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A229216
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If 1, 2, and 3 represent the three 2D vectors (1,0), (0.5,sqrt(3)) and (-0.5,sqrt(3)) and -1, -2 and -3 are the negation of these vectors, then this sequence represents Koch's snowflake.
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1
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1, -3, 2, 1, -3, -2, 1, -3, 2, 1, 3, 2, 1, -3, 2, 1, -3, -2, 1, -3, -2, -1, -3, -2, 1, -3, 2, 1, -3, -2, 1, -3, 2, 1, 3, 2, 1, -3, 2, 1, 3, 2, -1, 3, 2, 1, 3, 2, 1, -3, 2, 1, -3, -2, 1, -3, 2, 1, 3, 2, 1, -3, 2, 1, 3, 2, -1, 3, 2, 1, 3, 2, -1, 3, -2, -1, 3, 2, -1, 3, 2, 1, 3, 2, 1, -3, 2, 1, 3, 2, -1, 3, 2, 1, 3, 2, -1, 3, -2, -1, 3, 2, -1, 3, -2, -1, -3, -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:
P(1) = 1,-3,2,1,
P(2) = 2,1,3,2,
P(3) = 3,2,-1,3,
P(-1) = -1,3,-2,-1,
P(-2) = -2,-1,-3,-2,
P(-3) = -3,-2,1,-3 (we have P(-x)=-P(x)), and 1, 3, -2 is the start.
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LINKS
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EXAMPLE
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Start 1,3,-2,
in the first step 1,-3,2,1,3,2,-1,3,-2,-1,-3,-2 and
in the second step 1, -3, 2, 1, -3, -2, 1, -3, 2, 1, 3, 2, ..., -2, -1, -3, -2.
With each step the length increases by a factor 4.
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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