The next iteration results in

$$\begin{equation*} \boldsymbol{w}(t=2\epsilon) = \boldsymbol{W}\boldsymbol{w}(t=\epsilon), \end{equation*}$$

resulting in

$$\begin{equation*} \boldsymbol{w}(t=2\epsilon)= \left(\begin{array}{c} 0.201389\\ 0.319444 \\ 0.055556 \\ 0.423611 \end{array} \right). \end{equation*}$$

Note that the vector $\boldsymbol{w}$ is always normalized to $1$.