more complex Hadamard-Sylvester Matric Self -Similar constructions

• To: mathgroup at smc.vnet.net
• Subject: [mg68644] more complex Hadamard-Sylvester Matric Self -Similar constructions
• From: Roger Bagula <rlbagula at sbcglobal.net>
• Date: Mon, 14 Aug 2006 06:44:20 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```I had this idea last night as the next Pisot level of complexity
for these self-similar matrices.
The Padovan/ Minmal Pisot matrix in the substitution-repartition
procedure gives a
dust like fractal at second level 81by81 .
I haven't attempted the third level 81^2by81^2 construction.

Clear[t, M, a, v, a0, aa]
t[n_, m_] := {{0, 1, 0}, {0, 0, 1}, {1, 1, 0}}[[n, m]]
a0 = Table[t[n, m]*t[i, j], {n, 1, 3}, {m, 1, 3}, {i, 1, 3}, {j, 1, 3}];
M = Flatten[Table[{Flatten[Table[a0[[
n, m]][[1, i]], {n,
1, 3}, {i, 1, 3}]], Flatten[Table[a0[[n, m]][[2,
i]], {n, 1, 3}, {i, 1, 3}]], Flatten[Table[a0[[n, m]][[3,
i]], {n, 1, 3}, {i, 1, 3}]]}, {m, 1, 3}], 1]
MatrixForm[M]
ListDensityPlot[M, Mesh -> False]
aa = Table[M[[n, m]]*M[[i, j]], {n, 1, 9 }, {m, 1, 9}, {i, 1, 9}, {j, 1,
9}];
M2 = Flatten[Table[{Flatten[Table[aa[[
n, m]][[1, i]], {n,
1, 9}, {i, 1, 9}]], Flatten[Table[aa[[n, m]][[2,
i]], {n, 1, 9}, {i, 1, 9}]], Flatten[Table[aa[[
n, m]][[3, i]], {n,
1, 9}, {i, 1, 9}]], Flatten[Table[aa[[
n, m]][[4, i]], {n,
1, 9}, {i, 1, 9}]], Flatten[Table[aa[[
n, m]][[5, i]], {n,
1, 9}, {i, 1, 9}]], Flatten[Table[aa[[n, m]][[6,
i]], {n, 1, 9}, {i, 1, 9}]], Flatten[Table[aa[[
n, m]][[7, i]], {n,
1, 9}, {i, 1, 9}]], Flatten[Table[aa[[
n, m]][[8, i]], {n,
1, 9}, {i, 1, 9}]], Flatten[Table[aa[[
n, m]][[9, i]], {n,
1, 9}, {i, 1, 9}]]}, {m, 1, 9}], 1];
ListDensityPlot[M2, Mesh -> False]

```

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