  In this work, a symbolic dynamical formulation based upon discrete iterative
mappings derived from the Collatz conjecture is introduced. It is demonstrated
that this formulation naturally induces a ternary alphabet useful for
characterizing the expansive and dissipative behavior of generated itineraries.
Furthermore, local and quasi-global analyses indicate cyclic behaviors that
should prove useful for describing global stability properties of itineraries.
Additionally, techniques for generating arbitrarily long divergent itineraries
are presented. Finally, this symbolic formulation allows itineraries to be
grouped into sequence families that retain equivalent dynamical behavior.
