Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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