Tilings and patterns
Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
An aperiodic set of 13 Wang tiles
Discrete Mathematics
A small aperiodic set of Wang tiles
Discrete Mathematics
Reliable cellular automata with self-organization
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Theory of Self-Reproducing Automata
Theory of Self-Reproducing Automata
Aperiodic Tilings: Breaking Translational Symmetry
The Computer Journal
An Almost Totally Universal Tile Set
TAMC '09 Proceedings of the 6th Annual Conference on Theory and Applications of Models of Computation
High Complexity Tilings with Sparse Errors
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Constructing New Aperiodic Self-simulating Tile Sets
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Aperiodicity Measure for Infinite Sequences
CSR '09 Proceedings of the Fourth International Computer Science Symposium in Russia on Computer Science - Theory and Applications
Tilings: Simulation and universality
Mathematical Structures in Computer Science
Effective closed subshifts in 1D can be implemented in 2D
Fields of logic and computation
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Fixed-point tile sets and their applications
Journal of Computer and System Sciences
Substitutions and strongly deterministic tilesets
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
Simulation of Effective Subshifts by Two-dimensional Subshifts of Finite Type
Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
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An aperiodic tile set was first constructed by R. Berger while proving the undecidability of the domino problem. It turned out that aperiodic tile sets appear in many topics ranging from logic (the Entscheidungsproblem) to physics (quasicrystals)We present a new construction of an aperiodic tile set that is based on Kleene's fixed-point construction instead of geometric arguments. This construction is similar to J. von Neumann self-reproducing automata; similar ideas were also used by P. Gács in the context of error-correcting computations.The flexibility of this construction allows us to construct a "robust" aperiodic tile set that does not have periodic (or close to periodic) tilings even if we allow some (sparse enough) tiling errors. This property was not known for any of the existing aperiodic tile sets.