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Search: id:A136640
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| A136640 |
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A limited integer Devil's staircase from a winding number function. |
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+0
1
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| 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 9, 13, 16, 18, 20, 22, 24, 26, 28, 29, 31, 33, 34, 36, 37, 39, 40, 41, 43, 44, 46, 47, 49, 50, 51, 51, 53, 54, 56, 58, 58, 60, 61, 63, 65, 67, 67, 67, 67, 67, 67, 70, 72, 73, 75, 76, 77, 79
(list; graph; listen)
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OFFSET
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1,33
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COMMENT
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Designed to be integer and 200 in length, this function is a limited
representation of a Devil's staircase function; a projection of a set of
rational numbers onto the Integers.
We should honor Per Bak's memory who saw this phase locking as the key
to self-organization.
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REFERENCES
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Per Bak, 1982, "Commensurate phases, incommensurate phases, and the devil's staircase", in: Reports on Progress in Physics, Vol 45, pp.587-629.
Weisstein, Eric W. "Devil's Staircase." http://mathworld.wolfram.com/DevilsStaircase.html
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FORMULA
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a(n)=Floor[1+200*Winding_Number(Omega)]: 0<=omega<=1;in steps of 1/200
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MATHEMATICA
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f[{omega_, t_}]:={omega, t+omega-Sin[2Pi t]/(2Pi)}; WindingNumber[n_, {omega_, t_}]:=(Nest[f, {omega, t}, n][[2]]-t)/n; a=Table[Floor[1+200*WindingNumber[1000, {omega, 0}]], {omega, 0, 1, .005}]
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CROSSREFS
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Adjacent sequences: A136637 A136638 A136639 this_sequence A136641 A136642 A136643
Sequence in context: A135740 A010412 A033662 this_sequence A068949 A010397 A020684
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 01 2008
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