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...
View ArticleTiling a staircase with staircases
BackgroundA 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 of...
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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,...
View ArticleDomino Recurrence Generator
ChallengeWe 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 why...
View ArticleCounting polydominoes
BackgroundA 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 size...
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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.Let...
View ArticleIs it a checkered tiling?
BackgroundA 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...
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Triangular domino tiling of an almost regular hexagon
BackgroundAn almost regular hexagon is a hexagon whereall of its internal angles are 120 degrees, andpairs of the opposite sides are parallel and have equal lengths (i.e. a zonogon).The following is an...
View ArticleCounting maximal domino placements
BackgroundA 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...
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Game of Life, but on a 4-8-8 tiling
BackgroundThe 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 be...
View ArticleAoCG2021 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're not...
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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 found a...
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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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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...
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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...
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