A073058 Define s(1)={1,2}, s(2)={1,3} and s(3)={1}. For a finite sequence A={a_1, ..., a_n}, with elements in {1,2,3}, define t(A) to be the concatenation of A, s(a_1), s(a_2), ... and s(a_n). Start with the sequence {1,2,3} and repeatedly apply t; limiting sequence is shown.

1, 2, 3, 1, 2, 1, 3, 1, 1, 2, 1, 3, 1, 1, 2, 1, 3, 1, 2, 1, 1, 2, 1, 2, 1, 3, 1, 1, 2, 1, 3, 1, 2, 1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 3, 1, 1, 2, 1, 3, 1, 2, 1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 1, 2, 1, 2, 1, 3, 1, 2, 1, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1

Offset: 1

Author

Roger L. Bagula, Aug 16 2002

Keywords

• nonn

Comments

A fractal sequence related to a sequence of Rauzy.

Links

• P. Arnoux and E. Harriss, What is a Rauzy Fractal?, Notices Amer. Math. Soc., 61 (No. 7, 2014), 768-770, also p. 704 and front cover.
• Vincent Canterini and Anne Siegel, Geometric Representations of Substitutions of Pisot Type, Trans. Amer. Math. Soc. 353 (2001), 5121-5144.

Crossrefs

Cf. A092782, A103684, A105083, A245553, A245554.

Programs

Mathematica

Nest[ Flatten[ Join[#, # /. {1 -> {1, 2}, 2 -> {1, 3}, 3 -> {1}}]] &, {1, 2, 3},
4] (* Robert G. Wilson v, Jan 01 2017 *)