Emergent Open-Endedness from Contagion of the Fittest

TL;DR

This paper demonstrates that in networked populations of computable systems following a contagion model, a certain prevalence threshold leads to unbounded growth in local emergent information, especially in scale-free networks.

Contribution

It introduces the concept of emergent open-endedness driven by contagion dynamics and proves its occurrence in Barabási-Albert scale-free networks.

Findings

Lower bound for prevalence triggers unbounded complexity growth.

Scale-free networks exhibit emergent open-endedness.

Expected local emergent information increases with population size.

Abstract

In this paper, we study emergent irreducible information in populations of randomly generated computable systems that are networked and follow a "Susceptible-Infected-Susceptible" contagion model of imitation of the fittest neighbor. We show that there is a lower bound for the stationary prevalence (or average density of "infected" nodes) that triggers an unlimited increase of the expected local emergent algorithmic complexity (or information) of a node as the population size grows. We call this phenomenon expected (local) emergent open-endedness. In addition, we show that static networks with a power-law degree distribution following the Barab\'asi-Albert model satisfy this lower bound and, thus, display expected (local) emergent open-endedness.