Evaluate
WOLFRAM|DEMONSTRATIONS PROJECT

Domino Substitution Tilings

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Domino Substitution Rule
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depth
1
2
3
4
5
6
style
Color
BW
deterministic substitution?
regenerate substitution
3 3 (23) .

Tiling substitution rules specify how to fill and then subdivide a tile into copies of itself. Iterating these rules, we can form larger and larger "supertiles" and ultimately define substitution tilings, which are divisions of the plane into infinite hierarchies of supertiles. The configuration shown here, of four dominoes (2×1 rectangles, also known as dimers) forming a larger one, does not give a well-defined substitution rule: in order to iterate such a rule, we must further specify how the smaller dominoes are oriented in the large one, possibly with several choices.