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Search: id:A106035
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| A106035 |
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Trajectory of 1 under the morphism 1->{1,2,1}, 2->{1}. |
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+0
2
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| 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Silver mean chain substitution sequence: characteristic polynomial = -x^2+2*x+1.
A space-filling lattice is given by: bb = aa /. 1 -> {-0.4142135623730951, 2.414213562373095} /. 2 -> {1,-0.414213562373095`} /. 3 -> 0; ListPlot[FoldList[Plus, {0, 0}, bb], PlotRange -> All, PlotJoined -> False, Axes -> False];
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REFERENCES
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M. Baake and R. V. Moody, "Self-Similar Measures for Quasicrystals", in Directions in Mathematical Quasicrystals (eds. M. Baake and R. V. Moody), CRM Monograph Series, vol. 13, AMS, Providence, RI (2000), pp. 1-42.
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MATHEMATICA
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s[1] = {1, 2, 1}; s[2] = {1}; s[3] = {}; t[a_] := Flatten[s /@ a]; p[0] = {1}; p[1] = t[p[0]]; p[n_] := t[p[n - 1]] aa = p[6]
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CROSSREFS
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Cf. A085301, A106036.
Sequence in context: A105240 A083894 A128257 this_sequence A105141 A103961 A071891
Adjacent sequences: A106032 A106033 A106034 this_sequence A106036 A106037 A106038
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), May 05 2005
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