Turing Trains | Isometric | Wang Tiles | Maze Arrays | i Logo HOME

# Wang Tiles

 edge and corner matched tilesets menu

## 2-corner Wang Tiles

Wang tilesets are usually edge tilesets. But we can also create a Wang tileset by considering the tile corners. Each tile has four corners so for 2 different types of corner we have 2^4 or 16 different tiles, the same number as 2 different edges.

It may seem that matching corners will produce similar results as matching edges, but this is not so. An edge only affects one adjacent tile, while matching a corner affects three adjacent tiles.

Corner Wang tiles create areas (or patches) of matching terrain. Although not a maze of paths or passages, a complex layout of terrain patches, separated by barriers (ditches, walls, fences etc) can provide a difficult course to navigate through.

### 2-corner Tileset

Here is a typical set of corner Wang tiles. You can see that every tile has two different types of corner: blue or yellow. This gives 2x2x2x2 or 2 to the power 4, (written as 2^4), giving 16 possible combinations. Hence 16 different tiles, with index numbers 0 to 15.

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

The tileset is said to be 'complete' as it includes every possible combination of two corners. We can use these to tile a grid where all tile corners match.

### Bitwise Tile Index

With some bitwise maths, we can compute a unique 'index' number for each tile.
Ignore blue corners and add up yellow corners using the following binary weightings:

Yellow NorthEast corner = 1
Yellow SouthEast corner = 2
Yellow Sout-West corner = 4
Yellow NorthWest corner = 8

Blue corners are ignored.

 NorthWest = 8 NorthEast = 1 SouthWest = 4 SouthEast = 2

This tile has yellow corners NorthEast(1) and NorthWest(8). Adding up gives a tile index of '9'.

### Random Wang Tiles

We can arrange Wang tiles in a grid array. For each position, a tile is selected at random from the tileset, always ensuring that all corners match adjacent tiles.

See Terrain Tiles.
See Stage for random terrain arrays.

Stage: Random 2-corner Wang Tiles

### Path Tileset

Here is a path tileset which as you can see is very similar to the 2-edge path tileset, which is shown here for comparison. The corner tilset appears rotated by 45°. A few different tile variations are also shown.

 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Here are four pairs of tile-15 variations.
Four pairs of Tile-15 variations

We can use these 2-corner tiles to tile a grid where all tile corners match.

Stage: Random 2-corner Path Tiles

### Terrain Tilesets

Wang corner tiles make good terrain tiles. You can see that every tile has two different types of corner.

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

We can use these terrain tiles to create a grid where all tile corners match.