wikipedia has an entry on the Collatz conjecture with a section on As an abstract machine that computes in base two. this apparently describes a construction of a FSM transducer computing sequential iterates starting from lsb to msb (least sig. bit to most sig. bit). [this is more a TCS, theoretical computer science construction.] however, there is no specific ref cited.
does anyone know where this FSM iterate transducer construction appears, or first appeared in the literature?
note, there is some relation to ref .
[ps, have some apparently new/possibly groundbreaking results related to this construction & intend to write it up on a blog, may edit this post later to incl the ref.]
 The ultimate challenge: the 3x+1 problem, Lagarias
 The 3x + 1 Problem: An Annotated Bibliography, Lagarias, arxiv
 Jeffrey O. Shallit and David W. Wilson (1991), The “3x + 1” Problem and Finite Au- tomata, Bulletin of the EATCS (European Association for Theoretical Computer Sci- ence), No. 46, 1991, pp. 182–185.