Takagi function
From specialfunctionswiki
The Takagi function (also called the blancmange function) is defined by $$\mathrm{takagi}(x)=\displaystyle\sum_{k=0}^{\infty} \dfrac{\mathrm{dist}_{\mathbb{Z}}(2^n x)}{2^n}.$$
Graph of $\mathrm{takagi}$ on $[0,1]$.
Properties
Takagi function is continuous
Takagi function is nowhere differentiable
