Implementation of quantum search algorithms as well as quantum machine learning are the tasks of extreme importance for the future technologies. These processes are characterized by the
hierarchy of specification levels: from global blurred contours to fine local details. This hierarchy and self-similarity of different scales finds immediate
representation in fractals, describing various things from forms of growing leaves and coastlines to the wave functions representing the probability of quantum particle locations. Thus, the scientists have an essential demand in the quantum models realizing simple and robust fractal wave functions, both in their distributions in spatial and energy domains.