Do you like calculus? No? Read on anyway.
The function y=|x| is continuous, but not differentiable at x=0, because it makes a 90 degree turn there. Would it be possible to construct a function which iscontinuous, but differentiable nowhere? Bolzano’s function is an example of such a curve. The animation shows how it is created by repeating a certain step, then zooms in to show it is infinitely detailed. Jaggy on all scales