Lunnon, W. F.; Pleasants, P. A. B. Characterization of two-distance sequences. (English) Zbl 0759.11005 J. Aust. Math. Soc., Ser. A 53, No. 2, 198-218 (1992). If the reader has already heard at least one of the expressions: two- distance sequences, linear sequence, characteristic sequences, Beatty sequences, mechanical sequences, Fibonacci sequences, cutting sequences, Markoff spectrum, Sturmian trajectories, chain-codes, quasicrystals, species…or if he or she plays (two-dimensional) billiard, he will definitely enjoy the paper under review, where all these notions are described, studied and compared. The subject is very rich but the length of the paper is reasonable, and the reader will be delighted by this “promenade”.The bibliography is wisely reduced to 22 titles [one of which, K. B. Stolarsky, Can. Math. Bull. 19, 473-482 (1976; Zbl 0359.10028), itself contains an impressive bibliography]. Finally the curious reader might try to follow the attempts of the authors towards a classification of \(f\)-distance sequences for \(f>2\). Reviewer: J.-P.Allouche (Bordeaux) Cited in 1 ReviewCited in 14 Documents MSC: 11B99 Sequences and sets 05B99 Designs and configurations 68R05 Combinatorics in computer science Keywords:minimal word; formal languages; two-symbol sequences; symbolic dynamics; digitized straight lines; Sturmian sequences; Beatty sequences; Fibonacci sequences; chain-codes; quasicrystals Citations:Zbl 0359.10028 PDFBibTeX XMLCite \textit{W. F. Lunnon} and \textit{P. A. B. Pleasants}, J. Aust. Math. Soc., Ser. A 53, No. 2, 198--218 (1992; Zbl 0759.11005)