On the constrained growth of complex critical systems

TL;DR

This paper introduces a new temporal scaling law for critical systems, supported by theoretical models and empirical data, aiming to develop a unified framework for understanding their growth.

Contribution

It proposes a novel law of temporal scaling for critical systems and demonstrates its applicability across diverse theoretical models and real-world systems.

Findings

The scaling law is supported by models of percolation, self-organized criticality, and fractal growth.

Empirical evidence of the scaling law is found in prose, productivity, citation networks, and Internet topology.

The results suggest a universal principle governing the growth of complex critical systems.

Abstract

Critical, or scale independent, systems are so ubiquitous, that gaining theoretical insights on their nature and properties has many direct repercussions in social and natural sciences. In this report, we start from the simplest possible growth model for critical systems and deduce constraints in their growth : the well-known preferential attachment principle, and, mainly, a new law of temporal scaling. We then support our scaling law with a number of calculations and simulations of more complex theoretical models : critical percolation, self-organized criticality and fractal growth. Perhaps more importantly, the scaling law is also observed in a number of empirical systems of quite different nature : prose samples, artistic and scientific productivity, citation networks, and the topology of the Internet. We believe that these observations pave the way towards a general and analytical framework for predicting the growth of complex systems.