I just watched one of the best episodes of Futurama about nano "gray
BTW the equation is somewhat wrong (thanks gnovice!)
but still very interesting, it's an example of
which is divergent, which means grows to infinity (although very
Ant On A Rubber Rope Paradox by Vsauce2
IRL (In Real Life) each gray goo machine keeps producing machines,
not just multiplying once, plus they are the same 100% size.
i liked very much the twist that Aaron Ehasz the writer of this
episode made the nano replicators independent of special raw
materials because they make their own from whatever they find (in
the episode they make ethanol from water and CO2).