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Dynamic Complexity is a phenomenon exhibited by a nonlinearly interactingsystem within which multitudes of different sizes of large scale coherentstructures emerge, resulting in a globally nonlinear stochastic behavior vastlydifferent from that could be surmised from the underlying equations ofinteraction. The hallmark of such nonlinear, complex phenomena is theappearance of intermittent fluctuating events with the mixing and distributionsof correlated structures at all scales. We briefly review here a relativelyrecent method, ROMA (rank-ordered multifractal analysis), explicitlyconstructed to analyze the intricate details of the distribution and scaling ofsuch types of intermittent structures. This method is then applied to theanalyses of selected examples related to the dynamical plasmas of the cuspregion of the magnetosphere, velocity fluctuations of classical hydrodynamicturbulence, and the distribution of the structures of the cosmic gas obtainedthrough large scale, moving mesh simulations. Differences and similarities ofthe analyzed results among these complex systems will be contrasted andhighlighted. The first two examples have direct relevance to the geospaceenvironment and are summaries of previously reported findings. The thirdexample on the cosmic gas, though involving phenomena much larger inspatiotemporal scales, with its highly compressible turbulent behavior and theunique simulation technique employed in generating the data, provides directmotivations of applying such analysis to studies of similar multifractalprocesses in various extreme environments. These new results are both excitingand intriguing.

Complexity Phenomena and ROMA of the Magnetospheric Cusp, Hydrodynamic Turbulence, and the Cosmic Web