Weierstrass function

In mathematics, the Weierstrass function was the first example found of a function with the property that it is continuous everywhere but differentiable nowhere. It turns out that almost all continuous functions are nowhere differentiable, and that this property is both stable and generic. The Weierstrass function is defined by

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

where 0 < a < 1 and

$ab>1+\frac{3}{2}\pi.$

The following graphs display the function $f(x)=\sum_{n=0}^\infty (1/2)^n\cos(20^n\pi x),$

Weierstrass function

See also