  The creativity and emergence of biological and psychological behavior are
nonlinear. However, that does not necessarily mean only that the measurements
of the behaviors are curvilinear. Furthermore, the linear model might fail to
reduce these measurements to a sum of independent random factors, implying
nonlinear changes over time. The present work reviews some of the concepts
implicated in linear changes over time and details the mathematical steps
involved. It introduces multifractality as a mathematical framework helpful in
determining whether and to what degree the measured time series exhibits
nonlinear changes over time. The mathematical steps include multifractal
analysis and surrogate data production for resolving when multifractality
entails nonlinear changes over time. Ultimately, when measurements fail to fit
the structures of the traditional linear model, multifractal modeling gives us
the means to make those nonlinear excursions explicit and perhaps permit the
development of theory that draws on both linear and nonlinear processes.
