This in fact is the plot of the movie 2001, which even today portrays perhaps the most realistic encounter with an alien intelligence. In that movie, aliens put a von Neumann machine, the monolith, on the moon, which sends signals to a relay station based on Jupiter in order to monitor and even influence the evolution of humanity.
Once it has landed, the probe will create a factory from the lunar material in order to manufacture a thousand copies of itself. Each clone in the second generation then blasts off to colonize other distant moons. So, starting with one robot, we then have a thousand. If each of them creates another thousand robots, then we have a million. Then a billion. Then a trillion. In just a few generations, we can have an expanding sphere containing quadrillions of these devices, which scientists call von Neumann machines.
This in fact is the plot of the movie 2001, which even today portrays perhaps the most realistic encounter with an alien intelligence. In that movie, aliens put a von Neumann machine, the monolith, on the moon, which sends signals to a relay station based on Jupiter in order to monitor and even influence the evolution of humanity.
