  For a Lipschitz $\mathbb{Z}-$periodic function $\phi:\mathbb{R}\to
\mathbb{R}^2$ satisfied that $\mathbb{R}^2\setminus\{\phi(x):x\in\mathbb{R}\}$
is not connected, an integer $b\ge 2$ and $\lambda\in (c/{b^{\frac12}},1)$, we
prove the following for the generalized Weierstrass-type function
$W(x)=\sum\limits_{n=0}^{\infty}{{\lambda}^n\phi(b^nx)}$: the box dimension of
its graph is equal to $3+2\log_b\lambda$, where $c$ is a constant depending on
$\phi$.
