\documentclass[tikz,border=10pt]{standalone}
\usetikzlibrary{braids}

\begin{document}
\begin{tikzpicture}[scale=0.4, every node/.style={scale=0.4}]
\pic[
  rotate=90,
  line width=1.5pt,
  braid/control factor=0,
  braid/nudge factor=0,
  braid/gap=0.11,
  braid/number of strands = 4,
  braid/strand 4/.style={purple},
  braid/strand 3/.style={blue},
  braid/strand 2/.style={orange},
  name prefix=braid,
] at (-0.25,0) {braid={
s_3^{-1}s_2^{-1}s_1^{-1}s_1^{-1}s_2s_3^{-1}s_3^{-1}s_2s_2s_3s_3s_3
s_2^{-1}s_1^{-1}s_1^{-1}s_2^{-1}s_2^{-1}s_1^{-1}s_1^{-1}s_2s_2s_1s_1s_2
s_1s_1
}};
\draw[dashed] (12,-0.5) -- (12,3.5);
\draw[dashed] (24,-0.5) -- (24,3.5);
\end{tikzpicture}
\end{document}