[math-fun] binaural lacktivity

I tried a binary version of Conway's "audioactive decay" process, wherein the bit string for n becomes x0y1, with x the number, written in binary, of 0s in the usual binary representation of n, and y the same for the number of 1s. Most every n seems to decay into 105, except for "boring old" 7. Are these the only fixpoints? Do any n diverge?