  The branching processes in parton showers are studied in perturbative QCD for
both quark and gluon jets. The emphasis is on the nature of fluctuations of
both the parton multiplicities and the spatial patterns of the final states.
Effective measures of such fluctuations are calculated from the data obtained
by Monte Carlo simulations. The entropy indices are used to characterize
chaoticity. Both running and fixed couplings are considered. The fixed coupling
case is used to study the onset of chaos. Implications of the results are
discussed.
