There are no iterated morphisms that define the Arshon sequence and the sigma-sequence

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Abstract

Berstel proved that the Arshon sequence cannot be obtained by iteration of a morphism. An alternative proof of this fact is given here. The $\sigma$-sequence was constructed by Evdokimov in order to construct chains of maximal length in the n-dimensional unit cube. It turns out that the $\sigma$-sequence has a close connection to the Dragon curve. We prove that the $\sigma$-sequence can not be defined by iteration of a morphism.
LanguageEnglish
Pages43-50
Number of pages8
JournalJournal of Automata, Languages and Combinatorics
Volume8
Issue number1
Publication statusPublished - 2003

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Morphisms
Morphism
Dragon curve
Iteration
Unit cube
n-dimensional
Alternatives

Keywords

  • Arshon sequence
  • morphism
  • dragon curve

Cite this

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abstract = "Berstel proved that the Arshon sequence cannot be obtained by iteration of a morphism. An alternative proof of this fact is given here. The $\sigma$-sequence was constructed by Evdokimov in order to construct chains of maximal length in the n-dimensional unit cube. It turns out that the $\sigma$-sequence has a close connection to the Dragon curve. We prove that the $\sigma$-sequence can not be defined by iteration of a morphism.",
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AB - Berstel proved that the Arshon sequence cannot be obtained by iteration of a morphism. An alternative proof of this fact is given here. The $\sigma$-sequence was constructed by Evdokimov in order to construct chains of maximal length in the n-dimensional unit cube. It turns out that the $\sigma$-sequence has a close connection to the Dragon curve. We prove that the $\sigma$-sequence can not be defined by iteration of a morphism.

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KW - dragon curve

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