Abstract :
Power laws as defined in 1926 by A. Lotka are increasing
in importance because they have been found valid in
varied social networks including the Internet. In this article
some unique properties of power laws are proven.
They are shown to characterize functions with the scalefree
property (also called self-similarity property) as
well as functions with the product property. Power laws
have other desirable properties that are not shared by
exponential laws, as we indicate in this paper. Specifically,
Naranan (1970) proves the validity of Lotka’s law
based on the exponential growth of articles in journals
and of the number of journals. His argument is reproduced
here and a discrete-time argument is also given,
yielding the same law as that of Lotka. This argument
makes it possible to interpret the information production
process as a self-similar fractal and show the relation
between Lotka’s exponent and the (self-similar)
fractal dimension of the system. Lotkaian informetric
systems are self-similar fractals, a fact revealed by Mandelbrot
(1977) in relation to nature, but is also true for
random texts, which exemplify a very special type of informetric
system.
