A continuous, nowhere differentiable function: the Blancmange function

Let h(x) be the sawtooth function equal to |x| on [-1,1] and repeated periodically elsewhere.

Let h_n(x)=h(2ⁿx)/2ⁿ.

Then g(x)=h₀(x)+h₁(x)+h₂(x)+... is a continuous and nowhere differentiable.

Created by Dave Richeson using GeoGebra.