Software for snowballing (data mining) academic papers
I don't think there's any such software available, and I doubt it would produce anything useful for the following reason:


  This goes on and on till I converge. 


Without any restriction such an approach would probably not converge, at least not before reaching a few millions papers since it would follow citations across fields. Even with restrictions, you're likely to end up with a vast amount of data which would be very hard to exploit manually.