Affiliation:
1. Department of Electrical Engineering, Katholieke Universiteit Leuven, Kasteelpark Arenberg 10, B3001 Leuven, Belgium
Abstract
This paper considers higher-dimensional generalizations of the classical one-dimensional two-automatic Thue–Morse sequence on ℕ. This is done by taking the same automaton-structure as in the one-dimensional case, but using binary number systems in ℤminstead of in ℕ. It is shown that the corresponding ±1-valued Thue–Morse sequences are either periodic or have a singular continuous spectrum, dependent on the binary number system. Specific results are given for dimensions up to six, with extensive illustrations for the one-, two- and three-dimensional case.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Modeling and Simulation,Engineering (miscellaneous)
Cited by
10 articles.
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