First described in 1903, the Blancmange Function is a type of fractal curve which can be constructed by repeated midpoint subdivisions and additions of a sawtooth wave.
The Future Media dept. at the University of Vienna provides an online Blancmange Function generator as part of their Nowhere Differentiable Functions app. It can form a convincingly blancmange-like graph after just seven or eight mouse-clicked iterations.
(Technical note: requires Java installed for your web browser.)