Function Repository Resource:

# TilingPatternPlot

Visualize a set of tiles

Contributed by: Wolfram Research
 ResourceFunction["TilingPatternPlot"][tiles] show tiles as a Graphics expression.

## Details and Options

A pattern is a rectangular array of positive integer values suitable for use in an ArrayPlot.
A tile mask is a subset of positions within a rectangular array, such as the a values in {{a,a,a},{_,a,_}}. This particular mask is also known as the Tetris T shape.
A tile is an array that can contain integers or blanks.
All tiles in a tileset fit in an array of the same size, say {a,b}. If all subarrays of that size in a larger pattern matches a tile in the tileset, then that tileset can be used to make the given pattern.
An all-zero tile leads to an all white or all zero pattern .
An all-one tile leads to an all black or all one pattern .
The two tiles lead to a checkboard pattern . No subset of the tiles will make a larger pattern, so these two tiles produce a minimal tiling.
The tileset will produce the all-white pattern, but the second tile is not necessary. Therefore, this is not a minimal tileset.
The above patterns have a size of 4×4.
The input tiles should be an array of integer or Blank (_) values.
Consider and {{_,0,0},{0,1,_}}. These both represent a 4-cell tile within a 6-cell array, where the integers indicate the coloring of the tile and the Blank (_) values are wildcards.

## Examples

### Basic Examples (2)

Show some tile patterns where the first two could overlap to make the third:

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Show a single tile:

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### Scope (2)

Multiple colors can be used:

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Use a tile specified as a SparseArray:

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### Neat Examples (1)

The following 42 tiles are believed to form an aperiodic tiling set equivalent to the minimal Wang tiling set:

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## Version History

• 1.1.0 – 15 March 2022
• 1.0.0 – 29 November 2021