  An operational approach to the Collatz Conjecture is presented. Scenarios are
defined as strings of characters "s" (for "spike") and "d" (for "down") which
symbolize the Collatz operations (3m+1)/2 and m/2 in a Collatz Series
connecting two odd integers, the startnumber and the endnumber. It is shown
that a scenario determines uniquely four integers, called startperiod,
startphase, endperiod, and endphase such that startnumber = startperiod x k
minus startphase, and endnumber = endperiod x k minus endphase, where k is any
natural number. Therefore, any scenario can be realized infinitely many times,
with well-defined startnumber and endnumber for each realization. It is shown
how the periods and phases for a given scenario are calculated. The results are
used to prove that any odd (even) number in a Collatz Series is less than 8 (7)
("up"- or "down"-) steps away from an odd integer which is divisible by 3. They
are also used for the construction of Collatz Series which exhibit prescribed
regular graphics patterns. Finally, the bearing of the present work on the
question of non-trivial cycles is discussed.
