Riemann's nondifferentiable function | Weierstrass-Mandelbrot function

The pathological function f_a(x) = sum_(k = 1)^∞ (sin(π k^a x))/(π k^a) (originally defined for a = 2) that is continuous but differentiable only on a set of points of measure zero. The plots above show f_a(x) for a = 2 (red), 3 (green), and 4 (blue).

Blancmange function | continuous function | differentiable | monsters of real analysis