The author uses an interesting methodology based on fractal interpolation functions to define new real maps (real fractal functions) on the circle generalizing the classical ones. Every periodic function with integrable square can be endowed with a family of fractal interpolants generalizing the original. In this way , the fractal methodology provides a degree of freedom to the classical functions on the circle. The diversity of the family allows to choose the most suitable element in order to satisfy the requirements. The main result obtained in the paper is the existence of a Hilbert basis of fractal maps on the circle (Theorem 2.13). Finally an suggestive application is given. The paper is very well written and the subject is actual, the procedures described are especially useful for interpolation and approximation of periodic signals.