Wang Tiles

 

edge and corner matched tilesets

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Angled Paths (2-corner Tilesets)

Wang 2-corner tiles usually show a present or an absent path, like this:

Complete 2-corner Wang tileset
tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile
tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Alternatively, we can denote the angle of the path, \ or / like this:

tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Look carefully and you can see yellow corners have North-West South-East paths (\) and blue corners North-East South-West (/) paths. If the path does not extend into the tile, only a small triangle is drawn, so the design will match adjoining tiles correctly.

Stage Array

The tiles automatically tile correctly using the existing Wang tiling method. Quite a complex maze results, with complex interlocking islands. It looks like the back of a Printed Circuit Board, hence named PCB.

Stage: Random 2-corner Angled (PCB) Tiles

PCB Tile Array

We could also use Wang edge tiles instaed of corner tiles.

Angled Paths (2-edge Tilesets)

Here is a 2-edge Wang tileset showing absent or present paths at each tile edge.

Complete 2-edge Wang and Path tilesets
tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile
tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

In this tileset design, we denote the angle of the path, \ or / like this:

Complete set of 2-edge Border tiles
tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

You can see yellow edges have North-West South-East paths (\) and blue edges have a North-East South-West (/) paths.

Stage: Random 2-corner Angled (Octal) Tiles

Octal Tile Array

Wang Tiles | cr31.co.uk | 2017