One aim of structural geology is to understand the processes that operate during deformation and metamorphism so that the conditions (P, T, strain-rates, stresses, rates of other processes such as grain-size reduction) that control these processes can be identified and quantified. In this paper we explore ways of quantifying the geometry of deformed metamorphic rocks in ways that are directly related to the processes that operated. We propose that structures we observe in nature are the result of coupling between nonlinear processes and hence deforming metamorphic systems behave as nonlinear dynamical systems. As such the descriptions of such systems should utilise the toolbox of methods that have been developed for dynamic systems over the past 50 years or so. These methods include the construction of attractors, multifractal analysis, recurrence plots, recurrence quantification analysis and dynamical network analysis. We illustrate the approach first using numerical models of fold systems, with linear and nonlinear constitutive relations and with and without initially imposed noise (imperfections). We then extend the illustrations to consider natural fold systems. Our conclusions are that the irregularity we see in natural fold systems is the result of nonlinear constitutive laws, not that of initial imperfections and that the number of processes operating to produce the observed fold shapes is relatively small.