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

Research output: Contribution to journalArticle

### 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.
Language English 43-50 8 Journal of Automata, Languages and Combinatorics 8 1 Published - 2003

Morphisms
Morphism
Dragon curve
Iteration
Unit cube
n-dimensional
Alternatives

### Keywords

• Arshon sequence
• morphism
• dragon curve

### Cite this

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title = "There are no iterated morphisms that define the Arshon sequence and the sigma-sequence",
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.",
keywords = "Arshon sequence, morphism, dragon curve",
author = "Sergey Kitaev",
year = "2003",
language = "English",
volume = "8",
pages = "43--50",
journal = "Journal of Automata, Languages and Combinatorics",
issn = "1430-189X",
number = "1",

}

In: Journal of Automata, Languages and Combinatorics, Vol. 8, No. 1, 2003, p. 43-50.

Research output: Contribution to journalArticle

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T1 - There are no iterated morphisms that define the Arshon sequence and the sigma-sequence

AU - Kitaev, Sergey

PY - 2003

Y1 - 2003

N2 - 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.

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.

KW - Arshon sequence

KW - morphism

KW - dragon curve

UR - https://personal.cis.strath.ac.uk/sergey.kitaev/index_files/Papers/Arshon.pdf

UR - http://theo.cs.uni-magdeburg.de/cgi-bin/theo/j_bibsearch/jalc/search/j00_i.html

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SN - 1430-189X

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