[math-fun] Diffusing number sequence

Suppose that one has four nonnegative integers in a row, A B C D. Create a subsequent row by abs(A-B) abs(B-C) abs(C-D) abs(D-A). Repeating this process will eventually produce 0 0 0 0, the end state. The object is to create a "long" chain of rows ending in 0 0 0 0. I can "backup" chains to create arbitrarily long chains, but the process seems a bit unwieldy. Is there any formulaic way of specifying an initial row that will produce a chain of length n? Bill C.