Substitution Tiling with Dense Tile Orientations and 5-fold Rotational Symmetry

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A substitution rule that gives rise to an aperiodic tiling with dense tile orientations and 5-fold rotational symmetry. The substitution factor is $\sqrt{6+\sqrt{5}}$. The tiling has finite local complexity with respect to rigid motions.

Substitution Rule

Rule Substitution Tiling with Dense Tile Orientations and 5-fold Rotational Symmetry

Patch

Patch Substitution Tiling with Dense Tile Orientations and 5-fold Rotational Symmetry download vectorformat Substitution Tiling with Dense Tile Orientations and 5-fold Rotational Symmetry

References

[fre17]
Frettlöh, D and Say-awen, A. L. D. and de las Peñas, M. L. A. N.
Substitution tilings with dense tile orientations and n-fold rotational symmetry.
Indagationes Mathematicae 2017, 28(1), pp. 120-131, arxiv 1602.00518