In [Föllmer 81] (English translation to be found here) writes: "The class of processes of quadratic variation is clearly larger than the class of semimartingales: Just consider a deterministic process of quadratic variation which is of unbounded variation."

Could anyone please give me examples (with references) of *deterministic processes of quadratic variation which are of unbounded variation*? Thank you!

(P.S.: What seems to make these deterministic processes interesting is that you also have to use Ito integrals to integrate them)