Takagi function

Define the function $s(x)=\min_{n \in \mathbb{Z}} |x-n|$. The Blancmange function is defined by $$\mathrm{blanc}(x)=\displaystyle\sum_{k=0}^{\infty} \dfrac{s(2^n x)}{2^n}.$$

• Blancmangefunction.png

  Graph of $\mathrm{blanc}$ on $[0,1]$.