OFFSET
0,1
FORMULA
M=N[a*({{0, 1, 0, 0}, {1, 1, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}/4+{{0, 1, 0, 0}, {0, 0, 1, 0}, {1, 1, 0, 0}, {0, 0, 0, 0}}/2+{{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, 1}}/4)]; A[n_]:=M.A[n-1]; A[0]:={{0, 1, 1, 2}, {1, 1, 2, 3}, {1, 2, 3, 5}, {2, 3, 5, 8}};
MATHEMATICA
(* Fractional Pisot 4 X 4 Markov sequence Bezier {1/2, 1/2}*) Clear[M, A, x] digits=Floor[21*3/4]; a=Sqrt[2]*2/3^(1/4); M=N[a*({{0, 1, 0, 0}, {1, 1, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}}/4+{{0, 1, 0, 0}, {0, 0, 1, 0}, {1, 1, 0, 0}, {0, 0, 0, 0}}/2+{{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 0, 0, 1}}/4)]; Det[M] A[n_]:=M.A[n-1]; A[0]:={{0, 1, 1, 2}, {1, 1, 2, 3}, {1, 2, 3, 5}, {2, 3, 5, 8}}; (* flattened sequence of 4 X 4 matrices made with a Fractional Pisot recurrence*) b=Flatten[Table[M.A[n], {n, 1, digits}]] Floor[Abs[b]] Dimensions[b][[1]] ListPlot[b, PlotJoined->True]
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Sep 08 2004
STATUS
approved