Spatial dispersion of interstellar civilizations: a probabilistic site percolation model in three dimensions

Abstract

A model of the spatial emergence of an interstellar civilization into a uniform distribution of habitable systems is presented. The process of emigration is modelled as a three-dimensional probabilistic cellular automaton. An algorithm is presented which defines both the daughter colonies of the original seed vertex and all subsequent connected vertices, and the probability of a connection between any two vertices. The automaton is analysed over a wide set of parameters for iterations that represent up to 250 000 years within the model's assumptions. Emigration patterns are characterized and used to evaluate two hypotheses that aim to explain the Fermi Paradox. The first hypothesis states that interstellar emigration takes too long for any civilization to have yet come within a detectable distance, and the second states that large volumes of habitable space may be left uninhabited by an interstellar civilization and Earth is located in one of these voids.

Invasion percolation solves Fermi Paradox but challenges SETI projects

“…We have also detected a shortcoming in Hair & Hedman's (2013) model: its failure in producing large voids is due to the use of a homogeneous and constant colonization probability per time step. Our model, with its exponential colonization probability, produces large voids, instantiating the percolation solution for Fermi Paradox in a more realistic way than Landis (1998) does.…”

“…The time step Δ t = 1000 years has been used also in the percolation model of Hair & Hedman (2013). In contrast to Landis model, but like our model, there are repetitive attempts to colonize the same site with a constant probability p = C , where C is a characteristic of the mother sites (propensity to colonize, uniform and fixed from start).…”

“…Hair & Hedman (2013) showed that, due to the repetitive attempts to colonization, there is no formation of large voids. They claim that their model does not support the percolation solution for Fermi Paradox.…”

Agent-based modelling of interstellar contacts using rumour spread models

“…Bjørk (2007) simulated a 3D model of Milky Way Galaxy and investigated the exploration of Milky Way by using space probes. Hair and Hedman (2013) adapted the percolation theory (for the diffusion of liquids) for modelling interstellar civilization distribution and evaluated two theories of interstellar emigration which both are presented as solutions to FP. Galera et al (2019) also used a method based on percolation theory and argued that SETI studies may largely exclude the Solar neighbourhood because there are large voids between inhabited regions.…”

Fermi's Paradox Is a Daunting Problem—Under Whatever Label

“…Research that deals with FP has greatly expanded in recent years on both a theoretical and observational stage (Davies 2010(Davies , 2012Vukotid and Dirkovid 2012;Barlow 2013;Hair and Hedman 2013;Davies and Wagner 2013;Armstrong and Sandberg 2013;Lampton 2013;Cartin 2014;Nunn, Guy, and Bell 2014;Wright et al 2014;Spivey 2015;Griffith et al 2015;Zackrisson et al 2015 -to give just a few post-2010 examples). Not all of these papers have been authored by astronomers or astrobiologists; the multidisciplinary nature of the whole effort is seen in titles such as "The Fermi Paradox and Coronary Artery Disease" in one of the world's most prestigious medical journals (Gottlieb and Lima 2014), and the subject matter is discussed even by personalities such as the (in)famous NSA whistleblower Edward Snowden.…”