An explanation of disproportionate growth using linear 3-dimensional informetrics and its relation with the fractal dimension

Summary

We study new and existing data sets which show that growth rates of sources usually are different from growth rates of items. Examples: references in publications grow with a rate that is different (usually higher) from the growth rate of the publications themselves; article growth rates are different from journal growth rates and so on. In this paper we interpret this phenomenon of “disproportionate growth' in terms of Naranan's growth model and in terms of the self-similar fractal dimension of such an information system, which follows from Naranan's growth model. The main part of the paper is devoted to explain disproportionate growth. We show that the “simple' 2-dimensional informetrics models of source-item relations are not able to explain this but we also show that linear 3-dimensional informetrics (i.e. adding a new source set) is capable to model disproportionate growth. Formulae of such different growth rates are presented using Lotkaian informetrics and new and existing data sets are presented and interpreted in terms of the used linear 3-dimensional model.