Fractal Haar system

The Haar system is an alternative to the classical Fourier bases, being particularly useful for the approximation of discontinuities. The article tackles the construction of a set of fractal functions close to the Haar set. The new system holds the property of constitution of bases of the Lebesgue spaces of pp-integrable functions on compact intervals. Likewise, the associated fractal series of a continuous function is uniformly convergent. The case p=2p=2 owns some peculiarities and is studied separately.