(Mandell and Russo, 1981; Knapp and Mandell, 1983; Russo and Mandell, 1984a; Russo and Mandell, 1986). Similar bifurcating and power law kinetics were found in receptor-ligand binding systems (Mandell, 1984) which were confirmed by more recent studies of diffusion-limited binding kinetics with receptors immobilized on a biosensor surface (Sadana, 1998). Hierarchical kinetics have also been reported in time courses of drug and metabolite levels (Koch and Zajcek, 1991), tissue tracer washout studies (Beard and Bassingthwaighte, 1998), carrier mediated transport processes (Ogihara et al, 1998), general pharmacokinetic functions (Macheras et al, 1996) and biochemical networks (Yates, 1992). It is likely that bifurcating and hierarchical, power law kinetic functions will be studied more commonly in the chemical literature in general (Shlesinger and Zaslavsky, 1996; Berlin et al, 1996) as well as applied to a variety of protein-mediated biological functions (Dewey, 1997). The first demonstration of and stochastic model for nonconvergent distributions of interspike intervals of a single neuron was by Gerstein and Mandelbrot (1964). Though rich with possibilities, it has been only very recently that additional work from this point of view has been published. This is likely due to the fact that most neuroscience oriented statistical packages, with rare exceptions, are without techniques for computing descriptive parameters for these divergent probability density distributions. This has not been the case for economic time series, download STABLE from http://Awww.cas.american.edu/~jpnolan. Recently, applications of the Fano and Allan factor as well as power spectral scaling exponents to observed and shuffled series of spike counts and interspike intervals in the auditory and visual systems (including spatial and/or time resolved single unit recordings in retinal ganglion, lateral geniculate and lateral superior olivary cells as well a auditory nerve fibers) demonstrate the ch