%I #9 Oct 01 2016 21:13:01
%S 1,2,3,2,1,2,3,4,5,2,1,2,1,2,3,2,1,2,3,4,5,4,3,4,5,6,1,2,1,2,1,2,3,2,
%T 1,2,1,2,3,2,1,2,3,4,5,2,1,2,1,2,3,2,1,2,3,4,5,4,3,4,5,6,1,4,3,4,3,4,
%U 5,4,3,4,5,6,1,6,5,6,1,2,3,2,1,2,1,2,3,2,1,2,1,2,3,2,1,2,3,4,5,2,1,2,1,2,3
%N Fixed point of the morphism 1 -> 123, 2 -> 212, 3 -> 345, 4 -> 434, 5 -> 561, 6 -> 656, starting from a(0) = 1.
%C Six-symbol substitution modeled on a hexagon loop.
%C Characteristic Polynomial: x^6-9*x^5+30*x^4-46*x^3+36*x^2-21*x+9=0 L-system shown as: bb = a /. 1 -> {1, 0} /. 2 -> {0.5, 0.8660254037844386} /. 3 -> {-0.5,0.8660254037844386} /. 4 -> {-1, 0} /. 5 -> {-0.5, -0.8660254037844386} /. 6 -> {0.5, -0.8660254037844386}; ListPlot[FoldList[Plus, {0, 0}, bb], PlotRange -> All, PlotJoined -> True, Axes -> False];
%H <a href="/index/Fi#FIXEDPOINTS">Index entries for sequences that are fixed points of mappings</a>
%t Flatten[ Nest[ Flatten[ # /. {1 -> {1, 2, 3}, 2 -> {2, 1, 2}, 3 -> {3, 4, 5}, 4 -> {4, 3, 4}, 5 -> {5, 6, 1}, 6 -> {6, 5, 6}} &], {1}, 5]] (* _Robert G. Wilson v_, May 07 2005 *)
%K nonn
%O 0,2
%A _Roger L. Bagula_, Apr 28 2005
%E Edited and corrected by _Robert G. Wilson v_, May 07 2005
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