Takagi (blancmange) curve

Add tent shapes, each half as tall and twice as many as the last. The sum is continuous everywhere and has a slope nowhere: zoom on any point and it is still all corners. The faint lines are the partial sums so far.

T(x) = Σ s(2ⁿx) / 2ⁿ, s(x) = distance to nearest integer

On mathcurve.com as Courbe du blanc-manger