No one may find this interesting, but in virtual worlds, this is a very big problem. For example, in Second Life, if a bug report/ticket contains the terms "Grey Goo" (or) "Gray Goo" it is immediately taken care of. To the point where, if you are a worker who can handle it, you will be given a phone call and you must drive to your office immediately- it doesn't matter what else you are doing. Grey Goo can destroy a server in a matter of seconds.
Presumably they have automatic safeguards against it, and these emergencies occur when somebody outsmarts them. I wonder if this can be generalized to an interesting theory--how do you prevent all-consuming self-replicating behavior in a system with minimal intervention otherwise? Is this question even meaningful?
You'd think so, but when all of those objects are (potentially) things purchased by players, it gets a bit more complex than kill it at the root. Also, I believe that (at least at one point), objects could attach scripts to other objects. So the family tree wouldn't work in all cases.
Internally Second Life calls their countermeasure the "gray goo fence" but I can't find many good descriptions of how it actually works online, except some mentions that the restrictions on how much something can "rez" increase exponentially. This link was the best description of it I could find:
I believe that, since the attack mentioned therein, they've done other things, such as restricting certain scripting functions to trusted people. But folks have been known to find exploits anyhow.
Of course, feel free to correct me if you actually play Second Life. I've only been following news of it from the outside. I've never actually played it.
I've never understood why people are that worried about it with nanomachines, though. We already have gray goo (though much of it, like algae, is green). I mean, most single-celled organisms are capable of that kind of mass replication. And they can be found pretty much everywhere already. I'd be more worried about accidentally engineering a super-virus or whatever than gray goo per se.