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In theory, a self-replicating spacecraft could be sent to a neighbouring star-system, where it would seek out raw materials (extracted from asteroids, moons, gas giants, etc.) to create replicas of itself. These replicas would then be sent out to other star systems, repeating the process in an exponentially increasing pattern. The original "parent" probe could then pursue its primary purpose within the star system. This mission varies widely depending on the variant of self-replicating starship proposed.
Given this pattern, and its similarity to the reproduction patterns of bacteria, it has been pointed out that von Neumann machines might be considered a form of life. In his short story, "Lungfish" (see Examples in fiction below), David Brin touches on this idea, pointing out that self-replicating machines launched by different species might actually compete with one another (in a Darwinistic fashion) for raw material, or even have conflicting missions. Given enough variety of "species" they might even form a type of ecology, or - should they also have a form of artificial intelligence - a society. They may even mutate with untold thousands of "generations".
It has been theorized that a self-replicating starship utilizing relatively conventional theoretical methods of interstellar travel (i.e. no exotic faster-than-light propulsion such as "warp drive", and speeds limited to an "average cruising speed" of 0.1c.) could spread throughout a galaxy the size of the Milky Way in as little as half a million years.
In 1981, Frank Tipler put forth an argument that extraterrestrial intelligences do not exist based on von Neumann probes. Given even a moderate rate of replication and the history of the galaxy, such probes should already be common throughout space and thus, we should have already encountered them. Because we haven't, this shows that extraterrestrial intelligences do not exist. This is thus a resolution to the Fermi paradox—that is, the question of why we haven't already encountered extraterrestrial intelligence if it's common throughout the universe.
Another objection to the prevalence of von Neumann probes is that civilizations of the type that could potentially create such devices may have inherently short lifetimes, and self-destruct before so advanced a stage is reached, through such events as biological or nuclear warfare, nanoterrorism, resource exhaustion, ecological catastrophe, pandemics due to antibiotic resistance, etc.