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]