A better closed-form solution to recursive equation

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Is there a way to represent \begin{equation} M(n)=-2\times |M(n-1)-0.5|+1 \end{equation}

in closed-form without using the $min$ function? i.e. not:

\begin{equation} M(n)=2\times\min{\big\{2^{n-1}M(1)-\lfloor2^{n-1}M(1)\rfloor,\lfloor2^{n-1}M(1)+1\rfloor-2^{n-1}M(1)\big\}} \end{equation}

where $ 0 \leq M(1)\leq 1$