Generating a self-similar set with an IFS

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Generate an image of the self-similar set generated by the following IFS:

[dmath]
\begin{align}
f_1(\vec{x}) &= \left(
\begin{array}{cc}
\frac{1}{2} & \frac{1}{2 \sqrt{3}} \\
-\frac{1}{2 \sqrt{3}} & \frac{1}{2}
\end{array}
\right) \cdot \vec{x} \\
f_2(\vec{x}) &= \left(
\begin{array}{cc}
0 & -\frac{1}{\sqrt{3}} \\
\frac{1}{\sqrt{3}} & 0
\end{array}
\right) \cdot \vec{x} + \left(
\begin{array}{c}
\frac{1}{2} \\
\frac{1}{2 \sqrt{3}} \
\end{array}
\right)\\
f_3(\vec{x}) &= \left(
\begin{array}{cc}
\frac{1}{2} & \frac{1}{2 \sqrt{3}} \\
-\frac{1}{2 \sqrt{3}} & \frac{1}{2}
\end{array}
\right) \cdot \vec{x} + \left(
\begin{array}{c}
\frac{1}{2} \\
\frac{1}{2 \sqrt{3}}
\end{array}
\right)
\end{align}
[/dmath]

Feel free to experiment with both our Mathematica packages and our Javascript toy. Also both those tools offer multiple algorithms and colors that you might want to play with.