  Dynamic Complexity is a phenomenon exhibited by a nonlinearly interacting
system within which multitudes of different sizes of large scale coherent
structures emerge, resulting in a globally nonlinear stochastic behavior vastly
different from that could be surmised from the underlying equations of
interaction. The hallmark of such nonlinear, complex phenomena is the
appearance of intermittent fluctuating events with the mixing and distributions
of correlated structures at all scales. We briefly review here a relatively
recent method, ROMA (rank-ordered multifractal analysis), explicitly
constructed to analyze the intricate details of the distribution and scaling of
such types of intermittent structures. This method is then applied to the
analyses of selected examples related to the dynamical plasmas of the cusp
region of the magnetosphere, velocity fluctuations of classical hydrodynamic
turbulence, and the distribution of the structures of the cosmic gas obtained
through large scale, moving mesh simulations. Differences and similarities of
the analyzed results among these complex systems will be contrasted and
highlighted. The first two examples have direct relevance to the geospace
environment and are summaries of previously reported findings. The third
example on the cosmic gas, though involving phenomena much larger in
spatiotemporal scales, with its highly compressible turbulent behavior and the
unique simulation technique employed in generating the data, provides direct
motivations of applying such analysis to studies of similar multifractal
processes in various extreme environments. These new results are both exciting
and intriguing.
