Wang Tiles

 

edge and corner matched tilesets

menu

Glossary P...S

A...B

C...F

G...O

P...S

T...Z

Pass-by
Alternative junction tiles where paths pass each other and do not join up. Will affect maze connectivity. Also see twin bend tiles. tile tile tile

Pass-over (bridge)
A path which crosses over another, without joining. tile When building a maze, paths are usually laid over (above) previously laid paths. Also see 'Pass-under' and 'Weave'.

Pass-thru
A path which, when being formed, passes 'through' and fuses with another path, forming a cross junction, where two passages intersect. tile

Trapped
tile tile tile
tile tile tile
tile tile tile
Pass-thru
tile tile tile
tile tile tile
tile tile tile
Pass-under
tile tile tile
tile tile tile
tile tile tile
Pass-over
tile tile tile
tile tile tile
tile tile tile

Pass-under (tunnel)
A path which crosses under another, without joining. tile See 'Pass-over' and 'Weave'.

Path (passage)
A route that can be traversed or followed through a maze. Paths are separated by a clearly marked impassable area, called a wall. Inverting all tiles swops paths and walls creating a 'negative' maze.

Path tiles
Wang (usually edge) tiles that form traversable paths or maze when laid out in a grid. Also see 'Terrain tiles'. tile

Perfect maze (simply connected)
A maze with no path loops, so no islands. All paths are connected, so all maze areas are reachable. There are no isolated paths or walls.
Pathways never re-connect with one another, so every path leads to additional paths (a junction tile) or to a dead end.
A perfect maze always has exactly one unique path (solution), from any tile to any other tile in the maze. Also see Tree maze.

Perspective
Tiles in a tileset must all be drawn with the same perspective...

Overhead
tile tile tile tile
tile tile tile tile
tile tile tile tile
tile tile tile tile
Elevated
tile tile tile tile
tile tile tile tile
tile tile tile tile
tile tile tile tile
Oblique
tile tile tile tile
tile tile tile tile
tile tile tile tile
tile tile tile tile
Depth
stacked tiles
Stacked
stacked tiles
Isometric
isometric tiles

Elevated tiles benefit from shadowing to emphasize the 3D edges.
Oblique tiles show the front and right-hand side of any raised levels.
Stacked tiles can partially overlap the tile in the cell above.
Isometric tiles are usually two cells wide and so overlap tiles either side.

Planair maze (Planes twisted through Air)
A maze layout where maze edges wrap top to bottom and side to side as if drawn on the surface of a cylinder or torus.

Random layout
If using block tiles, then simply selecting a tile from the tileset at random and placing it on the grid.
If using Wang tiles , then same as above, but also ensuring that all edges (or corners) match any already paced tiles.

Reduced Tileset (Compact or Sub-set)
A tileset that does not contain all possible tile combinations. Tiles can be removed for economic or aesthetic reasons. Some algorithms will never use some tiles. For instance cross or dead-end tiles. See Labyrinth and Crystal mazes.

A reduced set of 2-edge road tiles
tile tile tile tile tile tile tile tile tile tile tile
3 5 6 7 9 10 11 12 13 14 15

Note that it might not be possible to completely tile a grid with a reduced set of Wang tiles. For instance, using only tile-3 can never fully fill a grid. tile

Reflection
See 'Flip'.

Room
A large open area. Rooms are interconnected by passages (or tubular paths). A Wang tileset utilising both edges and corners is often needed to create a good passage and room maze layout.

Rotation
Turning a square tile through 90°, 180° or 270°. Not always the same as flipping a tile vertically or horizontally, (see 'Flip').
Also, it is possible to display a large tileset by only showing one tile from each rotation group. Thus it is only necessary to show tiles 0, 1, 3, 5, 7 and 15 from a Wang 2-edge tileset. See Puzzle Tiles page.

2-edge Path tile rotations
tile tile tile tile tile tile
  tile tile tile tile  
  tile tile   tile  
  tile tile   tile  
0 1
2
4
8
3
6
12
9
5
10
7
14
13
11
15
2-corner Path tile rotations
tile tile tile tile tile tile
  tile tile tile tile  
  tile tile   tile  
  tile tile   tile  
0 1
2
4
8
3
6
12
9
5
10
7
14
13
11
15

Blank tile-0 and crossroads tile-15 have only one rotation. Other tile-15 variations (Pass-over and Twin bend tiles) may have more.
Straight paths, tile-5 and tile-10 have two rotations, horizontal and vertical.
Dead-end, bend and branch paths have four rotations each.

Rotations can be calculated directly from the tile value. To rotate right 90 degree, simply double the value, modulo 16 (or modulo 81 in the case of a 3-edge or 3-corner tileset). To rotate left, divide by 2. If the value is odd, add 15 and divide by 2.

Run
When creating a maze, the path can often 'run' for a long time before it is trapped and forms a dead-end. If stage wrap or maze weave is allowed, then the maze algorithm can produce very long winding paths with just a few junctions. To prevent this, the algorithm forces the path to terminate when it exceeds a certain 'run' limit. By setting the limit very low, a tree (or crystal) maze results.

Note that this is slightly different to other users definitions where 'run' refers to the length of a straight path.

Seamless texture
An image tile often used for web page backgrounds which tiles without producing a visible edge, so creating an 'all-over' pattern. In Adobe Photoshop, use the 'offset' filter to help create seamless tiles. tile

Shortest Path
See A* algorithm.

Simply connected
Same as 'Perfect maze'.

Sink (trap)
A one way directed path tile with all paths flowing into the tile. eg tile

Source (spring)
A one way directed path tile with all paths flowing out of the tile. eg tile

Solution
A maze path from start tile to finish tile.

Solver sprite
A sprite that attempts to solve the maze by using a solver algorithm eg A* or right-hand-rule, instead of selecting paths at random. May not find the shortest route.

Sparse maze
A maze where some cells do not contain a path. Random tree mazes often have empty cells which are not filled as the maze tree grows, (or filled with tile-0).
Upper layers of a layered maze are sometimes more sparse to make it easier to see paths in the denser lower levels.

Sprite
An animated object, eg person or vehicle, that follows the maze paths. If wandering randomly, sprites turn or move off a tile by any allowable exit at random. Sprites must turn around and move back at a dead end. Random wandering of a sprite will eventually solve a maze. tile

Straight
A path tile with no bends or forks. tile or tile

Stage
The Stagecast window (or array) onto which tiles are placed. Default size of 18x12 (width x height) tiles. Both width and height even values.

Start point
A grid cell where the first maze tile is placed. Maze generation algorithms will build the maze by growing out from the initial start point.

Start tile (entrance)
A tile where sprites first enter the maze. They then randomly follow the maze paths until they find the finish tile to solve the maze

 

Wang Tiles | cr31.co.uk | 2018