I think we are talking past each other. In base ten if you start with 1234 and cycle though asdf - fdsa > new number you hit a single stable number 6174 .

In base 11 using 6174 you cycle:

4808, 87A3, 7094, 9272, 3098, 9452, 7094 (cycle)

I was thinking of a http://en.wikipedia.org/wiki/Logistic_map for this equation abcd - dcba > might be interesting across different bases.