Two-block substitutions and morphic words
Michel Dekking, Mike Keane
TL;DR
This paper investigates two-block substitutions and their fixed points, revealing that some are morphic sequences while others, like the Kolakoski sequence, exhibit greater complexity, exemplified by the Thue-Morse sequence in base 3/2.
Contribution
It characterizes the structure of fixed points of two-block substitutions, distinguishing between morphic sequences and more complex examples like the Kolakoski sequence.
Findings
Some fixed points are morphic sequences.
The Kolakoski sequence is intrinsically complex.
Thue-Morse sequence in base 3/2 is analyzed.
Abstract
We consider in general two-block substitutions and their fixed points. We prove that some of them have a simple structure: their fixed points are morphic sequences. Others are intrinsically more complex, such as the Kolakoski sequence. We prove this for the Thue-Morse sequence in base 3/2.
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Taxonomy
Topicssemigroups and automata theory · Authorship Attribution and Profiling · Historical Linguistics and Language Studies