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].
50
questions
17
votes
7
answers
1k
views
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 ...
53
votes
4
answers
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 ...
- 4,765
17
votes
4
answers
650
views
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 ...
- 188k
24
votes
16
answers
3k
views
Triangular domino tiling of an almost regular hexagon
Background
An almost regular hexagon is a hexagon where
all of its internal angles are 120 degrees, and
pairs of the opposite sides are parallel and have equal lengths (i.e. a zonogon).
The ...
- 11.8k
21
votes
3
answers
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 ...
- 6,229
15
votes
5
answers
532
views
Simplest Tiling of the Floor
You should write a program or function which receives a string describing the floor as input and outputs or returns the area of the simplest meta-tiling which could create the given pattern of the ...
- 73.8k
9
votes
6
answers
338
views
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'...
- 6,723
10
votes
7
answers
2k
views
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 ...
- 166k
30
votes
12
answers
2k
views
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 ...
- 9,811
15
votes
6
answers
529
views
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 ...
- 16.2k
7
votes
1
answer
286
views
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.
...
- 171
9
votes
2
answers
297
views
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 ...
- 21.3k
10
votes
3
answers
368
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 ...
- 41.3k
22
votes
18
answers
2k
views
Concentric rings on a snub square tiling
This challenge takes place on the snub square tiling.
Start by choosing any triangle, and color it \$c_1\$.
Next, find all tiles which touch this triangle at any vertex, and color them \$c_2\$. Next, ...
- 27k
19
votes
2
answers
671
views
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 ...
- 166k
21
votes
1
answer
934
views
How should I tile my kitchen?
I recently ordered some new and colorful tiles to replace my boring old white tiling for my kitchen. However, when the tiles arrived, they were all in a weird shape! Therefore, I need a program to ...
- 6,229
15
votes
6
answers
622
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 ...
- 104k
12
votes
12
answers
4k
views
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, ...
- 11.3k
10
votes
5
answers
986
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). ...
- 29.9k
13
votes
7
answers
1k
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 ...
- 29.9k
7
votes
2
answers
341
views
ASCII Exact Cover with Rectangles
Challenge
Given a rectangular area arrange a group of rectangles such that they cover the rectangular area entirely.
Input
An integer denoting the height.
An integer denoting the width.
The ...
- 29.9k
32
votes
6
answers
1k
views
Integers, Assemble!
Your task is to assemble the integers from 1 to N (given as input) into a rectangle of width ...
- 38k
16
votes
3
answers
294
views
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. ...
- 11.3k
13
votes
3
answers
614
views
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 ...
- 166k
9
votes
3
answers
537
views
Number of tilings on a triangular board with triangular tiles
Background
Consider the shape \$T(n)\$ consisting of a triangular array of \$\frac{n(n+1)}{2}\$ unit regular hexagons:
John Conway proved that \$n = 12k + 0,2,9,11\$ if and only if \$T(n)\$ can be ...
CommunityBot
- 1
8
votes
1
answer
570
views
Test a polyomino against Conway criterion
Background
Conway criterion is a method to test if a given polygon can tile (i.e. cover without overlapping) an infinite plane. It states that a polygon can tile the plane if the following conditions ...
- 22.3k
22
votes
6
answers
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 ...
- 13.1k
27
votes
2
answers
2k
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 ...
- 26.1k
14
votes
7
answers
690
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 ...
CommunityBot
- 1
32
votes
7
answers
2k
views
Finite tilings in one dimension
The purpose of this challenge is to determine if a collection of one-dimensonal pieces can be tiled to form a finite continuous chunk.
A piece is a non-empty, finite sequence of zeros and ones that ...
- 104k
7
votes
1
answer
227
views
Arranging arbitrary shapes to fill a rectangular space
A while ago, I posted a challenge asking to determine whether or not it's possible to arrange arbitrary rectangles to fill a rectangular space, here. That got answers, so clearly it was too easy. (...
- 19.8k
11
votes
2
answers
596
views
Mondrian Puzzle Sequence
Partition an n X n square into multiple non-congruent integer-sided rectangles. a(n) is the least possible difference between ...
CommunityBot
- 1
18
votes
4
answers
528
views
Let's Tessellate!
Introduction
From Wikipedia:
A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.
A fairly well known ...
CommunityBot
- 1
27
votes
6
answers
1k
views
10
votes
4
answers
529
views
Make a ASCII Hexagon Ring Tiling
Using ASCII print a section of a hexagon ring tiling.
Here's a small section:
...
CommunityBot
- 1
21
votes
2
answers
584
views
Rotate a diamond tiling
Any regular hexagon can be tiled with diamonds, for instance like so (stolen from this question):
...
CommunityBot
- 1
5
votes
1
answer
320
views
Tiling by substitution
EDIT: The incorrect A rhomb substitution has been fixed. Apologies to anoyone who had started working on a solution.
Consider the following substitutions, where the substituted rhomb(us) is scaled up ...
- 849
11
votes
10
answers
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. ...
CommunityBot
- 1
23
votes
5
answers
2k
views
Seamless conversion from square to hexagon
For many games played on a grid, hexagons are the Clearly Superior Choice™. Unfortunately, many free game art sites only have seamless tile sets for square maps. On a past project, I used some of ...
CommunityBot
- 1
14
votes
7
answers
2k
views
Tiling a 2^N by 2^N Grid with L-Shaped Trominoes
When students are first taught about the proof technique of mathematical induction, a common example is the problem of tiling a 2N×2N grid with L-shaped trominoes, leaving one predetermined grid ...
CommunityBot
- 1
25
votes
3
answers
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 ...
- 39.4k
24
votes
6
answers
5k
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 ...
CommunityBot
- 1
19
votes
11
answers
2k
views
64 bit ASCII weaving
Input
Two integers:
A non-negative integer W in the range 0 to 2^64-1, specifying the weave.
A positive integer S in the range 1 to 255, specifying the side length.
These can be taken in whichever ...
CommunityBot
- 1
40
votes
13
answers
5k
views
Me Want Honeycomb
Write the shortest program that prints this ASCII art section of a hexagonal tiling or honeycomb:
...
CommunityBot
- 1
27
votes
7
answers
1k
views
Scale up a Diamond Tiling
Any regular hexagon can be tiled with diamonds, for instance like so:
______
/_/_/\_\
/_/\_\/\_\
/\_\/_/\/_/\
\/_/\_\/_/\/
\_\/_/\_\/
\_\_\/_/
We'll ...
CommunityBot
- 1
10
votes
3
answers
687
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 ...
CommunityBot
- 1
22
votes
10
answers
2k
views
Tile the plane with this modified circle
Take a unit circle centered on the origin. In any two neighboring quadrants, mirror the curve of the circle across the lines connecting the circle's x and y intercepts.
With the resulting shape, you ...
CommunityBot
- 1
12
votes
4
answers
1k
views
Tiling, given vertex configuration
Task
The task is to tile polygons, given a vertex configuration.
Scoring
Your score is equal to the "complexity level" your submission reaches. Complexity levels are cumulative, meaning that to ...
CommunityBot
- 1
7
votes
4
answers
678
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 ...
CommunityBot
- 1
9
votes
0
answers
717
views
Create a popular penrose tiling [closed]
The recent question about Wang tiles has led me to think that creating Penrose tilings might be an interesting popularity contest.
Background
Wang tiles are tiles that can tile the plane, but only ...
CommunityBot
- 1