Questions tagged [tiling]
For challenges that involve partitioning a space (usually the plane) into small tiles without gaps (usually using a finite set of proto-tiles). See also [set-partitions].
51 questions
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Index into a Fibonacci tiling
The Cartesian plane can be tiled with increasingly large squares like so:
This tiling can be generated by starting with a square of side length 1, placed at the origin ...
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Complete the landscape
Carcassonne is a tile-based game, where the objective is to construct Roads, Cities and Monasteries, in order to score points. The game works by players taking turns to draw and place tiles to ...
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Draw the GKMS aperiodic tile
Chaim Goodman-Strauss, Craig Kaplan, Joseph Myers and David Smith found the following simple (both objectively and subjectively) polygon that tiles the plane, but only aperiodically:
Indeed they ...
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AoCG2021 Day 25: Stitching maps together
Part of Advent of Code Golf 2021 event. See the linked meta post for details.
Related to AoC2020 Day 20, Part 1. (This day is a dreaded one for many of you, I know :P)
Obligatory final "but you'...
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Game of Life, but on a 4-8-8 tiling
Background
The 4-8-8 tiling looks like this:
For the purpose of this challenge, we take the orientation of the tiling as exactly shown above. In plain English words, we take the tiling so that it can ...
- 79.3k
15
votes
6
answers
660
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Counting maximal domino placements
Background
A maximal domino placement (MDP) on a rectangular grid is a non-overlapping placement of zero or more dominoes, so that no more dominoes can be added without overlapping some existing ...
- 79.3k
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votes
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Is it a checkered tiling?
Background
A checkered tiling of a rectangular grid is a tiling using some polyominoes, where each region can be colored either black or white so that no two polyominoes sharing an edge has the same ...
- 79.3k
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The number of tilings of a grid
Setup:
A block is any rectangular array of squares, specified by its dimensions \$(w,h)\$. A grid is any finite ordered list of blocks. For example, \$\lambda = ((3,2),(3,1),(1,2))\$ defines a grid.
...
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Counting polydominoes
Background
A polyomino of size \$n\$ is a contiguous shape made from joining \$n\$ unit squares side by side. A domino is a size-2 polyomino.
A polydomino of size \$2n\$ is defined as a polyomino of ...
- 79.3k
15
votes
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Maximal saturated domino covering of a rectangle
Inspired by this OEIS entry.
Background
A saturated domino covering is a placement of dominoes over an area such that
the dominoes are completely inside the area,
the dominoes entirely cover the ...
- 79.3k
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Is this a robbery?
Backstory
You own a tiny jewellery shop in the suburbs of the city. The suburbs are too much overpopulated, so your shop has a thickness of only one character to fit in the busy streets.
Recently, ...
- 2,709
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votes
2
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Tiling a staircase with staircases
Background
A staircase polyomino is a polyomino made of unit squares whose shape resembles a staircase. More formally, a staircase polyomino of size \$n\$ is defined as follows:
A staircase polyomino ...
- 79.3k
10
votes
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Domino Recurrence Generator
Challenge
We once had a challenge to count domino tilings of m by n grid, and we all know that, for any fixed number of rows, the number of domino tilings by columns forms a linear recurrence. Then ...
- 79.3k
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votes
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Identify the smallest possible tile in the matrix
Challenge
Given a matrix of digits (0-9), find the smallest (in terms of area) rectangular matrix of digits where one or more copies of itself, possibly rotated, can tile the original matrix. ...
- 79.3k
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Can this polyomino tile the toroidal grid?
Inspired by certain puzzles on Flow Free: Warps.
Background
We all know that L-triominos can't tile the 3x3 board, and P-pentominos can't tile the 5x5 board. But the situation changes if we allow the ...
- 79.3k
