The Weierstrass function is continuous but not differentiable:

The function is defined by the Fourier cosine series

$f(x) = \sum_{k=0}^\infty a^k \cos( b^k \pi x )$

with $$0 < a < 1$$. When $$a b > 1$$ the series for the derivative diverges and hence does not exist.

The animation changes the parameter b from .1 to 5 and back again, as on the linked page.

Complete code for this example:

Examples Page