Universal growth scaling law determined by dimensionality

Abstract

Growth patterns of complex systems predict how they change in sizes, numbers, masses, etc. Understanding growth is important, especially for many biological, ecological, urban, and socioeconomic systems. One noteworthy growth behavior is the 3/4- or and 2/3-power scaling law. It's observed in worldwide aquatic and land biomass productions, eukaryote growth, mammalian brain sizes, and city public facility distributions. Here, I show that these complex systems belong to a new universality class whose system dimensionality determines its growth scaling. The model uses producer-consumer dynamics to derive the n/(n+1) power scaling law for an n-dimensional system. Its predictions are validated with real-world two- and three-dimensional data. Dimensionality analysis thus provides a new paradigm for understanding growth and growth-related problems in a wide range of complex systems.