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%I #4 Mar 30 2012 17:34:15
%S 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,
%T 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,
%U 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
%N Triangular three level substitution for chair tiling.
%C 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}.
%D Matching Rules and Substitution Tilings, Annals of Mathematics, 147 (1998), 181-223 by Chaim Goodman -Strauss (http://comp.uark.edu/~strauss/papers/index.html)
%F The substitution was derived by hand, one at a time.
%t 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}]
%K nonn
%O 0,3
%A _Roger L. Bagula_, May 16 2005
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