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: