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

### Keywords

• Arshon sequence
• morphism
• dragon curve