It needs DigraphFractals ( Dr. McClures program) in the applications
directrory.
I'm attaching it.
This code runs at 53 megabyte on my system.
These are 2 dimensional fractals (all) with some tiles.
I used Veerman's affine matrix set up and Riddle's rotationg transform.
If you have more memory the {n,0,4} should be increased to 6 , 8,or 12.
Clear[A, A1, At, k, t, f, d, det, trace, b]
(* Matrix*)
A = {{b, -Sqrt[8 - b^2]}, {Sqrt[8 - b^2], b}}/2;
CharacteristicPolynomial[A, x]
b = Sqrt[k/9];
A1 = Inverse[A];
d = {{0, 0}, {0 + t/2, 1 - t/2}};
At = {{Re[Exp[I*Pi*t]], Im[Exp[I*Pi*t]]}, {-Im[Exp[I*Pi*t]], \
Re[Exp[I*Pi*t]]}};
f[1] = {A1, d[[1]]};
f[2] = {At.A1, d[[2]]};
ff = N[Table[f[i], {i, 1, 2}]];
Needs["DigraphFractals`"];
VMDigraph = {{ff}};
t = n/4;
Table[ShowDigraphFractals[VMDigraph, 14], {n, 0, 4}, {k, 0, 25}]
a0 = Flatten[Table[Table[ComputeDimension[VMDigraph], {k, 0,
25}], {n, 0, 4}]]
ListPlot[a0, PlotJoined -> True, PlotRange -> All]
Length[a0]
Here is a shorter one using another of Veerman's matrices:
It defines the characteristic Polynomial in terms of the determinant and
trace.
Clear[A, A1, At, k, t, f, d, det, trace]
(* Matrix*)
A = {{trace, det}, {-1, 0}};
CharacteristicPolynomial[A, x]
det = 2;
trace = k/9;
A1 = Inverse[A];
d = {{0, 0}, {0 + t/2, 1 - t/2}};
At = {{Re[Exp[I*Pi*t]], Im[Exp[I*Pi*t]]}, {-Im[Exp[I*Pi*t]], Re[Exp[I*Pi*
t]]}};
f[1] = {A1, d[[1]]};
f[2] = {At.A1, d[[2]]};
ff = N[Table[f[i], {i, 1, 2}]];
Needs["DigraphFractals`"];
VMDigraph = {{ff}};
t = 0;
Table[ShowDigraphFractals[VMDigraph, 14], {k, 0, 25}]
a0 = Table[ComputeDimension[VMDigraph], {k, 0, 25}]
ListPlot[a0, PlotJoined -> True, PlotRange -> All]
I'll try to get the movie up which comes to about 6 megabytes as an avi.
Less as Mov. It's too big to upload timewise from here it appears.
Here's an older one:
http://www.mathematica-users.org/mediawiki/images/7/7c/tame_td_lv_hw.avi
Respectfully, Roger L. Bagula
11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814
:http://www.geocities.com/rlbagulatftn/Index.html
alternative email: rlbagula@[EMAIL PROTECTED]
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