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A106788
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Triangular three level substitution for chair tiling.
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0
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1, 1, 2, 3, 2, 3, 4, 4, 3, 3, 4, 1, 4, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 2, 4, 1, 3, 3, 4, 1, 4, 1, 2, 2, 4, 1, 3, 4, 3, 4, 1, 1, 2, 2, 3, 3, 4, 1, 4, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 2, 4, 1, 3, 3, 4, 1, 4, 1, 2, 2, 4, 1, 3, 4, 3, 4, 1, 1, 2, 2, 1, 1, 4, 3, 4, 3, 2, 2, 1, 1, 1, 1, 4, 4, 3, 2, 3, 2, 4, 3, 1
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OFFSET
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0,3
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COMMENTS
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TriangularForm: {1, 1, 2, 3, 2, 3, 4, 4}, {3, 3, 4, 1, 4, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 2, 4, 1, 3, 3, 4, 1, 4, 1, 2, 2, 4, 1, 3, 4, 3, 4, 1, 1, 2, 2}, {3, 3, 4, 1, 4, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 2, 4, 1, 3, 3, 4, 1, 4, 1, 2, 2, 4, 1, 3, 4, 3, 4, 1, 1, 2, 2, 1, 1, 4, 3, 4, 3, 2, 2, 1, 1, 1, 1, 4, 4, 3, 2, 3, 2, 4, 3, 1, 1, 4, 3, 4, 3, 2, 2, 4, 3, 1, 4, 1, 4, 3, 3, 2, 2, 3, 3, 4, 1, 4, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 2, 4, 1, 3, 3, 4, 1, 4, 1, 2, 2, 4, 1, 3, 4, 3, 4, 1, 1, 2, 2, 1, 1, 4, 3, 4, 3, 2, 2, 1, 1, 1, 1, 4, 4, 3, 2, 3, 2, 4, 3, 1, 1, 4, 3, 4, 3, 2, 2, 4, 3, 1, 4, 1, 4, 3, 3, 2, 2}.
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REFERENCES
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Matching Rules and Substitution Tilings, Annals of Mathematics, 147 (1998), 181-223 by Chaim Goodman -Strauss (http://comp.uark.edu/~strauss/papers/index.html)
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LINKS
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FORMULA
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The substitution was derived by hand, one at a time.
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MATHEMATICA
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a[1] = {1, 1, 2, 3, 2, 3, 4, 4}; a[2] = {3, 3, 4, 1, 4, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 2, 4, 1, 3, 3, 4, 1, 4, 1, 2, 2, 4, 1, 3, 4, 3, 4, 1, 1, 2, 2}; a[3] = {3, 3, 4, 1, 4, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 2, 4, 1, 3, 3, 4, 1, 4, 1, 2, 2, 4, 1, 3, 4, 3, 4, 1, 1, 2, 2, 1, 1, 4, 3, 4, 3, 2, 2, 1, 1, 1, 1, 4, 4, 3, 2, 3, 2, 4, 3, 1, 1, 4, 3, 4, 3, 2, 2, 4, 3, 1, 4, 1, 4, 3, 3, 2, 2, 3, 3, 4, 1, 4, 1, 2, 2, 3, 3, 3, 3, 4, 4, 1, 2, 1, 2, 4, 1, 3, 3, 4, 1, 4, 1, 2, 2, 4, 1, 3, 4, 3, 4, 1, 1, 2, 2, 1, 1, 4, 3, 4, 3, 2, 2, 1, 1, 1, 1, 4, 4, 3, 2, 3, 2, 4, 3, 1, 1, 4, 3, 4, 3, 2, 2, 4, 3, 1, 4, 1, 4, 3, 3, 2, 2} atable=Table[a[i], {i, 1.3}] MatrixForm[atable] aa = Table[a[i] /. 1 -> {1, 0} /. 2 -> {0, 1} /. 3 -> {-1, 0} /. 4 -> { 0, -1}, {i, 1, 3}] Table[ListPlot[FoldList[Plus, {0, 0}, aa[[i]]], PlotRange -> All, PlotJoined -> True, Axes -> False], {i, 1, 3}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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