Wang Tiles

 

edge and corner matched tilesets

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Shape Tiles

In a shaped tile, the edge between two tiles is distorted into a curve, jigsaw or other outline shape. All adjacent tile edges fit snugly together, without overlapping or gaps.

The Wang tile designs remain square and are never extended to cover any neighboring tile. To ensure tile shapes are compatable with same colored edge tiles we've already used, we need to define yellow and blue edges.

Curve edge shape

We can have a curved edge like this: curve

We use the following rules:

1/ Blue edges curve up or right (away from the origin)
2/ Yellow edges curve down or left (towards the origin)

2-edge shape tileset

Here is a set of Wang tiles. You can see that every tile has two different types of edge, corresponding to a yellow edge, or a blue edge. We have 16 different tile shapes.

Four complete 2-edge shape 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
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

We can use these to tile a square grid where all tile edges match.
As these are Wang tiles, we only need to draw the curve within the tile. In the real world, we could cut out 16 differently shaped tile pieces. Some packing puzzles use such tilesets.

6 14 8 4
1 7 12 5
2 15 11 13
3 3 8 1
6 14 8 4
1 7 12 5
2 15 11 13
3 3 8 1
6 14 8 4
1 7 12 5
2 15 11 13
3 3 8 1
6 14 8 4
1 7 12 5
2 15 11 13
3 3 8 1

Pretty, but not useful as a maze.

Stage: Random Shape Tiles

Shaped Tiles

Wang Tiles | cr31.co.uk | 2017