A symmetry group of a Thue-Morse quasicrystal
Jean-Pierre Gazeau, Jacek Miekisz
TL;DR
This paper introduces a method for coding self-similar structures and constructs a symmetry group for a one-dimensional Thue-Morse quasicrystal, revealing its nonperiodic ground state symmetries.
Contribution
It presents a novel approach to coding self-similar structures and explicitly constructs the symmetry group of a Thue-Morse quasicrystal.
Findings
Constructed a symmetry group for the Thue-Morse quasicrystal
Demonstrated the nonperiodic ground state symmetry properties
Developed a coding method for self-similar structures
Abstract
We present a method of coding general self-similar structures. In particular, we construct a symmetry group of a one-dimensional Thue-Morse quasicrystal, i.e., of a nonperiodic ground state of a certain translation-invariant, exponentially decaying interaction.
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