A105500 - OEIS

A105500

Trajectory of 1 under the morphism 1->{1,2}, 2->{3,2}, 3->{3,4}, 4->{1,4}.

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

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OFFSET

0,2

COMMENTS

Harter-Heighway dragon when interpreting 1, 2, 3, and 4 respectively as unit edge to right, up, left, and down. - Joerg Arndt, Jun 03 2021

The characteristic polynomial of the transition matrix is x^4-4*x^3+6*x^2-4*x = x*(x-2)*(x^2 - 2*x + 2).

LINKS

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

Joerg Arndt, Iterate six of the Harter-Heighway dragon

F. M. Dekking, Recurrent sets, Advances in Mathematics, vol. 44, no. 1 (1982), 78-104; page 89, section 4.5.

Index entries for sequences that are fixed points of mappings

FORMULA