As usual, for a function $f: \mathbb{R} \to \mathbb{R}$ the graph of $f$ is the set $\{ (x,f(x)) \mid x \in \mathbb{R} \}$. For which continuous nowhere differentiable functions $f: \mathbb{R} \to \mathbb{R}$ does the graph of $f$ have fractional fractal (Box or Hausdorff) dimension?
The Weirstrass function has fractional Hausdorff dimension. But, as explained in this answer, one can construct examples of such functions with integer fractal dimension.
Are there sufficient conditions for such functions to have fractional fractal dimension?
