FRACTAL RENEWAL PROCESSES GENERATE 1 F NOISE

1/f(D) noise occurs in an impressive variety of physical systems, and numerous complex theories have been proposed to explain it. We constru ct two relatively simple renewal processes whose power spectral densit ies vary as 1/f(D): (i) a standard renewal point process, with 0 < D < 1; and (ii) a finite-valued alternating renewal process, with 0 < D < 2. The resulting event number statistics, coincidence rates, minimal coverings, and autocorrelation functions are shown also to follow powe r-law forms. These fractal characteristics derive from interevent-time probability density functions which themselves decay in a power-law f ashion. A number of applications are considered: trapping in amorphous semiconductors, electronic burst noise, movement in systems with frac tal boundaries, the digital generation of 1/f(D) noise, and ionic curr ents in cell membranes.