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.