Use this tag for questions about (not necessarily periodic) tilings of metric spaces, their combinatorial, topological and dynamical properties, as well as basic definitions and concepts.
Questions tagged [tiling]
745 questions
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New Spectre tile moire pattern is very different from that of the Penrose tiling, why?
When you take two copies of the Penrose tiling, as Penrose himself demonstrated, they form a 5 fold symmetric Moire pattern which matches the 5 fold symmetry of their construction. When you "zoom into" one of the bright spots, being a region where…
3
votes
1 answer
Are local rearrangements in aperiodic tilings possible?
Is it possible to perform a local rearrangement of tiles in an aperiodic tiling (such as the Penrose tiling or certain sets of Wang tiles), such that all matching rules are maintained? By "local" I mean that the number of rearranged tiles is…
Alehud
- 65
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3
votes
1 answer
Looking to vectorize P2 Penrose tiling
I'm looking for a tool to vectorize a P2 Penrose tiling.
I've been able to find tools to vectorize P3 tilings, but not P2.
Goal is to put p2 tiling on cycling kit
Retired account
- 1,080
3
votes
0 answers
Generating aperiodic tilings, with a twist
A common technique for generating aperiodic tilings is inflation — given a starting point and some rules, you "grow" the tiling outwards from there.
This works, but suppose you choose such a tiling, then want to explore a small portion of it "far…
jwd
- 463
3
votes
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Are there isotropic grids in dimensions greater than 1?
In greater detail, is it possible to tile space such that the number of cells that a ray of a length $l$ will pass through (or, equivalently, the ratio of cell number to $l$) tends to become uniform in all directions as $l \rightarrow \infty$,…
Logan R. Kearsley
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2
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How get closest vertex in triangular tiling from coordinates on plane?
Currently I have a plane with square tiling. It pretty trivial to get point on plane mapped to vertex of square tiling: plane point (x; y) -> vertex of square tiling (x div A; y div A). How to get same, but for Triangular tiling?
This is important!…
oooooooook
- 21
- 2
2
votes
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Coordinate system to uniquely refer to penrose tiling tiles?
Suppose I have a rhombus based penrose tiling like the following:
Is there some coordinate system that allows me to easily uniquely refer to a specific tile, and also from the coordinates efficiently calculate the coordinates of the tiles that…
mousetail
- 131
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Which repeated shape covers a circle most efficiently
Imagine you have a ring and you want to fill as much of this ring as possible with one type of shape (triangle, square, hexagon, must be the entire shape repeated within the ring no overlaps). To be efficient filling up the ring you want the total…
Jl137
- 29
2
votes
1 answer
What's difference between Penrose Arc Decoration and Ammann Line Decoration for tiling kite and dart?
Penrose Arc for edge tiling rule
Ammann line for edge tiling rule
The result seemingly the same. It could be use to join the tile to be penrose tiling. So what is the difference between these two method? I try to look for detail but only could…
Thaina
- 672
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Given 4 tile types, what are the chances that there are no sets of 3 in a 6x6 array?
I know this question seems arbitrary, but it actually applies to a matching game that I'm writing.
I randomly typed the following letters and created a 6x6 array using the letters A, S, D, and F.
SADFSD
ASDASD
FDASAS
DFDASD
FDAFSD
ADSFAS
Note that…
HappyEngineer
- 175
2
votes
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How to accurately tile a Conch tiling with no knowledge of any of it.
I am trying to use this tiling but I can't reconstruct it accurately and really have no knowledge of this type of math. I'm seriously really ignorant to how this can be produced.
If there is anyway someone can explain how to construct these tiles in…
Jimswid
- 21
2
votes
1 answer
Are tilings by completely symmetric polyominoes always unique?
Suppose you have a (finite) figure $F$ and a polyomino $P$ with the same symmetries as a square that tiles $F$. It seems obviously true that the tiling must be unique, but I cannot find a nice proof of this.
There is a generic proof described below…
Herman Tulleken
- 3,608
2
votes
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Why is the 14th convex pentagon tiling unique?
According to the wikipedia article on pentagonal tilings, the 14th type of pentagonal tiling is
completely determined, with no degrees of freedom
However, I was wondering why an affine stretch of the plane would (thus preserving the tiling) would…
Wen
- 1,966
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Prove there is a unique tiling with L-tiles
Prove or Disprove:
For all $n$ contained in positive integers
For any single square removed from a $2^n \times 2^n$ grid, there is a unique tiling with $L$-tiles.
The word that messes with me is "unique", I know that this statement is true, as I can…
user377558
- 83
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vote
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Is there an aperiodic tiling consisting of deformed hexagons?
The typical Penrose tiling consists of two deformed quadrangles. But it's there any aperiodic tiling consisting entirely of two or more deformed hexagons? Maybe even one that shares some properties of a hexagonal tiling such as only edge-neighbours?
Tobias Kienzler
- 6,609