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MathGroup Archive 2009

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Hadamard von Koch

  • To: mathgroup at smc.vnet.net
  • Subject: [mg99142] Hadamard von Koch
  • From: Roger Bagula <rlbagula at sbcglobal.net>
  • Date: Tue, 28 Apr 2009 04:45:53 -0400 (EDT)

Hadamard von Koch:
http://www.geocities.com/rlbagulatftn/hadamard_vonkoch.gif
I turned my Hadamard matrix self-similarity type programming
to making other fractals this morning.
This one gives an von Koch like internal  hole.
Mathematica:
Clear[HadamardMatrix];

MatrixJoinH[A_, B_] := Transpose[Join[Transpose[A], Transpose[B]]];

KroneckerProduct[M_, N_] := Module[{M1, N1, LM, LN, N2},

M1 = M;

N1 = N;

LM = Length[M1];

LN = Length[N1];

Do[M1[[i, j]] = M1[[i, j]]N1, {i, 1, LM}, {j, 1, LM}];

Do[M1[[i, 1]] = MatrixJoinH[M1[[i, 1]], M1[[i, j]]], {j, 2, LM}, {i, 1, 
LM}];

N2 = {};

Do[AppendTo[N2, M1[[i, 1]]], {i, 1, LM}];

N2 = Flatten[N2];

Partition[N2, LM*LN, LM*LN]]

HadamardMatrix[2] := {{1, 1}, {1, 0}};
HadamardMatrix[3] := {{1, 1, 0}, {1, 0, 1}, {0, 1, 1}}
HadamardMatrix[n_] := Module[{m}, m = {{1, 1, 0}, {1, 0, 1}, {0, 1,
          1}}; KroneckerProduct[m, HadamardMatrix[n/3]]];

M = HadamardMatrix[27]

Table[D[Sum[M[[n]][[m]]*x^(m - 1), {m, 1, n}], {x, 1}], {n, 1, Length[M]}];

Table[CoefficientList[D[Sum[ M[[
   n]][[m]]*x^(m - 1), {m, 1, n}], {x, 1}], x], {n, 1, Length[M]}];

Flatten[%]
ListDensityPlot[HadamardMatrix[37], Axes -> False,
    Mesh -> False, AxesLabel -> None, Frame -> False]


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