Christopher J. Kimmer, Ph.D.

IU Southeast Informatics

Next: Minimal Surface Approximations Up: An Ensemble of Quasiperiodic Previous: Core and Variable Vertices

Conclusions

This three-dimensional ensemble of tilings is of interest because of the myriad ways their ADs obey the gluing constraints along 5-fold and 3-fold directions while the inflation rules used to construct them are varied. This family of constant density tilings contains a core of immutable vertices that form a scaffolding for constructing a tiling by choosing among the possible configurations of variable vertices.

The fractal nature of the ADs for particular choices of inflation rules makes it difficult to fathom an underlying principle that would allow one to construct an AD from scratch, say in a manner akin to the pinwheel theorem[ 37 ], but these tilings are mathematically extremely fertile and worthy of further study. In particular, it is of interest to classify the ADs formed by the inflation rules by their connectedness and to study whether any polyhedral ADs can be constructed for this tiling.

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