47
votes
Accepted
Is there mathematical significance to the LaGuardia floor tiles?
You can view this pattern as consisting of major and minor tiles. The major tiles are the union of four hexagons. These tiles are all identically subdivided into eleven minor tiles.
In the picture ...
- 1,538
27
votes
Is there mathematical significance to the LaGuardia floor tiles?
Concerning the secondary question who designed the pattern:
The tiled floor in LaGuardia terminal B was designed by HOK and installed by Consolidated Flooring. They received an award for this. The ...
- 188k
22
votes
Accepted
(non-)existence of the aperiodic monotile
This recent preprint claims to find such a tile.
David Smith, Joseph Samuel Myers, Craig S. Kaplan, Chaim Goodman-Strauss, “An aperiodic monotile”, (2023-03-20) arXiv:2303.10798
A longstanding open ...
21
votes
Accepted
Aperiodic monotile without reflections?
The same authors have just released a preprint claiming a positive answer to this question.
EDIT: Here is a picture of the reflection-free aperiodic monotile:
More visualizations and other data are ...
- 114k
13
votes
Is there mathematical significance to the LaGuardia floor tiles?
For those who can't quite see the underlying hexagonal tiling mentioned in David Speyer's comment, I have highlighted part of it below. Please excuse my crude digital editing skills.
.
10
votes
Decidability of completing Penrose tilings
Apparently it is decidable, as proved in theorem 27 here: https://people.maths.ox.ac.uk/ritter/masterclasses/ritter-lectures-on-penrose-tilings.pdf
- 509
4
votes
Accepted
Is there an L-system for aperiodic tilings of the plane with the "hat" monotile?
(a second answer because this one is an answer)
So, I misled myself staring at the H8 in Smith et al. The way to solve this is to look at the F-supertile. That tile has 5 edges, and 4 of them are F-...
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4
votes
Is there an L-system for aperiodic tilings of the plane with the "hat" monotile?
I don't know the answer to the second part of your question (yet), about the self-avoiding fylfot fractal, but here's an L-system generating outlines of patches of monotiles, implied by the H7/H8 ...
- 196
2
votes
How much of an aperiodic tiling is needed to force aperiodicity?
While your question does not specify all details, in general it follows from the undecidability of the Domino problem that this is also undecidable. In fact, your problem seems slightly easier, as if ...
- 18.7k
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