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Wang tiles (or Wang dominoes), first proposed by mathematician, logician, and philosopher Hao Wang in 1961, is a class of formal systems. They are modeled visually by square tiles with a color on each side. A set of such tiles is selected, and copies of the tiles are arranged side by side with matching colors, without rotating or reflecting them.
The matching rules distinguish sides of the tiles, and entail that tiles may be juxtaposed in certain particular ways but not in others. Two ways to describe these matching rules are shown in the image on the right. In one form, tiles must be assembled such that the curves on the faces match in color and position across an edge.
Sometimes these geometric matching condition is enough to force a tile set to be aperiodic, this is e.g. the case for Robinsion's tilings discussed below. Sometimes additional matching rules are required to hold. These usually involve colors or markings that have to match over several tiles across boundaries.
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Qwirkle comes with 108 wooden tiles. Each tile is painted with one of six shapes (clover, four-point star, eight-point star, square, circle and diamond) in one of six colors (red, orange, yellow, green, blue and purple); there are three examples of each of the 36 tile color and shape combinations. [1]
A partially completed Eternity II edge-matching puzzle. An edge-matching puzzle is a type of tiling puzzle involving tiling an area with (typically regular) polygons whose edges are distinguished with colours or patterns, in such a way that the edges of adjacent tiles match.
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