Wang Tiles

 

edge and corner matched tilesets

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4-order Wang Tile Recursive Layouts

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. All layouts place the '0' tile in the lower left. For each layout, 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 | 2018