All Questions
Tagged with tiling ds.dynamical-systems
13 questions
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Computing the language of an $S$-adic shift
I have been looking online for how or if one can compute the language of an $S$-adic subshift generated by finitely many substitutions. I know that one can compute the language of a substitution ...
- 633
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52
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Does a substitution tiling being FLC depend on starting seed?
I've been trying to understand more on "geometric" substitutions rather than just symbolic ones. As symbolic substitutions always yield FLC tilings, I wanted to know whether a tiling coming ...
- 633
2
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116
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Aperiodic SFT equal to a substitution subshift
I was wondering whether there are primitive symbolic substitutions over $\mathbb{Z}^d$ and alphabet $\mathcal{A}$ whose associated subshift is equal to an aperiodic SFT. By SFT here I mean a subshift ...
- 633
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74
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Computing admissible patches of a substitution
I have been recently trying to look at substitution tilings with finite local complexity by examining their admissible patch\pattern atlas, which is sometimes called their language. I have also seen ...
- 633
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A variation of domino tiling problem with fusions
I know several specific variations of the domino tiling problem has been determined to be decidable or undecidable, such as the seed domino problem. I have a variation which I have not been able to ...
- 633
2
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1
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129
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Reference on relation between SFTs and Wang-tiles
I've been looking at several papers which allude to a relation between SFTs. Namely, given an SFT $\Omega \subseteq \mathcal{A}^{\mathbb{Z}^2}$ with allowed patches $\mathcal{F}$, we can associate a ...
- 633
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1
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192
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Topological full groups of subshifts: differences between one-dimensional and multi-dimensional subshifts
For a multidimensional subshift $X$ over $\mathbb Z^d$, the topological full group $[X]$ is the set of homeomorphisms $f$ of $X$ that can be written as $f : x \mapsto \sigma_{c(x)}(x)$ with $c : X \to ...
- 113
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2
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329
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Sufficient conditions for periodic tiling by Wang tiles
I'm recently interested in whether a sub-shift of finite type contains a doubly-periodic problem, when the set of configurations is of the sort $\mathcal{A}^{\mathbb{Z}^2}$. When $Q_2=\{0,1\}^2$, and ...
- 633
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213
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Possible weaker version of the Domino/Wang tiling problem
This may be a dumb question, but I was wondering whether the question of 'periodically tiling the plane from a finite set of tiles' is the same as the domino tiling problem or a weaker version. I ...
- 633
11
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1
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392
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Growing a chain of unit-area triangles: Fills the plane?
Define a process to start with a unit-area equilateral triangle,
and at each step glue on another unit-area triangle.
$50$ ...
- 151k
1
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125
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Minimal period for a bounded Langton's ant moving on a tessellation
We consider Langton's ant on the 2D plane, but we replace the square lattice by a Voronoi tessellation obtained from a finite set of points (it could be another tessellation, however directions such ...
- 111
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295
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Aperiodic tiling of compact space by small number of basic tiles
Suppose we have compact space, like sphere or torus in particular dimension $d$.
Is it possible to construct aperiodic tiling in such setting? It seems obvious, answer is yes, because we may just ...
- 1,626
10
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2
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1k
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Decidability of periodic tilings of the plane
I'm interested in tilings of the plane by squares, with labels on the edges. It's well known that (1) the question "can one tile the plane with the following finite set of tiles?" is undecidable, and (...
- 2,519