Wang Tiles

 

edge and corner matched tilesets

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Glossary T...Z

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T...Z

T-junction (fork)
A three way path tile. See 'Fork Tile'. tile

Terrain tiles
Wang (usually corner) tiles that form a traversable landscape when randomly laid out on a grid. May not be an interesting maze structure. Ddifficult to build a perfect maze using corner terrain tiles. tile Also see 'Path tiles'.

Tidy Tiling Method
Tiling method to prevent clumping or corner touching of block tiles. See Block Tiles page.

Tile-0
A blank or empty tile. tile As it has no exits, its index sum is '0' (zero). The blank tile is the only tile which has the same index for any order. Also see alternative tiles.

Tile-15 Alternatives
A 2-edge Wang tile with a path on all four edges is indexed as tile-15. It can have different design variations. Also see alternative tiles.

Tile-15 variations
tile tile tile tile tile
tile tile tile tile tile

This does not effect the Wang tile maze building process, but does effect the sprite path followers who must choose the correct path. For instance, the third tile above, sprites can only move straight ahead, they cannot turn and exit.
Also, tile-15 variations may render the maze no longer 'perfect'. The middle tile above is not 'internally connected', it has two separate paths which are not joined. So the final maze may not be connected. See 'Twin bend', 'Perfect maze', and 'Weave'.

Tile Design
The image depicted on a tile. Tiles in a tileset have a similar artistic or graphical design so that they aesthetically 'go' together. Must also all have the same perspective. Design styles can be flat graphics, isometric pixel art or more realistic looking 'pixel art' imagery.

Tileset
A collection of tiles which are used to create a path, terrain or maze layout. Usually, all tiles have a similar style, so that the completed maze is aesthetically pleasing.

Toroidal / Torous
A stage which wraps top/bottom and left/right.

Transparent tiles
Tile designs with a transparent background. This allows mazes or terrains to be layered. Upper layers (especially terrains) may need to be sparse. Or a path (edge tile) maze can be placed over a terrain (corner tile) background.

Tree maze
A perfect maze which is constructed using a slightly different algorithm. All paths are allowed to grow at the same time. The maze spreads outwards from an initial start point. Can be sparse.

Twin Bend Tile (Pass-by)
A tile with two unjoined path bends. A possible Tile-15 variation.

Twin bends
tile tile
tile tile

Twin maze
A maze which uses two (or more?) tilesets to build seperate mazes that co-exist on the same stage. Special 'cross-over' tiles are added wherever any paths from one maze cross-over the paths of the other. Can be constructed 'free-form' or more usually restricted to an intermeshed lattice.
See 2-edge page.

Twin maze design
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

Tube (river)
A long path with no junctions. Opposite style to a tree maze where paths are short with many junctions. If the tube is straight with no bends then called a run.

U-turn
A path following sprite can usually only turn around by 180° if facing a dead-end.

Unicursal
See labyrinth maze.

Value
The number given to each edge (or corner) of a Wang tile. For 2-order tilesets, values are either '0' or '1'. Usually, '0' depicts no path and '1' a path. 3-order tilesets, can have values of '0', '1' or '2'.
These values can be used to calculate a unique tile Index number.

Vortex
A spiral pattern of maze paths with a single (3 or 4 way) junction at the center.

Wall
An impassable barrier between maze paths (or terrain areas). A path following sprite cannot jump over or pass through a wall. Also see Block maze.

Wandering sprite
A sprite that selects a random exit to leave a junction tile. Cannot U-turn.

Wang Tile
A tile that uses edge or corner matching to allow it to be correctly placed in a grid to produce a seamless layout of paths or terrain. Cannot be reflected (flipped) or rotated.

Wang Tileset
A set of square tiles which can be arranged in a regular grid so that all neighboring tile edges or corners match. Tiles can have two or more different types (or color) of edge or corner. Usually, all tiles have a similar design.

A set of 2-edge and a set of 2-corner Wang tiles
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

As you can see, corner tiles are similar to edge tiles, but rotated 45° clockwise. However, an edge tile affects two adjacent tiles, whereas a corner tile affects four adjacent tiles. Also see 'Complete' and 'Reduced' tilesets.

Weave maze
A maze where paths are allowed to pass under or over each other. Paths should not be ambiguous, so usually cross perpendicularly. tile tile
Paths can cross as they form, randomly, or depending on their chequer grid position.

Weighting
Allocating a 'weight' to each tile edge or corner depending on the order. This allows a unique index number to be calculated.
For 2-edge or 2-corner tiles, which have an order of 2, the weightings are 2^0, 2^1, 2^2 and 2^3, which produces the binary weightings 1, 2, 4, and 8. This produces 16 unique index values from 0 to 15.
An order 3 tileset will have tertiary weightings of 3^0, 3^1, 3^2 and 3^3, which produces 1, 3, 9 and 27. This produces unique index values from 0 to 81.

Similarly, 4-order tiles will be powers of 4, so 1, 4, 16, 64 etc.

2-edge weightings
  North
= 1
 
West
= 8
tile East
= 2
  South
= 4
 
2-corner weightings
NorthWest
= 8
  NorthEast
= 1
  tile  
SouthWest
= 4
  SouthEast
= 2

Wrap
A stage that allows tiles to 'join' or edge match from one side of the stage to the opposite side. If only left/right or top/bottom wrap is allowed then the stage behaves like a cylinder. If both opposite stage edges wrap then it behaves like a torus. A maze on such a surface is called 'Planair'.

Zeta maze
A maze layout of horizontal, vertical and diagonal paths. This combines edge and corner Wang tiles on a square grid.

 

Wang Tiles | cr31.co.uk | 2018