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generalized 2d IFS for D_n Cartan group using MathWorld DihedralGroupMatrices

• To: mathgroup at smc.vnet.net
• Subject: [mg80313] generalized 2d IFS for D_n Cartan group using MathWorld DihedralGroupMatrices
• From: Roger Bagula <rlbagula at sbcglobal.net>
• Date: Fri, 17 Aug 2007 01:51:13 -0400 (EDT)

This affine IFS uses the DihedralGroupMatrices[]
to set up a general IFS with  Moran similarity dimension 2
based on D_n Cartan groups( same as SO(2*n) special orthogonal
groups): n0 is the group level.
These just get two complex too fast after n0=3!
Too much overlap results.
Clear[f, dlst, pt, cr, ptlst, M, r, p, rotate]
n0 = 3;
dlst = Table[ Random[Integer, {1, 2*n0}], {n, 25000}];
<< MathWorld`Groups`
M = DihedralGroupMatrices[n0];
Table[Det[M[[n]]], {n, 1, 2*n0}]
in = N[Table[{M[[n]][[1, 1]], M[[n]][[1, 2]]}, {n, 1, 2*n0}]]
f[j_, {x_, y_}] := M[[j]]. {x, y}/Sqrt[2*n0] + in[[j]]

pt = {0.5, 0.5};

cr[n_] := Flatten[Table[If[i ==
   j == k == 1, {}, RGBColor[i, j, k]], {i,
    0, 1}, {j, 0, 1}, {k, 0, 1}]][[1 + Mod[n, 7]]];
ptlst[n_] := Table[{cr[dlst[[j]]], Point[pt = f[dlst[[j]], Sequence[pt]]]},
   {j, Length[dlst]}];

Show[Graphics[Join[{PointSize[.001]}, ptlst[
          n]]], AspectRatio -> Automatic, PlotRange -> All]

• Follow-Ups:
  • Re: generalized 2d IFS for D_n Cartan group using MathWorld
    • From: Murray Eisenberg <murray@math.umass.edu>