Large-scale fluctuations of the H component magnetic field at Earth's equator during the period from 1981 to 2002 were examined using multifractal tools. We computed, analyzed, and modeled a measure representation of the Dst data. This representation can be viewed as a probability measure that characterizes the Dst series. The measure representation in fact gives the probabilities of specific strings of events in the complete Dst time series. The raw time series clearly shows intermittency and non-Gaussianity, which are reflective of large magnetic storms. The relevance of the multifractal analysis is that it suggests physical processes that may lead to this kind of data. The evidence we have found suggests that the ring current is always out of equilibrium and may undergo state changes via multiplicative cascades. We attempted to model the process using recurrent iterated function systems (RIFS). The RIFS model, in particular, provided an excellent fit to the Dst measure representation. Because of these results it can be concluded that multifractal RIFS models for the description of space weather will certainly play a greater role in the future.