Enumerative Geometrical Genealogy (Or: The Sex Life of Points and Lines)

Joshua Cooper and Mark Walters initiated the subject that we call here Enumerative Geometric Genealogy, (and that lead to the hard-to-count OEIS sequence A140468) but they did not realize the broader impact of their research to the population explosion of a certain far-away planet, whose inhabitants are much smarter, and more civilized, than we are.