  The notion of chaotic behavior is examined for particle production in
branching processes. Two types of branching are considered: non-Abelian gauge
interaction and an Abelian cascade model. Properties of the production
processes are investigated by Monte Carlo stimulation. The ``temporal''
behavior is studied by following the fluctuations in the multiplicities of each
generation as the branching evolves. The ``spatial'' behavior is described in
terms of the fluctuations of the normalized factorial moments from event to
event. The information dimension and a new entropy index are determined. When
all the measures are taken together, they collectively give a strong suggestion
that the QCD branching process is chaotic, while the Abelian cascade model is
not.
