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].

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27
votes
2answers
1k views

Arranging arbitrary rectangles to fill a space

Can these rectangles fill a rectangular space? Given a bunch of rectangles, you are asked whether or not they can be arranged to fill a rectangular space. Specs Given a bunch of arbitrary ...
22
votes
6answers
2k views

Random ASCII Art of the Day #5: Diamond Tilings

Mash Up Time! This is instalment #5 of both my Random Golf of the Day and Optimizer's ASCII Art of the Day series. Your submission(s) in this challenge will count towards both leaderboards (which you ...
40
votes
13answers
5k views

Me Want Honeycomb

Write the shortest program that prints this ASCII art section of a hexagonal tiling or honeycomb: ...
11
votes
10answers
2k views

Fibonacci domino tiling

There's classic combinatorial result that the number of ways to tile a 2*n strip by 1*2 dominoes is the nth Fibonacci number. ...
50
votes
2answers
2k views

Extending OEIS: Counting Diamond Tilings

I promise, this will be my last challenge about diamong tilings (for a while, anyway). On the bright side, this challenge doesn't have anything to do with ASCII art, and is not a code golf either, so ...
24
votes
6answers
4k views

ASCII connected hexagons

Overview Given a number of hexagons, arrange them into a connected shape within the confines of a 50 by 50 ASCII art image. The shape you choose can be arbitrary - whatever you find most amenable to ...
27
votes
7answers
1k views

Scale up a Diamond Tiling

Any regular hexagon can be tiled with diamonds, for instance like so: ______ /_/_/\_\ /_/\_\/\_\ /\_\/_/\/_/\ \/_/\_\/_/\/ \_\/_/\_\/ \_\_\/_/ We'll ...
9
votes
3answers
306 views

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 ...
20
votes
3answers
2k views

Piet (Mondrian)'s Puzzle

For more information, watch this video, and go to A276523 for a related sequence. The Mondrian Puzzle (for an integer n) is the following: Fit non-congruent ...
24
votes
3answers
3k views

Fill the Screen with Wang Tiles

It has been proven that the following 13 square Wang tiles always tile the plane aperiodically. This means that when the squares are arranged in a grid with all neighboring sides the same color, a ...
21
votes
2answers
554 views

Rotate a diamond tiling

Any regular hexagon can be tiled with diamonds, for instance like so (stolen from this question): ...
15
votes
6answers
573 views

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 ...
14
votes
7answers
650 views

Is my kids' alphabet mat properly grouped by colors?

My kids have an alphabet mat to play with, something like this: After months with the tiles of the mat randomly placed, I got tired and placed all the tiles of the mat grouped by sections according ...
10
votes
5answers
958 views

Generate valid Fibonacci tilings

Background The Fibonacci tiling is a tiling of the (1D) line using two segments: a short one, S, and a long one, L (their length ratio is the golden ratio, but that's not relevant to this challenge). ...
13
votes
7answers
986 views

Number of domino tilings

Write a program or function that given positive n and m calculates the number of valid distinct domino tilings you can fit in a n by m rectangle. This is sequence A099390 in the Online Encyclopedia of ...
10
votes
3answers
658 views

Supersonic domino tilings

Task Write a program that reads three integers m, n either from STDIN or as command-line arguments, prints all possible tilings of a rectangle of dimensions m × n by 2 × 1 and 1 × 2 dominos and ...
7
votes
4answers
650 views

Print all domino tilings of 4x6 rectangle

This is an extension of Fibonacci Domino Tiling. Your goal is to print all 281 ways to tile a 4x6 rectangle with 1x2 and 2x1 dominoes. Fewest bytes wins. Use the vertical bar ...