Quartic pinwheel

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Info

One of the rare examples of a tiling where the prototiles occur in infinitely many orientations. Apart from the pinwheel tiling and its generalizations [Sad98] there are only a few examples known which show infinite rotations.

The inflation factor of this one is a complex algebraic PV number of degree four. As the scaling and the rotations for the tiles are all given by algebraic units, every vertex of the tiling lies within a finitely generated Z-module.

Substitution Rule

Rule Quartic pinwheel

Patch

Patch Quartic pinwheel

References

[Sad98]
Sadun, L.
Some generalizations of the pinwheel tiling
Discrete Comput. Geom. 1998, 20,1, pp. 79–110, 1626703