A176416 Fixed point of morphism 0->0PPMM00, P->0PPMM0P, M=0PPMM0M (where P=+1, M=-1).

0, 1, 1, -1, -1, 0, 0, 0, 1, 1, -1, -1, 0, 1, 0, 1, 1, -1, -1, 0, 1, 0, 1, 1, -1, -1, 0, -1, 0, 1, 1, -1, -1, 0, -1, 0, 1, 1, -1, -1, 0, 0, 0, 1, 1, -1, -1, 0, 0, 0, 1, 1, -1, -1, 0, 0, 0, 1, 1, -1, -1, 0, 1, 0, 1, 1, -1, -1, 0, 1, 0, 1, 1, -1, -1, 0, -1, 0, 1

Offset: 0

Author

Joerg Arndt, Apr 17 2010

Keywords

• sign

Comments

Turns by 120 degrees of a dragon curve (see fxtbook link below).

Also fixed point of morphism F->F0FPFPFMFMF0F, 0->0, P->P, M->M (after deleting all F).

Let d(n) be the lowest nonzero digit in the radix-7 expansion of (n+1), then if d(n)==[1,2,3,4,5,6] ==> a(n):=[0,+1,+1,-1,-1,0].

This is a 7-automatic sequence. - Joerg Arndt, Nov 09 2023

Links

• Paolo Xausa, Table of n, a(n) for n = 0..10000
• Joerg Arndt, Matters Computational (The Fxtbook), section 1.31.5 "Dragon curves based on radix-R counting", pp.95-101; image on p.98

Crossrefs

Cf. A080846 (with terdragon curve), A014577 (with Heighway dragon), A175337 (with R5-dragon), and A176405 (with R7-dragon).

Programs

Mathematica

First[SubstitutionSystem[{t_ :> {0, 1, 1, -1, -1, 0, t}}, {0}, {3}]] (* Paolo Xausa, Jun 04 2025 *)