Box dimension of the graphs of the generalized Weierstrass-type functions

Haojie Ren

For a Lipschitz $\mathbb{Z}-$periodic function $\varphi :\mathbb{R}\to {\mathbb{R}}^2$ satisfied that ${\mathbb{R}}^2\setminus \{\varphi (x):x\in \mathbb{R}\}$ is not connected, an integer $b\ge 2$ an…