The Blancmange curve, also known as the Takagi Curve, was first described by the Japanese mathematician Teiji Takagi in 1901.
The name blancmange comes from its resemblance to a blancmange pudding.
It can be constructed by adding the triange wave function successively, using triangles which are half the height of the triangles of the previous order.
It is everywhere continuous but nowhere differentiable.