Colourings of aperiodic tilings
Molly Evans, Dylan Gawlak, Christopher Ramsey, Nicolae Strungaru, and, Ryan Trang
TL;DR
This paper presents explicit optimal colourings for various aperiodic tilings, including the chair, Ammann-Beenker, and pinwheel tilings, enhancing understanding of their combinatorial properties.
Contribution
It provides the first explicit optimal vertex, edge, and face colourings for several well-known aperiodic tilings, advancing tiling theory and applications.
Findings
Explicit optimal colourings for chair tiling
Explicit optimal colourings for Ammann-Beenker tiling
Explicit optimal colourings for pinwheel tiling
Abstract
We find explicit optimal vertex, edge and face coulourings for the chair tiling, the Ammann--Beenker tiling, the rational pinwheel tiling and the pinwheel tiling.
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Taxonomy
TopicsQuasicrystal Structures and Properties · Cellular Automata and Applications