Summands of the fractal Takagi (blancmange) curve

We generate the "sawtooth funktions" from the initial function $g(x) := \min \{x - k : k \in \mathbb{Z} \}$ also known as "poor man's sine".

The sum over all sawtooth functions has interesting properties and is explored here:
http://www.geogebratube.org/student/m15409