\newcommand{\mayberandompath}[2]{
	\pgfmathsetmacro{\choice}{random(5)}
	\pgfmathsetmacro{\myrand}{random(12)*30}
	\ifthenelse{\equal{\choice}{1.0}}{
		\draw (#1:2) -- (#2+\myrand:2);
	}{
		\draw (#1:2) -- (#2:2);
	}
}

\begin{tikzpicture}[thick,inner sep=0.1cm]
	\foreach \t in {30,60,...,360}{
		\node [fill,circle] at (\t:2) {};
		\mayberandompath{\t}{\t+30}
		\mayberandompath{\t}{\t+60}
	}
\end{tikzpicture}
