## 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(2^{n}x)/2^{n}.
Then g(x)=h_{0}(x)+h_{1}(x)+h_{2}(x)+... is a continuous and nowhere differentiable.
Created by Dave Richeson using GeoGebra. |