Ebook: Automatic Sequences (De Gruyter Expositions in Mathematics, 36)

Automatic sequences are sequences which are produced by a finite automaton. Although they are not random, they may look as being random. They are complicated, in the sense of not being ultimately periodic. They may also look rather complicated, in the sense that it may not be easy to name the rule by which the sequence is generated; however, there exists a rule which generates the sequence. This text deals with different aspects of automatic sequences, in particular: a general introduction to automatic sequences; the basic (combinatorial) properties of automatic sequences; the algebraic approach to automatic sequences; and geometric objects related to automatic sequences.