A229217 If 1 and 2 represent the 2D vectors (1,0) and (0,1) and -1 and -2 are the negation of these vectors, then this sequence represents the Koch curve.

1, 2, 1, -2, 1, 2, -1, 2, 1, 2, 1, 2, 1, -2, 1, -2, 1, -2, -1, -2, 1, 2, 1, -2, 1, 2, -1, 2, 1, 2, -1, -2, -1, 2, -1, 2, -1, 2, 1, 2, 1, 2, 1, -2, 1, 2, -1, 2, 1, 2, 1, 2, 1, -2, 1, 2, -1, 2, 1, 2, 1, 2, 1, -2, 1, -2, 1, -2, -1, -2, 1, 2, 1, -2, 1, -2, 1, -2, -1, -2, 1, 2, 1, -2, 1, -2, 1, -2, -1, -2, -1, -2, -1, 2, -1, -2, 1, -2, -1, -2, 1, 2, 1, -2, 1, 2, -1

Offset

1,2

Comments

The sequence is generated by the rewriting rules:

P(1) = 1,2,1,-2,1;

P(2) = 2,-1,2,1,2 and

P(-1) = -1,-2,-1,2,-1;

P(-2) = -2,1,-2,-1,-2, so P(-x)=-P(x).

The start is 1.

Links

Table of n, a(n) for n=1..107.

Arie Bos, Index notation of grid graphs, arXiv:1210.7123 [cs.CG], 2012.

Wikipedia, Koch curve

Index entries for sequences that are fixed points of mappings

Example

Start with 1, you get
in the first step 1,2,1,-2,1, and
in the 2nd step 1,2,1,-2,1,2,-1,2,1,2,1,2,1,-2,1,-2,1,-2,-1,-2,1,2,1,-2,1.
With each step the length increases by a factor 5.

Crossrefs

Coordinates: A332249, A332250.

Cf. A229216, A166253.

Sequence in context: A000034 A040001 A134451 * A347526 A167965 A270370

Adjacent sequences: A229214 A229215 A229216 * A229218 A229219 A229220

Keyword

sign

Author

Arie Bos, Sep 25 2013

Status

approved