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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].

15
votes
7answers
593 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 ...
32
votes
7answers
1k 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 ...
6
votes
1answer
179 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. (...
5
votes
1answer
164 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 ...
18
votes
4answers
415 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 ...
27
votes
6answers
830 views

ASCII Jigsaw Puzzle

This is a 3x3 ASCII jigsaw puzzle: ...
11
votes
4answers
403 views

Make a ASCII Hexagon Ring Tiling

Using ASCII print a section of a hexagon ring tiling. Here's a small section: ...
12
votes
2answers
525 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 ...
19
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 ...
25
votes
2answers
976 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 ...
30
votes
5answers
1k views

Integers, Assemble!

Your task is to assemble the integers from 1 to N (given as input) into a rectangle of width ...
5
votes
1answer
280 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 ...
10
votes
0answers
344 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 ...
23
votes
5answers
1k 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 ...
9
votes
4answers
606 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 ...
20
votes
6answers
2k 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 ...
18
votes
11answers
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 ...
21
votes
2answers
474 views

Rotate a diamond tiling

Any regular hexagon can be tiled with diamonds, for instance like so (stolen from this question): ...
45
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 ...
21
votes
5answers
1k 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 ...
10
votes
3answers
597 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 ...
27
votes
7answers
1k views

Scale up a Diamond Tiling

Any regular hexagon can be tiled with diamonds, for instance like so: ______ /_/_/\_\ /_/\_\/\_\ /\_\/_/\/_/\ \/_/\_\/_/\/ \_\/_/\_\/ \_\_\/_/ We'll ...
39
votes
13answers
4k views

Me Want Honeycomb

Write the shortest program that prints this ASCII art section of a hexagonal tiling or honeycomb: ...
10
votes
1answer
228 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 ...
22
votes
11answers
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 ...
14
votes
7answers
1k 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 ...
11
votes
4answers
986 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 ...
9
votes
3answers
793 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). ...
7
votes
4answers
549 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 ...
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. ...
9
votes
0answers
618 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 ...
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 ...