Exploring Fermi's Paradox using an Intragalactic Colonization Model

Abstract

We explore Fermi's Paradox via a system of differential equations and using simulations of dispersal and interactions between competing interplanetary civilizations. To quantify the resources and potentials of these worlds, three different state variables representing population, environment, and technology, are used. When encounters occur between two different civilizations, the deterministic Lanchester Battle Model is used to determine the outcome of the conflict. We use the Unity engine to simulate the possible outcomes of colonization by different types of civilizations to further investigate Fermi's question. When growth rates of population, technology and nature are out of balance, planetary civilizations can collapse. If the balance is adequate, then some civilizations can develop into dominating ones; nevertheless, they leave large spatial gaps in the distribution of their colonies. The unexpected result is that small civilizations can be left in existence by dominating civilizations in a galaxy due to those large gaps. Our results provide some insights into the validity of various solutions to Fermi's Paradox.

Figures (10)

• Figure 1: Progression of population $P$ (red), technology $T$ (green), and environmental conditions $E$ (blue) over time on one planet by PET model.
• Figure 2: Zoom-in of the first 50 time-steps from Fig. \ref{['F:PETprogress']}.
• Figure 3: Randomly dispersed planets with no life yet (initial stage).
• Figure 4: The purple civilization has colonized a second planet, while the orange civilization still only consists of one planet.
• Figure 5: Red colony has a larger initial size but smaller fighting effectiveness, while Green colony is smaller initially but with higher coefficient of fighting effectiveness. In this simulation, the Green wins (the horizontal axis is time), and hence, will colonize a given planet.