%I #17 Sep 26 2020 02:39:21
%S 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,
%T -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,
%U 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
%N 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.
%C The sequence is generated by the rewriting rules:
%C P(1) = 1,2,1,-2,1;
%C P(2) = 2,-1,2,1,2 and
%C P(-1) = -1,-2,-1,2,-1;
%C P(-2) = -2,1,-2,-1,-2, so P(-x)=-P(x).
%C The start is 1.
%H Arie Bos, <a href="http://arxiv.org/abs/1210.7123">Index notation of grid graphs</a>, arXiv:1210.7123 [cs.CG], 2012.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Koch_snowflake">Koch curve</a>
%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>
%e Start with 1, you get
%e in the first step 1,2,1,-2,1, and
%e 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.
%e With each step the length increases by a factor 5.
%Y Coordinates: A332249, A332250.
%Y Cf. A229216, A166253.
%K sign
%O 1,2
%A _Arie Bos_, Sep 25 2013