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Tilings, substitution systems and dynamical systems generated by them
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1002/j.1538-7305.1961.tb03975.xopenalex-snapshot
Proving Theorems by Pattern Recognition - II
inferredcites →https://doi.org/10.1007/bf01418780openalex-snapshot
Undecidability and nonperiodicity for tilings of the plane
inferredcites →https://doi.org/10.1007/bf01824809openalex-snapshot
Minimal flows arising from substitutions of non-constant length
inferredcites →https://doi.org/10.1090/memo/0066openalex-snapshot
The undecidability of the domino problem
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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A Small Aperiodic Set of Planar Tiles
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Introduction to Hierarchical Tiling Dynamical Systems
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The Undecidability of the Domino Problem
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Cohomology of Hierarchical Tilings
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Solutions to the Multi-dimensional Equal Powers Problem Constructed by Composition of Rectangular Morphisms
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Hierarchy and Expansiveness in 2D Subshifts of Finite Type
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Effective S-adic Symbolic Dynamical Systems
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The Domino Problem for Self-similar Structures
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About the Domino Problem for Subshifts on Groups
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Two-by-Two Substitution Systems and the Undecidability of the Domino Problem
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Fixed Point and Aperiodic Tilings
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Effective Closed Subshifts in 1D Can Be Implemented in 2D
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Densities and Entropies in Cellular Automata
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Substitutions and Strongly Deterministic Tilesets
inferred← citeshttps://doi.org/10.1007/978-94-015-8784-6_19openalex-snapshot
Aperiodic Tilings, Ergodic Theory, and Rotations
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Aperiodic Hierarchical Tilings
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How should one define a (weak) crystal?
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Artistic design with fractal matrices
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Fractal Penrose tilings I. Construction and matching rules
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Space tilings and local isomorphism
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Conjugacies for Tiling Dynamical Systems
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On the dynamics and recursive properties of multidimensional symbolic systems
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Conway and Aperiodic Tilings
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Substitutive Structure of Jeandel–Rao Aperiodic Tilings
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A Family of Non-Periodic Tilings of the Plane by Right Golden Triangles
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Simulation of Effective Subshifts by Two-dimensional Subshifts of Finite Type
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Fusion: a general framework for hierarchical tilings of $$\mathbb{R }^d$$ R d
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A self-similar aperiodic set of 19 Wang tiles
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Diffraction of Return Time Measures
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Deterministic Coloring of a Family of Complexes
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Entropies realizable by block gluing ℤ d shifts of finite type
inferred← citeshttps://doi.org/10.1007/s11854-021-0172-5openalex-snapshot
Quantified block gluing for multidimensional subshifts of finite type: aperiodicity and entropy
inferred← citeshttps://doi.org/10.1007/s11856-017-1582-zopenalex-snapshot
Weak local rules for planar octagonal tilings
inferred← citeshttps://doi.org/10.1007/s11856-018-1822-xopenalex-snapshot
Factor maps and embeddings for random ℤd shifts of finite type
inferred← citeshttps://doi.org/10.1016/0024-3795(95)00676-1openalex-snapshot
On the entropy of Zd subshifts of finite type
inferred← citeshttps://doi.org/10.1016/j.aim.2024.109906openalex-snapshot
Zero-temperature chaos in bidimensional models with finite-range potentials
inferred← citeshttps://doi.org/10.1016/j.chaos.2024.114807openalex-snapshot
Tiling iterated function systems
inferred← citeshttps://doi.org/10.1016/j.exmath.2008.02.001openalex-snapshot
A primer of substitution tilings of the Euclidean plane
inferred← citeshttps://doi.org/10.1016/j.geomphys.2021.104217openalex-snapshot
Relating diffraction and spectral data of aperiodic tilings: Towards a Bloch theorem
inferred← citeshttps://doi.org/10.1016/j.ic.2016.06.008openalex-snapshot
Solutions to the multi-dimensional Prouhet–Tarry–Escott problem resulting from composition of balanced morphisms
inferred← citeshttps://doi.org/10.1016/j.jcss.2011.11.001openalex-snapshot
Fixed-point tile sets and their applications
inferred← citeshttps://doi.org/10.1016/j.jcss.2014.10.001openalex-snapshot
A uniquely ergodic cellular automaton
inferred← citeshttps://doi.org/10.1016/j.jcss.2022.04.002openalex-snapshot
Resource-bounded Kolmogorov complexity provides an obstacle to soficness of multidimensional shifts
inferred← citeshttps://doi.org/10.1016/j.jcta.2018.07.002openalex-snapshot
Lots of aperiodic sets of tiles
inferred← citeshttps://doi.org/10.1016/j.physa.2015.07.035openalex-snapshot
Substitution systems and nonextensive statistics
inferred← citeshttps://doi.org/10.1016/j.tcs.2008.12.010openalex-snapshot
Perfectly quilted rectangular snake tilings
inferred← citeshttps://doi.org/10.1016/j.tcs.2009.11.018openalex-snapshot
A hierarchical strongly aperiodic set of tiles in the hyperbolic plane
inferred← citeshttps://doi.org/10.1016/j.tcs.2024.114883openalex-snapshot
Geometrical Penrose tilings are characterized by their 1-atlas
inferred← citeshttps://doi.org/10.1016/s0921-5093(00)01193-xopenalex-snapshot
The impact of aperiodic order on mathematics
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Chapter 10 Symbolic and algebraic dynamical systems
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An Introduction to Symbolic Dynamics and Coding
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Preface to the First Edition
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Preface to the Second Edition
inferred← citeshttps://doi.org/10.1017/9781108899727.008openalex-snapshot
Shifts as Dynamical Systems
inferred← citeshttps://doi.org/10.1017/9781108899727.010openalex-snapshot
Finite-to-One Codes and Finite Equivalence
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Degrees of Codes and Almost Conjugacy
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Embeddings and Factor Codes
inferred← citeshttps://doi.org/10.1017/cbo9780511626302.007openalex-snapshot
SHIFTS AS DYNAMICAL SYSTEMS
inferred← citeshttps://doi.org/10.1017/cbo9780511626302.009openalex-snapshot
FINITE-TO-ONE CODES AND FINITE EQUIVALENCE
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DEGREES OF CODES AND ALMOST CONJUGACY
inferred← citeshttps://doi.org/10.1017/cbo9780511626302.011openalex-snapshot
EMBEDDINGS AND FACTOR CODES
inferred← citeshttps://doi.org/10.1017/cbo9780511626302.014openalex-snapshot
GUIDE TO ADVANCED TOPICS
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The dynamical theory of tilings and Quasicrystallography
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Asymptotic structure in substitution tiling spaces
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Medvedev degrees of two-dimensional subshifts of finite type
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On intrinsic ergodicity of factors of subshifts
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Spectral theory of substitutions
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Weak colored local rules for planar tilings
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A generalization of the simulation theorem for semidirect products
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Strongly aperiodic subshifts of finite type on hyperbolic groups
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Decidability of the isomorphism problem between multidimensional substitutive subshifts
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Metallic mean Wang tiles I: self-similarity, aperiodicity and minimality
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Metallic mean Wang tiles II: the dynamics of an aperiodic computer chip
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Isomorphism of hierarchical structures
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Repetitive Delone sets and quasicrystals
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Genericity in topological dynamics
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Finite entropy for multidimensional cellular automata
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On the finite-dimensional marginals of shift-invariant measures
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Dynamics of self-similar tilings
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AN APERIODIC TILE WITH EDGE-TO-EDGE ORIENTATIONAL MATCHING RULES
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An Algebraic Invariant for Substitution Tiling Systems
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An Ultimate Frustration in Classical Lattice-Gas Models
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Stable Quasicrystalline Ground States
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Bounded Wang tilings with integer programming and graph-based heuristics
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A construction of two-dimensional random substitution systems
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Periodicity, Quasiperiodicity, and Bieberbach's Theorem on Crystallographic Groups
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shifts of finite type without equal entropy full shift factors
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Crystallization by stochastic flips
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Open problems in symbolic dynamics
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SFT covers for actions of the first Grigorchuk group
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The decomposition theorem for two-dimensional shifts of finite type
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Multidimensional sofic shifts without separation and their factors
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The dynamical properties of Penrose tilings
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Global order from local sources
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Symmetry of tilings of the plane
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On the Determinism of Paths on Substitution Complexes
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An Integrodifferential Model for Orientational Distributions of F-actin in Cells
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DECIDABILITY OF UNIFORM RECURRENCE OF MORPHIC SEQUENCES
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DISORDERED GROUND STATES OF CLASSICAL LATTICE MODELS
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Chaos and Turing machines on bidimensional models at zero temperature
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Ordered amorphous spin system
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Decidability of the isomorphism and the factorization between minimal substitution subshifts
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Matching Rules and Substitution Tilings
inferred← citeshttps://doi.org/10.2748/tmj/1325886278openalex-snapshot
Mass problems associated with effectively closed sets
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Pisot family self-affine tilings, discrete spectrum, and the Meyer property
inferred← citeshttps://doi.org/10.3934/dcds.2021143openalex-snapshot
Characterizing entropy dimensions of minimal mutidimensional subshifts of finite type
inferred← citeshttps://doi.org/10.3934/dcds.2023001openalex-snapshot
Parametrization by horizontal constraints in the study of algorithmic properties of $ \mathbb{Z}^2 $-subshifts of finite type
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Dynamical cubes and a criteria for systems having product extensions
inferred← citeshttps://doi.org/10.3934/jmd.2021017openalex-snapshot
Rauzy induction of polygon partitions and toral $ \mathbb{Z}^2 $-rotations
inferred← citeshttps://doi.org/10.4007/annals.2010.171.2011openalex-snapshot
A characterization of the entropies of multidimensional shifts of finite type
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A counterexample to the periodic tiling conjecture
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An Order on Sets of Tilings Corresponding to an Order on Languages
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A primer on substitution tilings of the Euclidean plane
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Fixed Point and Aperiodic Tilings
inferred← citeshttps://doi.org/10.48550/arxiv.1003.2801openalex-snapshot
Fixed point theorem and aperiodic tilings
inferred← citeshttps://doi.org/10.48550/arxiv.1009.5167openalex-snapshot
Combinatorial substitutions and sofic tilings
inferred← citeshttps://doi.org/10.48550/arxiv.1012.1222openalex-snapshot
Computing (or not) Quasi-Periodicity Functions of Tilings
inferred← citeshttps://doi.org/10.48550/arxiv.1101.3369openalex-snapshot
Quotient Cohomology for Tiling Spaces
inferred← citeshttps://doi.org/10.48550/arxiv.1101.4930openalex-snapshot
Fusion: a general framework for hierarchical tilings of $R^d$
inferred← citeshttps://doi.org/10.48550/arxiv.1103.0895openalex-snapshot
Multidimensional effective S-adic systems are sofic
inferred← citeshttps://doi.org/10.48550/arxiv.1204.0949openalex-snapshot
Densities and entropies in cellular automata
inferred← citeshttps://doi.org/10.48550/arxiv.1303.2000openalex-snapshot
A non FLC regular pentagonal tiling of the plane
inferred← citeshttps://doi.org/10.48550/arxiv.1305.1062openalex-snapshot
Cohomology of the continuous hull of a combinatorial pentagonal tiling
inferred← citeshttps://doi.org/10.48550/arxiv.1405.6134openalex-snapshot
Pattern-Equivariant Homology of Finite Local Complexity Patterns
inferred← citeshttps://doi.org/10.48550/arxiv.1406.1220openalex-snapshot
Dynamical cubes and a criteria for systems having products extensions
inferred← citeshttps://doi.org/10.48550/arxiv.1410.8106openalex-snapshot
Spectral Theory of Substitutions in $\mathbb{Z}^d$
inferred← citeshttps://doi.org/10.48550/arxiv.1603.05464openalex-snapshot
Hierarchy and Expansiveness in Two-Dimensional Subshifts of Finite Type
inferred← citeshttps://doi.org/10.48550/arxiv.1605.09623openalex-snapshot
Subshifts with sparse traces
inferred← citeshttps://doi.org/10.48550/arxiv.1705.00042openalex-snapshot
Factor maps and embeddings for random $\mathbb{Z}^d$ shifts of finite type
inferred← citeshttps://doi.org/10.48550/arxiv.1712.03182openalex-snapshot
A characterization of entropy dimensions of minimal tridimensional subshifts of finite type
inferred← citeshttps://doi.org/10.48550/arxiv.1806.07799openalex-snapshot
Simulation of minimal effective dynamical systems on the Cantor sets by minimal tridimensional subshifts of finite type
inferred← citeshttps://doi.org/10.48550/arxiv.2002.03538openalex-snapshot
Tiling Iterated Function Systems
inferred← citeshttps://doi.org/10.48550/arxiv.2012.03892openalex-snapshot
Three characterizations of a self-similar aperiodic 2-dimensional subshift
inferred← citeshttps://doi.org/10.48550/arxiv.2105.00443openalex-snapshot
Fixed Point Constructions in Tilings and Cellular Automata
inferred← citeshttps://doi.org/10.48550/arxiv.math-ph/9812016openalex-snapshot
Isomorphism of Hierarchical Structures
inferred← citeshttps://doi.org/10.48550/arxiv.math/0507091openalex-snapshot
Spectral domain boundaries in cellular automata
inferred← citeshttps://doi.org/10.70675/13735c7ez51b8z4d5fzb342zf1c2ce1a3266openalex-snapshot
Ιndécidabilité des invariants géοmétriques dans les pavages
inferred← citeshttps://doi.org/10.70675/227b8686z1ee0z4156za2a9zc0590b828670openalex-snapshot
Subshifts of Finite Type on Groups : Emptiness and Aperiodicity
inferred← citeshttps://doi.org/10.70675/24c8743fz02d4z4d8fza94aza2b1b795455aopenalex-snapshot
Dynamique symbolique des systèmes 2D et des arbres infinis
inferred← citeshttps://doi.org/10.70675/42f6c1a3z2874z487ez9c1dz31924b5ff0f3openalex-snapshot
Chaos and Turing Machines on Bidimensional Models at Zero Temperature
inferred← citeshttps://doi.org/10.70675/56a998ebz65adz47d5z973bzf6dfdf993a9aopenalex-snapshot
On the study of homomorphisms between Z^d-topological dynamical systems
inferred← citeshttps://doi.org/10.70675/88f8398bz6e76z43a8z9367z3b175d397074openalex-snapshot
Shift spaces on groups : computability and dynamics
inferred← citeshttps://doi.org/10.70675/c5f56a9dz730az45f3z8d22z46c16887fa04openalex-snapshot
Contributions to ergodic theory and topological dynamics : cube structures and automorphisms
inferred← citeshttps://doi.org/10.70675/f88ace55z694cz4abaza9c6z7025778be73fopenalex-snapshot
Algorithmic complexity of growth-type invariants of SFT under dynamical constraints
inferred← citeshttps://doi.org/10.70675/f9b271ffz62f0z43fez9f1az95a2ee9fdecaopenalex-snapshot
Plans discrets substitutifs
inferred← citeshttps://doi.org/10.7146/math.scand.a-24183openalex-snapshot
Construction of the Discrete Hull for the Combinatorics of a Regular Pentagonal Tiling of the Plane
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