Sequences of substitutions and related topics. (Chinese. English summary) Zbl 0694.10006

Wen, Zhiying; Wen, Zhixiong

Adv. Math., Beijing 18, No. 3, 270-293 (1989).

Summary: During the recent years a great deal of progress has been made for the study of sequences of substitutions, and more and more applications and relations to other fields are discovered. This paper gives a survey of this field. It contains four parts, preliminaries and the fundamental theorem (§ 1); three typical 2-automatic sequences and their properties (§ 2); applications and relations to other fields (§ 3); some generalized sequences of substitutions (§ 4). A detailed list of 122 references is given at the end.

MSC:

11A63	Radix representation; digital problems
68Q42	Grammars and rewriting systems
11B99	Sequences and sets
11-02	Research exposition (monographs, survey articles) pertaining to number theory

Keywords:

Thue-Morse sequence; Rudin-Shapiro sequence; fractals; paperfolding sequence; finite automata; Ising chains; sequences of substitutions; survey; 2-automatic sequences