Wang Tiles

 

edge and corner matched tilesets

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Glossary G...O

A...B

C...F

G...O

P...S

T...Z

Grid
A regular layout of cells that structure the maze. Stagecast grids are always square. But mazes can also be built on triangular, hexagonal or other regular grids. Also See 'Chequer'.

Square 'omega'
tile tile tile tile tile
tile tile tile tile tile
Triangular 'delta'
tile tile tile tile tile
tile tile tile tile tile
Hexagonal 'sigma'
tile tile tile tile tile
tile tile tile tile tile

Other types of grid are:

Isometric
tile tile tile tile tile
tile tile tile tile tile
Octogonal 'upsilon'
icon icon icon icon icon
icon icon icon icon icon
Herringbone
icon icon icon icon icon
icon icon icon icon icon

Isometric grids use isometric tilesets, which can overlap neighboring tiles. Sprites must move diagonally.
Herringbone grids require two separate tilesets, for horizontal and vertical tiles. They can emulate a hexagonal grid, as each tile is a distorted hexagon.

Hexadecimal (hex)
Counting (and maths) using base 16 requires 16 distint symbols, so '10' to '15' usually denoted as 'a' to 'f'. Useful for labelling the 16 tiles of a 2 order tileset.

Hexadecimal encoding 0-f
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 a b c d e f

Index
A positive integer calculated by summing all tile edge or corner weighted values. For a 2-order Wang tile the weightings are 1, 2, 4, and 8.

Edge tile weightings are allocated clockwise from the top (North) edge. This follows the order North, East, South and West, as well as the order in which CSS (Cascading Style Sheets) applies borders to an image (top, right, bottom and left).
Corner tile weightings are allocated clockwise from the top-right (NorthEast) corner.

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

The edge tile has a yellow North and West edge, so has an index of 8+1=9.
The corner tile has a yellow NorthEast and NorthWest corner, so also has an index of 8+1=9. Corner tiles appear as edge tiles rotated clockwise by 45 degrees.

This method ensures that each tile in a Wang tileset has a unique index number.

The index number is also a useful way to name each tile. Stagecast allows specific character appearances to be referenced by their name.

Also note each allocated weight is twice the previous weight. Therefore, rotating a tile by 90 degrees clockwise will double its index.

Intersection Tile
See Junction Tile.

Inverted Maze
See Negative maze.

Inverted Tile Index
Swopping path and no-path tile edges. This produces a negative maze. Can also swop tile corners in a similar manner producing a negative terrain.
To invert a 2-order Wang tile, swop edge (or corner) '0' and '1' values and recalculate the tile index. You can see below that tile-0 becomes tile-15, tile-1 becomes tile-14 etc.

A complete set of 2-edge 'Path' tiles and their inverts
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
tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile
15 14 13 13 11 10 9 8 7 6 5 4 3 2 1 0

To invert a 3-order Wang tile, swop edge (or corner) '1' and '2' values and recalculate the tile index. This leaves all '0' values untouched, so usually empty ground or 'no path' remains the same. Flow tile paths will swop direction.

Island
An unconnected detatched maze wall, surrounded by a loop or noose.

Junction Tile (Intersection or Node)
A tile where 3 or more paths meet. Can be a Fork, Cross, but not a Pass-over or Pass-under tile. A path following sprite must choose which tile exit path to follow. See wandering and solver sprites. tile or tile

Knot Maze (Circuit maze)
Depicting different kinds of knots as tiled paths in order to simplify and explore complex mathematical structures. For instance, here are all possible 3x3 knot structures, not including rotations. These knots are a form of Circuit maze.

Knots 3x3
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 tile tile
tile tile tile
tile tile tile
Labyrinth Maze (Unicursal or Finger maze)
A maze without any junctions, (fork or cross), so one long path is traversed from start to finish. If start and finish are linked then it is a Circuit maze, also a kind of Knot maze. Uses a reduced tileset. Opposite to a crystal maze.
Labyrinth Maze
labyrinth

Layered maze (or terrain)
A maze which has several layers, one above the other. Upper layer tiles need to be transparent, and possibly sparse. An agent can graphically link both mazes with interconnecting steps or trap-doors to allow sprites to move between mazes on different layers. Can also layer terrain patches. Also see 'twin maze'.

Layered tile
A tile which is created from several transparent layers to create more complex designs. For instance, the following four tiles are given a binary weighting of 1, 2, 4, and 8.

Possible tile layers
tile tile tile tile
1 2 4 8
result
tile
7

If the first three tiles are placed on top of each other, then the resultant sum is (1+2+4)=7, and so they can be replaced with a single path tile of index 7. This is how some of the Stagecast mazes are built. Note that the completed tile may or may not be transparent.
Tilesets of order 4 (requiring 256 tiles) may be more easily created from two transparent tilesets of order 2 (requiring only 32 tiles).

Line Follower
A small table-top robot that is programmed to solve a simple line maze. Hobbyists hold competitions to build the fastest, most efficient maze solver robots. In some mazes, all crossroads are seen as Pass-overs.

 

Tileset
tile tile tile tile tile tile tile

Plus rotations for each tile.

Simple Maze
tile tile tile tile
tile tile tile tile
tile tile tile tile
Line following robot
robot

Loop
A path that joins back on itself forming a single circuit surrounding an island. A maze containing a looped path cannot be perfect. The loop may pass under or over other paths. If it has no branches, it may be part of a multi loop maze. An isolated loop will cause a path following sprite to circle forever in an infinite loop.

Maze
A network of interconnected paths or passages, seperated by impassable walls, that can be traversed by a wandering sprite.
A maze can also be created using a layout of terrain tiles, forming traverseable and impassable areas.
Some mazes have defined start and finish tiles. Most mazes on this site do not. You can always add your own. If the maze is perfect, any two path tiles will do.
Comes from the Old English word to confuse or confound.

Modulo
A mathematical term for 'clock' arithmetic. Also used in compass bearings. So turning 90° clockwise from a bearing of 320° gives 50°, as 320+90=50 (mod 360).

Monotype (typewriter font)
A font where all letters and numbers have the same width. Used by Teletext and Ceefax tiled text computer screens. eg tile tile

Multiple loop maze
A maze which consists of only single looped paths. The paths can pass under or over each other, unless the maze is flat.

Multiple path maze
A maze where two or more separate paths coexist on the same grid. Paths can be overlaid on separate layers (see 'Layered maze'), or woven together on a regular layout (see 'Weave'), as Twin Path mazes. If path fusing is not allowed then multiple mazes can be built concurrently by choosing multiple initial start points.

Negative maze
Swopping path and no-path (wall) tile edges will produce a negative maze. Can also swop tile corners in a similar manner producing a negative terrain. Achieved by inverting all tile index numbers.

Noose
A path that joins back on itself creating a simple island. The path has no extra junctions. Often formed when dead-ends are fused with a neighboring path. If the noose path passes under or over other paths, or the island contains other paths, then the noose is a loop path. A maze containing a noose or loop cannot be perfect.

Order
The number of different edges (or corners) in a Wang tileset. So a 2-edge or 2-corner tileset has an order of 2 and contains 16 (4^order) tiles. An order 3 tileset contains 4^order = 81 tiles.

Origin
The point on a graph or array with a (0,0) x-y co-ordinate. Graphs and Stagecast have their origin at the lower left-hand corner. Values of x and y increase as you move to the right and up. Note however that Javascript and web pages have their origin at the upper left, because web pages are rendered as you normally read. Values of y increase as you go down the page.

Orthogonal maze
A maze layout of perpendicular passages. The natural solution for tiles on a square grid. Also see 'Zeta maze'.

Overlap tiles
Tiles taller than 32 pixels, so that they overlap tiles in the row above, creating an added stacked perspective effect. Best to fill grid row by row from the top left, as Javascript does, so that tall tiles overlay previouly placed tiles correctly. Overlap tiles are difficult to remove and replace as Stagecast adds new tiles 'on top' of all other tiles. Overlap tiles can also be wider than 32 pixels (usually isometric perspective). Again, care must be taken to add tiles so that they overlap correctly.

 

Wang Tiles | cr31.co.uk | 2018