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There are no iterated morphisms that define the Arshon sequence and the -sequence
Berstel proved that the Arshon sequence cannot be obtained by iteration of a
morphism. An alternative proof of this fact is given here. The
-sequence was constructed by Evdokimov in order to construct chains of
maximal length in the n-dimensional unit cube. It turns out that the
-sequence has a close connection to the Dragon curve. We prove that the
-sequence can not be defined by iteration of a morphism.Comment: 10 page