# Reiterative Graphics- Fractals and Isometries

I am trying to reiterate a program on mathematica.

Say, I begin with a circle partitioned into 3 symmetric regions. The code is below:

R0 = {{Cos[2 Pi/3], -Sin[2 Pi/3]}, {Sin[2 Pi/3], Cos[2 Pi/3]}};
V1 = {{-Cos[Pi/6]}, {-Sin[Pi/6]}};
R1 = R0.V1;
R2 = R0.R1;
X1 = V1[[1]][[1]];
Y1 = V1[[2]][[1]];
X2 = R1[[1]][[1]];
Y2 = R1[[2]][[1]];
X3 = R2[[1]][[1]];
Y3 = R2[[2]][[1]];
C1 = {Opacity[.2], Yellow, Disk[{0, 0}, 1, {0, 2 Pi/3}]};
C2 = {Opacity[.2], Orange, Disk[{0, 0}, 1, {2 Pi/3, 2*2 Pi/3}]};
C3 = {Opacity[.2], Blue, Disk[{0, 0}, 1, {2*2 Pi/3, 2 Pi}]};
T1 = Graphics[Translate[C1, {0, 0}]];
T2 = Graphics[Translate[C2, {0, 0}]];
T3 = Graphics[Translate[C3, {0, 0}]];
Show[T1, T2, T3, PlotRange -> All, Axes -> True]

And I have this image:

Suppose I fix the boundaries of these regions and translate the parts using a symmetric translation. I now utilize the original V1 vector for this translation, which corresponds to the first vector being a translation on V1 and each part gets translated by the same vector rotated by \$2 pi /3\$ successively. My updated code looks like this:

R0 = {{Cos[2 Pi/3], -Sin[2 Pi/3]}, {Sin[2 Pi/3], Cos[2 Pi/3]}};
V1 = {{-Cos[Pi/6]}, {-Sin[Pi/6]}};
R1 = R0.V1;
R2 = R0.R1;
X1 = V1[[1]][[1]];
Y1 = V1[[2]][[1]];
X2 = R1[[1]][[1]];
Y2 = R1[[2]][[1]];
X3 = R2[[1]][[1]];
Y3 = R2[[2]][[1]];
C1 = {Opacity[.2], Yellow, Disk[{0, 0}, 1, {0, 2 Pi/3}]};
C2 = {Opacity[.2], Orange, Disk[{0, 0}, 1, {2 Pi/3, 2*2 Pi/3}]};
C3 = {Opacity[.2], Blue, Disk[{0, 0}, 1, {2*2 Pi/3, 2 Pi}]};
T1 = Graphics[Translate[C1, {X1, Y1}]];
T2 = Graphics[Translate[C2, {X2, Y2}]];
T3 = Graphics[Translate[C3, {X3, Y3}]];
Show[T1, T2, T3, PlotRange -> All, Axes -> True]

And we have this image:

Now, what I want to do is to repeat the translation, this time only taking parts of the new pieces that lie inside the original boundaries. I want to do this two ways. The first is to just repeat the translation on the new pieces that lie on the original boundary as the first image. The other way is to do this while truncating the pieces that lie outside the original boundary. The result should be a fractal like image. How could I do this?

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