolation on regular tilings of the hyperbolic plane." In 2010 IEEE Information Theory Workshop (ITW 2010). IEEE, 2010. http://dx.doi.org/10.1109/cig.2010.5592863.

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