Aperiodic structures and notions of order and disorder

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Abstract

The fabrication of artificial heterostructures is mainly based on substitution systems. We present simple ways to construct double-sided versions of the Fibonacci, Prouhet-Thue-Morse, paperfolding, period doubling and Golay-Rudin-Shapiro sequences. We also construct a generic instance of the two-dimensional Prouhet-Thue-Morse structure and explore its symbolic complexity. The complexity turns out to be polynomial and hence, the entropy goes to zero.

Original languageEnglish
Pages (from-to)2718-2727
Number of pages10
JournalPhilosophical Magazine
Volume91
Issue number19-21
DOIs
StatePublished - 1 Jul 2011

Keywords

  • 2D Prouhet-Thue-Morse structure
  • double-sided sequences
  • heterostructures
  • symbolic complexity

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