  The Fermi paradox highlights the dichotomy between the lack of physical
contact with other civilizations and the expectation that technological
civilizations are assumed likely to evolve in many locations in the Milky Way
galaxy, given the large number of planetary systems within this galaxy. Work by
Landis and others has modeled this question in terms of percolation theory and
cellular automata, using this method to parametrize our ignorance about
possible other civilizations as a function of the probability of one system to
colonize another, and the maximum number of systems reachable from each
starting location (i.e. the degree in the network used for percolation). These
models used a fixed lattice of sites to represent a stellar region, so the
degree of all sites were identical. In this paper, the question is examined
again, but instead of using a pre-determined lattice, the actual physical
positions of all known star systems within 40 parsecs of the Solar System are
used as percolation sites; in addition, the number of sites accessible for
further colonization from a given system is determined by a choice of maximum
distance such efforts can travel across. The resulting simulations show that
extraterrestrial colonization efforts may reach the Solar System, but only for
certain values of the maximum travel distance and probability of an occupied
system further colonizing other systems. Indeed, large numbers of systems may
be colonized with either vessels that lack insufficient travel distance to
reach the Solar System or else have a colonization probability where they are
statistically unlikely to reach us.
