A175337 Fixed point of morphism 0 -> 00110, 1 -> 00111.

0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0

Offset: 0

Author

Joerg Arndt, Apr 15 2010

Keywords

• nonn

Comments

Turns (by 90 degrees) of a dragon curve (called R5-dragon in the fxtbook, see link below) which can be rendered as follows:

[Init] Set n=0 and direction=0.

[Draw] Draw a unit line (in the current direction). Turn left/right if a(n) is zero/nonzero respectively.

[Next] Set n=n+1 and goto (draw).

With counting in radix 5: whether the lowest nonzero digit is >2 (see C++ code).

With morphism F -> F0F0F1F1F, 0 -> 0, 1 -> 1: fixed point with all 'F' omitted.

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.96

Crossrefs

Cf. A080846 (with terdragon curve) and A014577 (with Heighway dragon).

Programs

Mathematica

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