Wang Tiles

 

edge and corner matched tilesets

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4-order Wang Tiles

A 4-order Wang tileset require 4^4 = 256 tiles in a complete tileset. Too many to be practical for Stagecast sims or the web Stage.

Edge Wang Tilesets

Tiles of any order can be arranged in a recursive manner. Below is shown the layouts for Wang edge tiles of orders 1, 2, 3, and 4. The lower left quadrant is a repeat of the previous order.

Tile-0 (shown) and also tile-1 always have the same index number. All other tiles have to be renumbered for each order. See Wang 2-edge and 3-edge for index number creation.

All layouts wrap top-bottom and left-right.

Recursive layouts


1-e
tile

Wang 2-edge
tile tile tile tile
tile tile tile tile
tile tile tile tile
tile tile tile tile
Recursive layout of 3-edge Wang tiles
Wang tiles 3 edge recursive packing
Recursive layout of 4-edge Wang tiles
wang 4 edge recursive layout

Corner Wang Tilesets

Again, the lower left quadrant is a repeat of the previous order. Tile-0 (shown) and also tile-1 always have the same index number. See Wang 2-corner and 3-corner for index number creation.
Also see Puzzle Tilesets for reduced 3-corner tile sets used in tile matching puzzles.

Recursive layouts


1-c
tile

Wang 2-corner
6 14 8 4
1 7 12 5
2 15 11 13
3 3 8 1
Recursive layout of 3-corner Wang tiles
Wang tiles recursive array
Recursive layout of 4-corner Wang tiles
wang 4 corner recursive layout

Order 4 Wang tile layouts waiting for tile index numbers to be added. The weightings will be 1, 4, 16 and 64.

2 x 2-order Wang Tiles

A possible alternative arrangement it is to overlay a 2-order Wang tileset on top of another 2-order tileset. This will produce 16x16=256 combinations. The upper tileset will need to have a transparent background so the lower tiles show through. It may also require wider paths or patch areas. In theory, and with a good tile design, this should produce a 4-corner Wang tileset.

Wang Tiles | cr31.co.uk | 2017