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A229217
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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.
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2
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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