Wang Tiles

 

edge and corner matched tilesets

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Glossary

A*
An algorithm for finding the shortest path between two points (or tiles) in a maze, usually start tile to finish tile, avoiding obstacles or dead-ends. A Maze can have more than one shortest path.

Active sprite
A maze wandering sprite that is able to alter its environment, ie the maze around it. For instance by pushing obstacle blocks (as in Sokoban), creating or removing pathways, or opening closing gates. This will affect the possible path choices for itself and any other wandering sprites. Note it might be possible for sprites to become trapped.

Agent
A Stagecast character that fulfils a specific function and then deletes itself. Agents make it easier to write more complex Stagecast rules as they are independent of specific characters or sims. Example agent functions are:
1/ Jump a character to a random stage location.
2/ Insert a fixed or random time delay (pause).
3/ Combine several 'layered' characters into a single character. See 'Layered Tile'.

Algorithm
A step by step set of rules. For instance to build a perfect maze, or to find the shortest path between two points (A-star).

Alternative
Tiles with the same index value can have different designs.
Tile-15 alternatives affect maze connections, so wandering sprites will need to take notice, but the tiles edge (or corner) matching requirements remains the same.

Alternative tile-15's
tile tile tile tile

Blank (Tile-0) alternatives do not affect maze connections and are usually applied at random to improve the look of a maze.

Alternative tile-0's
tile tile tile tile

Straight (Tile-5/Tile-10) alternatives can also be used.

Tile-5/10's
tile tile

Array
The square grid onto which the Wang tiles are placed. Same as Stagecast 'stage'.

Arrow Maze
See Directed maze.

Bend tile
An edge or corner path tile with a 90 degree turn or curve. tile or tile Also see twin bend tile.

Bias (balance)
Duplicating some of the tiles in a Wang Tileset to alter the balance (or density) of paths in a maze layout. Because tiles are picked at random from the tileset, adding, say, an extra cross-over tile will increase the number of cross over paths in the final layout.
Adding extra blank tiles will make the layout sparse.
Adding extra bend tiles will make paths more twisty.
Adding extra straight tiles will make the layout more tubular.
Adding extra junction tiles will make the layout more tree like.
Adding extra crossover tiles will increase the weave of the layout.

Bifurcation
A maze path that branches (splits into two). See 'Fork Tile'.

Bitwise
A mathematical procedure for adding up binary (or tertiary) numbers to produce a unique index number. For example, a 2-edge tile edges are given 'weightings' of 1, 2, 4, and 8. Every combination of edge then produces a unique index between 0 and 15.
3-edge tiles are weighted 1, 3, 9 and 27.

Blank tile
An empty tile, tile-0. Usually included in a ceramic tileset. tile

Blob tileset
A reduced 2-edge 2-corner tileset containing 47 from a possible 256 tiles. There are a couple of reliable methods of generating the required 47 tiles. See Blob tileset page. The tiles are good for covering carpet (or rug) like areas.

Blob tileset
tile tile tile tile tile tile tile tile tile tile tile tile tile tile tile
0 1 5 7 17 21 23 29 31 85 87 95 119 127 255
  4
16
64
20
80
65
28
112
193
68 84
81
69
92
113
197
116
209
71
124
241
199
  93
117
213
125
245
215
221 253
247
223
 

Tile weightings are allocated clockwise from the top (North) edge as follows:

2-edge 2-corner weightings
NorthWest
=128
North
= 1
NorthEast
= 2
West
= 64
tile East
= 4
SouthWest
= 32
South
= 16
SouthEast
= 8

The Blob 2-order tile has a yellow North, East and West edge, as well as a North-East corner, and so has an index of 1+2+4+64=71.

Block tiles
Tiles that do not need to be edge or corner matched. Can be used to create random path or terrain layouts. floor2

Block maze (Hedge maze)
The maze creation algorithm separates the paths with impassable wall block tiles (or hedges). Walls may also need to be added around the stage border.

Wall blocks joined only at their corners are best avoided. Floor tiles may show wall shadows for 3d effect.

6x4 block and space maze
floor2 floor2 floor2 floor2 floor2 floor2
floor2 floor2 floor2 floor2 floor2 floor2
floor2 floor2 floor2 floor2 floor2 floor2
floor2 floor2 floor2 floor2 floor2 floor2

Border
The stage perimeter. Wang tiles adjoining the stage border can have their edges or corners set to a particular type, or set to the 'opposite' border if the stage wraps.

Braid maze
A maze without dead-end paths. Dead-ends that do form are fused with an adjacent path. Braid mazes cannot be perfect. They are more difficult/interesting to solve than a perfect maze, as you spend a great deal of time simply going around in circles.

Branch Tile
See 'Fork Tile'.

Brigid's Cross
The distinctive 'cross' shape which forms with a 4x4 layout of a Wang 2-corner tileset. The pattern 'wraps' top/bottom and left/right and so can cover any area seamlessly.
There are a total of 32 variations allowing for row/column translations and color swopping.
Patch Tileset
6 14 8 4
1 7 12 5
2 15 11 13
3 3 8 1

Cell
The stage grid consits of a regular array of cells. Each is filled with a single tile. Stagecast grids are always square. It is possible to use tiles that overlap the cell edges and extend into neighboring cells.

Chequer
A square grid where tiles are colored black or white as in a chequer (draughts or chess) board. The top-left tile is defined as white. This can help with some algorithms. For instance, paths can cross like this tile on white squares and like this tile on black squares. See 'Weave'.

Circuit Maze
A Labyrinth or Finger maze which returns to its starting point so creating a single closed circuit (or loop). Pass-under tiles are allowed, so Similar to an F1 Grand Prix racing circuit. Also a form of Knot maze.

Circuit 1
6 6 14 7 4
6 8 1 12 1
1 7 15 1 4
2 15 11 4 6
3 3 8 1 6
Circuit 2
6 14 8 4 4
1 7 12 5 4
2 15 11 13 4
3 3 8 1 4
6 14 8 4 4

Creating a perfect maze using a 2-corner 'border' tileset always produces a circuit maze.

Compact Tileset
See 'Reduced Tileset'.

Compass Directions North, East, South and West
Make sure you know you're compass directions, they are used a lot!!

Compass directions
NorthWest
corner
North
edge
NorthEast
corner
West
edge
tile East
edge
SouthWest
corner
South
edge
SouthEast
corner

Complete Tileset
A tileset that contains all possible tile combinations. For instance a 2-edge Wang tileset contains 2^4 = 16 tiles and a 3-edge contains 3^4 = 81 tiles.

A complete set of 2-edge Wang tiles
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

Connected maze
A maze where every path is reachable from any other path. Can include loops, unless it is simply connected as a 'Perfect maze'.

Connectivity
A measure of how easy it is to move between any two points in a maze. Too low, and many places are unreachable. Too high, and all places are easily reachable, so the maze may not be very interesting to traverse or solve. Best value around 50% (??).
Maze connectivity can be altered by swopping between different tile-15 variations. tile tile tile and dead end fusing. See braid maze.

Corner tile
A set of Wang tiles that are matched by their corners. tile Also see 'Edge tile'.

Cross-fuse
Allowing two adjacent paths to join together. Usually randomly applied to paths after a maze is completed, in order to increase connectivity. Also see 'Dead-end Fuse'.

Adjacent paths
tile tile tile
tile tile tile
Added fuse
tile tile tile
tile tile tile
Adjacent paths
tile tile tile
tile tile tile
Added fuse
tile tile tile
tile tile tile

Crossover
An intersection of two paths that do not join. Sprites cannot turn onto a perpendicular path. tile See 'Pass-over' and 'Pass-under'.

Cross tile
A 'four way' tile where four paths join. tile or tile Also see 'Pass-thru'. Wandering sprites must choose a random direction to correctly exit (step off) the tile.

Crystal maze
A maze with junctions but no bends. So uses a reduced tileset. Opposite to a labyrinth or finger maze.

Cylindrical / Cylinder
A stage which wraps top/bottom or left/right only. If it wraps both, then it is a toroidal.

Dead-end (nub or stub)
A cul-de-sac path. A path following sprite must turn round and go back. tile

Dead-end fuse (remove or cull)
Allowing a dead end to bond (fuse) with a neighboring path. This removes the dead-end and often forms a noose. The maze is no longer 'perfect'. Also see Cross-fuse.

Trapped
tile tile tile
tile tile tile
tile tile tile
Fuse forward
tile tile tile
tile tile tile
tile tile tile
Fuse left
tile tile tile
tile tile tile
tile tile tile
Fuse right
tile tile tile
tile tile tile
tile tile tile

Directed Maze (arrow maze)
A maze where paths are 'one way' and must be traversed in the correct direction. Usually indicated by an arrow. Or a step where path following sprites can only step down but not up. tiletile It is possible that sprites in a directed maze can become trapped in an infinite loop. Also see source and sink tiles. See Directed Mazes page.

Edge tile
A set of Wang tiles that are matched by their edges.tile Also see 'Corner tile'.

Exits
A maze tile will have a number of allowable exits, usually contained in a list. Sprites can read this list and know which way to turn and move off (exit) the tile. Using the list means sprites do not have to check all adjacent tiles which keeps rules simple. For instance, this path tile contains the list 'north, east, south'. tile

Flat maze
A maze which has no weaving of under-pass or over-pass path tiles.

Finish tile (end)
A tile where sprites complete the maze. A path from Start to Finish tile shows the maze solution. Not all mazes have start and finish tiles. Some are simply wandered randomly.

Flip (reflection)
Turning a tile design over, horizontally or vertically.
So tile-7 tile becomes tile-13 tile when flipped or reflected horizontally. Wang tiles cannot be reflected (or rotated). However, useful for when producing tiles in an image editing application such as Photoshop. Simply rotate and reflect the tile as necessary and re-save with appropiate name.

Horizontal and vertical tile flips
  Index  0  1  2  3  4  5  6  7  8  9 10 11 12 13 14 15
Edge
Tiles
Flip Horiz - - 8 9 - - 12 13 2 3 - - 6 7 - -
Flip Vert - 4 - 6 1 - 3 - - 12 - 14 9 - 11 -
Corner
Tiles
Flip Horiz - 8 4 12 2 10 - 14 1 - 5 13 3 11 7 -
Flip Vert - 2 1 - 8 10 9 11 4 6 5 7 - 14 13 -

Font Set
A set of tile designs packaged as a monotype font. When installed on a computer, typed characters appear as maze tiles. eg tile tile

Fork Tile
A 'three way' or T-junction path tile. tile or tile Wandering sprites must choose a random direction to correctly exit (step off) the tile.

Fossilised
A character (tile) with no attached rules, so needs no Stagecast processing time. Other characters can react to it, but it does not react to anything else.

Fractal maze
A maze which contains smaller self-similar copies of itself.

Fuse
See 'Dead-end fuse'.

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.

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.

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 | 2017