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# Wang Tiles

 edge and corner matched tilesets menu

## Overall 4x4 Patterns

One goal is to arrange a complete tileset in a square array so that it can seamlessly cover any area. This requires stage borders to wrap correctly top to bottom and left to right.

## 2-corner Wang Tileset

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

The 2-corner tileset has a unique solution. The 16 tiles are arranged in a Brigids Cross pattern. It can tile an area seamlessly. Corner tilesets in the gallery are all use this pattern.

### Brigid's Cross

The pattern also has a mirror image form.
Inverting the tiles does not produce a new pattern. It results in the same pattern shifted two tiles diagonally.

### 2-edge Wang Tileset

Using a 2-edge tileset results in very many possible solutions.

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

In the gallery, tilesets are shown as Layout 0. This is the simplist layout, but it has three disconnected paths. To reduce the number of possible solutions we can restict the layouts to connected mazes only.

Here are mazes with a '0' stage border. Note that tile-15 is placed in the same position in each layout. This removes similar rotation solutions. Each layout can be reflected though in the xy axis for a second solution.

If the maze paths are not confined and can wrap the stage borders then there are a few symmetrical solutions. Edge 3 and Edge 4 layouts produce a connected maze, as paths connect top - bottom and left - right stage borders.

The last solution is both symmetrical and connected. It is similar to the unique Brigid's Cross solution for a 2-corner tileset. It also has a mirror image by inverting the tiles.

Patt-1 and Patt-4 overall patterns are shown below. Patt-1 paths are limited to a diagonal pattern, while Patt-4 produces a fully connected maze.

Stage: Patt 1 and Patt 4 overall patterns

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