International Journal of Astrobiology

Research Article

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

Thomas W. Haira1 c1 and Andrew D. Hedmana1

a1 College of Arts and Sciences, Florida Gulf Coast University, 10501 FGCU Blvd, South, Fort Myers, FL 33965, USA


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.

(Received April 19 2012)

(Accepted August 03 2012)

(Online publication October 02 2012)

Key words

  • astrobiology;
  • extraterrestrial intelligence;
  • Fermi paradox;
  • percolation theory;
  • spatial dispersion


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