A105584 Fixed point of the morphism 1 -> 34, 2 -> 32, 3 -> 12, 4 -> 14, starting from a(0) = 1.

1, 2, 1, 4, 1, 2, 3, 2, 1, 2, 1, 4, 3, 4, 1, 4, 1, 2, 1, 4, 1, 2, 3, 2, 3, 4, 3, 2, 1, 2, 3, 2, 1, 2, 1, 4, 1, 2, 3, 2, 1, 2, 1, 4, 3, 4, 1, 4, 3, 4, 3, 2, 3, 4, 1, 4, 1, 2, 1, 4, 3, 4, 1, 4, 1, 2, 1, 4, 1, 2, 3, 2, 1, 2, 1, 4, 3, 4, 1, 4, 1, 2, 1, 4, 1, 2, 3, 2, 3, 4, 3, 2, 1, 2, 3, 2, 3, 4, 3, 2, 3, 4, 1, 4, 3

Offset

0,2

Comments

A triangle space fill substitution: characteristic polynomial:x^4-2*x^3-2*x^2-4*x.

This triangle set was obtained by shifting the Heighway's dragon matrix about: M(Heighways's)={{1, 1, 0, 0}, {0, 1, 1, 0}, {0, 0, 1, 1}, {1, 0, 0, 1}} M(triangle)={{0, 0, 1, 1}, {0, 1, 1, 0}, {1, 1, 0, 0}, {1, 0, 0, 1}} This result is a permutation of the rows of the matrix. I have obtained three triangle sets and two Heighway's sets by experiments like these.

Links

Table of n, a(n) for n=0..104.

F. M. Dekking, Recurrent Sets, Advances in Mathematics, vol. 44, no.1, April 1982, page 96, section 4.11.

Index entries for sequences that are fixed points of mappings

Mathematica

Flatten[ Nest[ Flatten[ # /. {1 -> {3, 4}, 2 -> {3, 2}, 3 -> {1, 2}, 4 -> {1, 4}} &], {1}, 8]] (* Robert G. Wilson v, May 07 2005 *)

Crossrefs

Sequence in context: A323300 A349128 A366450 * A072064 A105498 A179289

Adjacent sequences: A105581 A105582 A105583 * A105585 A105586 A105587

Keyword

nonn

Author

Roger L. Bagula, May 03 2005

Extensions

Edited by Robert G. Wilson v, May 07 2005

Status

approved