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Journal articles on the topic 'Hyperbolic tilings'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

Loquias, Manuel Joseph Cruz, and Dirk Frettlöh. "Perfect colorings of hyperbolic buckyball tilings." Acta Crystallographica Section A Foundations and Advances 73, a2 (December 1, 2017): C289. http://dx.doi.org/10.1107/s2053273317092841.

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12

Castle, Toen, Myfanwy E. Evans, Stephen T. Hyde, Stuart Ramsden, and Vanessa Robins. "Trading spaces: building three-dimensional nets from two-dimensional tilings." Interface Focus 2, no. 5 (January 25, 2012): 555–66. http://dx.doi.org/10.1098/rsfs.2011.0115.

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We construct some examples of finite and infinite crystalline three-dimensional nets derived from symmetric reticulations of homogeneous two-dimensional spaces: elliptic ( S 2 ), Euclidean ( E 2 ) and hyperbolic ( H 2 ) space. Those reticulations are edges and vertices of simple spherical, planar and hyperbolic tilings. We show that various projections of the simplest symmetric tilings of those spaces into three-dimensional Euclidean space lead to topologically and geometrically complex patterns, including multiple interwoven nets and tangled nets that are otherwise difficult to generate ab initio in three dimensions.

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13

BARGE, MARCY, and JEAN-MARC GAMBAUDO. "Geometric realization for substitution tilings." Ergodic Theory and Dynamical Systems 34, no. 2 (April 2012): 457–82. http://dx.doi.org/10.1017/etds.2012.142.

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AbstractGiven an n-dimensional substitution Φ whose associated linear expansion Λ is unimodular and hyperbolic, we use elements of the one-dimensional integer Čech cohomology of the tiling space ΩΦ to construct a finite-to-one semi-conjugacy G:ΩΦ→𝕋D, called a geometric realization, between the substitution induced dynamics and an invariant set of a hyperbolic toral automorphism. If Λ satisfies a Pisot family condition and the rank of the module of generalized return vectors equals the generalized degree of Λ, G is surjective and coincides with the map onto the maximal equicontinuous factor of the ℝn-action on ΩΦ. We are led to formulate a higher-dimensional generalization of the Pisot substitution conjecture: if Λ satisfies the Pisot family condition and the rank of the one-dimensional cohomology of ΩΦ equals the generalized degree of Λ, then the ℝn-action on ΩΦhas pure discrete spectrum.

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14

Pedersen, Martin Cramer, and Stephen T. Hyde. "Hyperbolic crystallography of two-periodic surfaces and associated structures." Acta Crystallographica Section A Foundations and Advances 73, no. 2 (February 7, 2017): 124–34. http://dx.doi.org/10.1107/s2053273316019112.

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This paper describes the families of the simplest, two-periodic constant mean curvature surfaces, the genus-two HCB and SQL surfaces, and their isometries. All the discrete groups that contain the translations of the genus-two surfaces embedded in Euclidean three-space modulo the translation lattice are derived and enumerated. Using this information, the subgroup lattice graphs are constructed, which contain all of the group–subgroup relations of the aforementioned quotient groups. The resulting groups represent the two-dimensional representations of subperiodic layer groups with square and hexagonal supergroups, allowing exhaustive enumeration of tilings and associated patterns on these surfaces. Two examples are given: a two-periodic [3,7]-tiling with hyperbolic orbifold symbol {\sf {2223}} and a {\sf {22222}} surface decoration.

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15

Panina, G. Yu. "Pointed spherical tilings and hyperbolic virtual polytopes." Journal of Mathematical Sciences 175, no. 5 (May 25, 2011): 591–99. http://dx.doi.org/10.1007/s10958-011-0374-y.

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16

Park, Jong-Youll. "AN APPLICATION OF TILINGS IN THE HYPERBOLIC PLANE." Honam Mathematical Journal 29, no. 3 (September 25, 2007): 481–93. http://dx.doi.org/10.5831/hmj.2007.29.3.481.

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17

Ahara, Kazushi, Shigeki Akiyama, Hiroko Hayashi, and Kazushi Komatsu. "Strongly nonperiodic hyperbolic tilings using single vertex configuration." Hiroshima Mathematical Journal 48, no. 2 (July 2018): 133–40. http://dx.doi.org/10.32917/hmj/1533088825.

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18

Dogru, Filiz, Emily M. Fischer, and Cristian Mihai Munteanu. "Outer billiards and tilings of the hyperbolic plane." Involve, a Journal of Mathematics 8, no. 4 (June 23, 2015): 637–51. http://dx.doi.org/10.2140/involve.2015.8.637.

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19

Leoni, Stefano. "Deconstructing Sodalite with Hyperbolic Tilings: A PNS Approach." Zeitschrift für anorganische und allgemeine Chemie 635, no. 4-5 (April 2009): 737–42. http://dx.doi.org/10.1002/zaac.200900021.

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20

Leoni, Stefano. "Deconstructing Sodalite with Hyperbolic Tilings: A PNS Approach." Zeitschrift für anorganische und allgemeine Chemie 635, no. 4-5 (April 2009): 619–23. http://dx.doi.org/10.1002/zaac.200900025.

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21

Margulis, G. A., and S. Mozes. "Aperiodic tilings of the hyperbolic plane by convex polygons." Israel Journal of Mathematics 107, no. 1 (December 1998): 319–25. http://dx.doi.org/10.1007/bf02764015.

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22

Dolbilin, Nikolai, and Dirk Frettlöh. "Properties of Böröczky tilings in high-dimensional hyperbolic spaces." European Journal of Combinatorics 31, no. 4 (May 2010): 1181–95. http://dx.doi.org/10.1016/j.ejc.2009.11.016.

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23

MARGENSTERN, MAURICE. "ON A CHARACTERIZATION OF CELLULAR AUTOMATA IN TILINGS OF THE HYPERBOLIC PLANE." International Journal of Foundations of Computer Science 19, no. 05 (October 2008): 1235–57. http://dx.doi.org/10.1142/s012905410800625x.

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In this paper, we look at the extension of Hedlund's characterization of cellular automata to the case of cellular automata in the hyperbolic plane. This requires an additional condition. The new theorem is proved with full details in the case of the pentagrid and in the case of the ternary heptagrid and enough indications to show that it also holds on the grids {p, q} of the hyperbolic plane.

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24

Margenstern, Maurice. "An Algorithmic Approach to Tilings of Hyperbolic Spaces: Universality Results." Fundamenta Informaticae 138, no. 1-2 (2015): 113–25. http://dx.doi.org/10.3233/fi-2015-1202.

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25

Krajčevski, Milé. "Tilings of the plane, hyperbolic groups and small cancellation conditions." Memoirs of the American Mathematical Society 154, no. 733 (2001): 0. http://dx.doi.org/10.1090/memo/0733.

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26

Floyd, W. J., and S. P. Plotnick. "Growth functions for semi-regular tilings of the hyperbolic plane." Geometriae Dedicata 53, no. 1 (November 1994): 1–23. http://dx.doi.org/10.1007/bf01264041.

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27

Stojanović, M. "Hyperbolic space groups and their supergroups for fundamental simplex tilings." Acta Mathematica Hungarica 153, no. 2 (October 9, 2017): 276–88. http://dx.doi.org/10.1007/s10474-017-0761-z.

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28

Szirmai, Jenő. "Congruent and non-congruent hyperball packings related to doubly truncated Coxeter orthoschemes in hyperbolic 3-space." Acta Universitatis Sapientiae, Mathematica 11, no. 2 (December 1, 2019): 437–59. http://dx.doi.org/10.2478/ausm-2019-0032.

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Abstract In [17] we considered hyperball packings in 3-dimensional hyperbolic space. We developed a decomposition algorithm that for each saturated hyperball packing has provided a decomposition of ℍ3 into truncated tetrahedra. Thus, in order to get a density upper bound for hyperball packings, it is sufficient to determine the density upper bound of hyperball packings in truncated simplices. Therefore, in this paper we examine the doubly truncated Coxeter orthoscheme tilings and the corresponding congruent and non-congruent hyperball packings. We prove that related to the mentioned Coxeter tilings the density of the densest congruent hyperball packing is ≈ 0.81335 that is – by our conjecture – the upper bound density of the relating non-congruent hyperball packings, too.

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29

Delfosse, Nicolas, and Gilles Zemor. "Upper bounds on the rate of low density stabilizer codes for the quantum erasure channel." Quantum Information and Computation 13, no. 9&10 (September 2013): 793–826. http://dx.doi.org/10.26421/qic13.9-10-4.

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Using combinatorial arguments, we determine an upper bound on achievable rates of stabilizer codes used over the quantum erasure channel. This allows us to recover the no-cloning bound on the capacity of the quantum erasure channel, $R \leq 1-2p$, for stabilizer codes: we also derive an improved upper bound of the form $R \leq 1-2p-D(p)$ with a function $D(p)$ that stays positive for $0<p<1/2$ and for any family of stabilizer codes whose generators have weights bounded from above by a constant -- low density stabilizer codes. We obtain an application to percolation theory for a family of self-dual tilings of the hyperbolic plane. We associate a family of low density stabilizer codes with appropriate finite quotients of these tilings. We then relate the probability of percolation to the probability of a decoding error for these codes on the quantum erasure channel. The application of our upper bound on achievable rates of low density stabilizer codes gives rise to an upper bound on the critical probability for these tilings.

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30

Johnson, Norman W., and Asia Ivić Weiss. "Quadratic Integers and Coxeter Groups." Canadian Journal of Mathematics 51, no. 6 (December 1, 1999): 1307–36. http://dx.doi.org/10.4153/cjm-1999-060-6.

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AbstractMatrices whose entries belong to certain rings of algebraic integers can be associated with discrete groups of transformations of inversive n-space or hyperbolic (n+1)-space Hn+1. For small n, thesemay be Coxeter groups, generated by reflections, or certain subgroups whose generators include direct isometries of Hn+1. We show how linear fractional transformations over rings of rational and (real or imaginary) quadratic integers are related to the symmetry groups of regular tilings of the hyperbolic plane or 3-space. New light is shed on the properties of the rational modular group PSL2(), the Gaussian modular (Picard) group PSL2([i]), and the Eisenstein modular group PSL2([ω]).

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31

Komatsu, Takao, László Németh, and László Szalay. "Tilings of hyperbolic (2 × n)-board with colored squares and dominoes." Ars Mathematica Contemporanea 15, no. 2 (June 26, 2018): 337–46. http://dx.doi.org/10.26493/1855-3974.1470.e79.

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32

Ramsden, S. J., V. Robins, and S. T. Hyde. "Three-dimensional Euclidean nets from two-dimensional hyperbolic tilings: kaleidoscopic examples." Acta Crystallographica Section A Foundations of Crystallography 65, no. 2 (January 28, 2009): 81–108. http://dx.doi.org/10.1107/s0108767308040592.

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33

Hyde, Stephen T., Ann-Kristin Larsson, Tiziana Di Matteo, Stuart Ramsden, and Vanessa Robins. "Meditation on an Engraving of Fricke and Klein (The Modular Group and Geometrical Chemistry)." Australian Journal of Chemistry 56, no. 10 (2003): 981. http://dx.doi.org/10.1071/ch03191.

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A non-technical account of the links between two-dimensional (2D) hyperbolic and three-dimensional (3D) euclidean symmetric patterns is presented, with a number of examples from both spaces. A simple working hypothesis is used throughout the survey: simple, highly symmetric patterns traced in hyperbolic space lead to chemically relevant structures in euclidean space. The prime examples in the former space are derived from Felix Klein's engraving of the modular group structure within the hyperbolic plane; these include various tilings, networks and trees. Disc packings are also derived. The euclidean examples are relevant to condensed atomic and molecular materials in solid-state chemistry and soft-matter structural science. They include extended nets of relevance to covalent frameworks, simple (lattice) sphere packings, and interpenetrating extended frameworks (related to novel coordination polymers). Limited discussion of the projection process from 2D hyperbolic to 3D euclidean space via mapping onto triply periodic minimal surfaces is presented.

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34

Evans, Myfanwy E., and Stephen T. Hyde. "Periodic entanglement III: tangled degree-3 finite and layer net intergrowths from rare forests." Acta Crystallographica Section A Foundations and Advances 71, no. 6 (October 20, 2015): 599–611. http://dx.doi.org/10.1107/s2053273315014710.

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Entanglements of two-dimensional honeycomb nets are constructed from free tilings of the hyperbolic plane ({\bb H}^2) on triply periodic minimal surfaces. The 2-periodic nets that comprise the structures are guaranteed by considering regular, rare free tilings in {\bb H}^2. This paper catalogues an array of entanglements that are both beautiful and challenging for current classification techniques, including examples that are realized in metal–organic materials. The compactification of these structures to the genus-3 torus is considered as a preliminary method for generating entanglements of finite θ-graphs, potentially useful for gaining insight into the entanglement of the periodic structure. This work builds on previous structural enumerations given inPeriodic entanglementParts I and II [Evanset al.(2013).Acta Cryst.A69, 241–261; Evanset al.(2013).Acta Cryst.A69, 262–275].

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35

Benjamini, Itai, and Tsachik Gelander. "An upper bound on the growth of Dirichlet tilings of hyperbolic spaces." Journal of Topology and Analysis 09, no. 02 (March 13, 2017): 221–24. http://dx.doi.org/10.1142/s1793525317500030.

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It is shown that the growth rate [Formula: see text] of any [Formula: see text] faces Dirichlet tiling of [Formula: see text] is at most [Formula: see text], for an [Formula: see text], depending only on [Formula: see text] and [Formula: see text]. We do not know if there is a universal [Formula: see text], such that [Formula: see text] upperbounds the growth rate for any [Formula: see text]-regular tiling, when [Formula: see text]?

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36

Dotera, Tomonari, Masakiyo Kimoto, and Junichi Matsuzawa. "Hard spheres on the gyroid surface." Interface Focus 2, no. 5 (January 18, 2012): 575–81. http://dx.doi.org/10.1098/rsfs.2011.0092.

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We find that 48/64 hard spheres per unit cell on the gyroid minimal surface are entropically self-organized. Striking evidence is obtained in terms of the acceptance ratio of Monte Carlo moves and order parameters. The regular tessellations of the spheres can be viewed as hyperbolic tilings on the Poincaré disc with a negative Gaussian curvature, one of which is, equivalently, the arrangement of angels and devils in Escher's Circle Limit IV .

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37

Yahya, Arnasli, and Jenő Szirmai. "Visualization of Sphere and Horosphere Packings Related to Coxeter Tilings by Simply Truncated Orthoschemes with Parallel Faces." KoG, no. 25 (2021): 64–71. http://dx.doi.org/10.31896/k.25.7.

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In this paper we describe and visualize the densest ball and horoball packing configurations to the simply truncated 3-dimensional hyperbolic Coxeter orthoschemes with parallel faces, using the results of [24]. These beautiful packing arrangements describe and show the very interesting structure of the mentioned orthoschemes and the corresponding Coxeter reflection group. We use the Beltrami-Cayley-Klein ball model of 3-dimensional hyperbolic space H^3, the images were made by the Python programming language.

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38

Moran, Judith Flagg. "The growth rate and balance of homogeneous tilings in the hyperbolic plane." Discrete Mathematics 173, no. 1-3 (August 1997): 151–86. http://dx.doi.org/10.1016/s0012-365x(96)00102-1.

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39

Stojanovic, Milica. "Coxeter groups as automorphism groups of solid transitive 3-simplex tilings." Filomat 28, no. 3 (2014): 557–77. http://dx.doi.org/10.2298/fil1403557s.

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In the papers of I.K. Zhuk, then more completely of E. Moln?r, I. Prok, J. Szirmai all simplicial 3-tilings have been classified, where a symmetry group acts transitively on the simplex tiles. The involved spaces depends on some rotational order parameters. When a vertex of a such simplex lies out of the absolute, e.g. in hyperbolic space H3, then truncation with its polar plane gives a truncated simplex or simply, trunc-simplex. Looking for symmetries of these tilings by simplex or trunc-simplex domains, with their side face pairings, it is possible to find all their group extensions, especially Coxeter?s reflection groups, if they exist. So here, connections between isometry groups and their supergroups is given by expressing the generators and the corresponding parameters. There are investigated simplices in families F3, F4, F6 and appropriate series of trunc-simplices. In all cases the Coxeter groups are the maximal ones.

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40

Hyde, S. T., and S. Ramsden. "Some novel three-dimensional Euclidean crystalline networks derived from two-dimensional hyperbolic tilings." European Physical Journal B - Condensed Matter 31, no. 2 (January 1, 2003): 273–84. http://dx.doi.org/10.1140/epjb/e2003-00032-8.

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41

Nesper, Reinhard, and Stefano Leoni. "On Tilings and Patterns on Hyperbolic Surfaces and Their Relation to Structural Chemistry." ChemPhysChem 2, no. 7 (July 16, 2001): 413–22. http://dx.doi.org/10.1002/1439-7641(20010716)2:7<413::aid-cphc413>3.0.co;2-v.

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42

Margenstern, Maurice. "Navigation tools for cellular automata in two families of tilings of the hyperbolic plane." International Journal of Parallel, Emergent and Distributed Systems 33, no. 1 (October 24, 2016): 12–34. http://dx.doi.org/10.1080/17445760.2016.1239267.

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43

Szirmai, Jenő. "The least dense hyperball covering of regular prism tilings in hyperbolic $$n$$ n -space." Annali di Matematica Pura ed Applicata (1923 -) 195, no. 1 (October 28, 2014): 235–48. http://dx.doi.org/10.1007/s10231-014-0460-0.

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44

Szirmai, Jenő. "The regular prism tilings and their optimal hyperball packings in the hyperbolic $n$-space." Publicationes Mathematicae Debrecen 69, no. 1-2 (July 1, 2006): 195–207. http://dx.doi.org/10.5486/pmd.2006.3388.

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45

Kirkensgaard, Jacob Judas Kain. "Kaleidoscopic tilings, networks and hierarchical structures in blends of 3-miktoarm star terpolymers." Interface Focus 2, no. 5 (January 11, 2012): 602–7. http://dx.doi.org/10.1098/rsfs.2011.0093.

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Dissipative particle dynamics simulations are used to explore blends of 3-miktoarm star terpolymers. The investigated system is a 50/50 blend of ABC and ABD stars, which is investigated as a function of composition and at different symmetric segregation levels. The study shows that in analogy to pure ABC star melts cylindrical tiling patters form, but now in four-coloured variants. Also, a large part of the phase diagram is dominated by multi-coloured network structures showing hierarchical features. Most prominently, a novel alternating gyroid network structure with a hyperbolic lamellar interface is predicted to form. Here, the two gyroidal nets are composed of respectively C and D components, with the minority A and B components forming the lamellar-like curved structure on the dividing interface between the two nets.

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46

Daly, Donnacha, and Didier Sornette. "The Altes Family of Log-Periodic Chirplets and the Hyperbolic Chirplet Transform." Symmetry 13, no. 10 (October 13, 2021): 1922. http://dx.doi.org/10.3390/sym13101922.

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This work revisits a class of biomimetically inspired waveforms introduced by R.A. Altes in the 1970s for use in sonar detection. Similar to the chirps used for echolocation by bats and dolphins, these waveforms are log-periodic oscillations, windowed by a smooth decaying envelope. Log-periodicity is associated with the deep symmetry of discrete scale invariance in physical systems. Furthermore, there is a close connection between such chirping techniques, and other useful applications such as wavelet decomposition for multi-resolution analysis. Motivated to uncover additional properties, we propose an alternative, simpler parameterisation of the original Altes waveforms. From this, it becomes apparent that we have a flexible family of hyperbolic chirps suitable for the detection of accelerating time-series oscillations. The proposed formalism reveals the original chirps to be a set of admissible wavelets with desirable properties of regularity, infinite vanishing moments and time-frequency localisation. As they are self-similar, these “Altes chirplets” allow efficient implementation of the scale-invariant hyperbolic chirplet transform (HCT), whose basis functions form hyperbolic curves in the time-frequency plane. Compared with the rectangular time-frequency tilings of both the conventional wavelet transform and the short-time Fourier transform, the HCT can better facilitate the detection of chirping signals, which are often the signature of critical failure in complex systems. A synthetic example is presented to illustrate this useful application of the HCT.

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47

Margenstern, Maurice. "An application of Grossone to the study of a family of tilings of the hyperbolic plane." Applied Mathematics and Computation 218, no. 16 (April 2012): 8005–18. http://dx.doi.org/10.1016/j.amc.2011.04.014.

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48

Szirmai, Jenő. "The regular p-gonal prism tilings and their optimal hyperball packings in the hyperbolic 3-space." Acta Mathematica Hungarica 111, no. 1-2 (April 2006): 65–76. http://dx.doi.org/10.1007/s10474-006-0034-8.

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49

Callens, Sebastien J. P., Christoph H. Arns, Alina Kuliesh, and Amir A. Zadpoor. "Metamaterial Design: Decoupling Minimal Surface Metamaterial Properties Through Multi‐Material Hyperbolic Tilings (Adv. Funct. Mater. 30/2021)." Advanced Functional Materials 31, no. 30 (July 2021): 2170214. http://dx.doi.org/10.1002/adfm.202170214.

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50

Jahn, A., M. Gluza, F. Pastawski, and J. Eisert. "Holography and criticality in matchgate tensor networks." Science Advances 5, no. 8 (August 2019): eaaw0092. http://dx.doi.org/10.1126/sciadv.aaw0092.

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The AdS/CFT correspondence conjectures a holographic duality between gravity in a bulk space and a critical quantum field theory on its boundary. Tensor networks have come to provide toy models to understand these bulk-boundary correspondences, shedding light on connections between geometry and entanglement. We introduce a versatile and efficient framework for studying tensor networks, extending previous tools for Gaussian matchgate tensors in 1 + 1 dimensions. Using regular bulk tilings, we show that the critical Ising theory can be realized on the boundary of both flat and hyperbolic bulk lattices, obtaining highly accurate critical data. Within our framework, we also produce translation-invariant critical states by an efficiently contractible tensor network with the geometry of the multiscale entanglement renormalization ansatz. Furthermore, we establish a link between holographic quantum error–correcting codes and tensor networks. This work is expected to stimulate a more comprehensive study of tensor network models capturing bulk-boundary correspondences.

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