Emergent Open-Endedness from Contagion of the Fittest

In this work, we study emergent 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. A phenomenon we have called as expected (local) emergent open-endedness. In addition, we show that static networks with a scale-free degree distribution in the form of a power-law following the Barabási-Albert model satisfy this lower bound and, thus, displays expected (local) emergent open-endedness.