A Tale of Two Tilings
Sharon C. Glotzer, Aaron S. Keys
TL;DR
This paper explores the mathematical and geometric relationships between crystals and quasicrystals, highlighting historical and modern tiling patterns from Fibonacci sequences to Kepler's work.
Contribution
It introduces new insights into the connection between periodic and aperiodic tilings, bridging historical and contemporary mathematical tiling theories.
Findings
Fibonacci sequences relate to quasicrystal structures
Kepler's tiling patterns inform modern quasicrystal research
Historical tiles of Archimedes connect to current geometric models
Abstract
What do you get when you cross a crystal with a quasicrystal? The surprising answer stretches from Fibonacci to Kepler, who nearly 400 years ago showed how the ancient tiles of Archimedes form periodic patterns.
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