In many books from mathematical analysis (for example in Rudin) is presented the following example of continuous nowhere differentiable function:
$$f(x)=\sum_{n=1}^\infty (\frac{3}{4})^n g(4^n x) \textrm{ for } x \in \mathbb{R},$$
where $g(x)=|x|$ for $x \in [-1,1]$ and $g(x+2)=g(x)$ for $x \in \mathbb{R}$.
Who found this example for the first time?