1. B. Mandelbrot, “The Fractal Geometry of Nature,” Freeman, San Francisco (1982).
2. E.g., P. Dutta and P.M. Horn, Rev. Mod. Phys. 53:497 (1981).
3. M.B. Weissman, Rev. Mod. Phys. 60:537 (1988).
4. M.J. Kirton and M.J. Uren, Adv. Phys. 38:367 (1989).
5. Recall that fractals are objects whose mass M increases as a power of their linear size L: M ~ L
D
; D, the “fractal dimension,” is typically a noninteger number, less than the (integer) number of dimensions d in which the object is embedded. The persistence of this power law to large L implies subtle long-range correlations among the positions of the individual particles constituting the object. In 1/f-noise, the time series q(t) of some physical quantity has a power spectrum, S(f) = ∫ dt < q(t′)q(t + t′) > cos(2π ft), that increases like 1/f
α at low frequencies f, the exponent α often being very close to unity. Here the angular brackets denote an average over times t′.