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

Author

Arie Bos, Sep 25 2013

Keywords

• sign

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.

Examples

			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.
		

Links

• 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

Crossrefs

Coordinates: A332249, A332250.

Cf. A229216, A166253.