Natural folds are too complex to know which rheological model best suits them due to the uncertainty about the mechanical flow laws appropriate to complex geological conditions. Fractal geometry is an effective theory to describe the complexity of folds. This paper combines fractals and rheology to study the rheological mechanism of buckle folding and derives the formula for this relationship, also suggesting that the viscosity and thickness are very important factors affecting the complexity of folds. The coupling of two factors is only studied in qualitative analysis, and is not yet confirmed by the limitation of two factors in quantitative analysis. A quantitative analysis should be investigated to understand how these two factors work in affecting the complexity of fractal folds in future. Otherwise, the complexity of folding is not controlled by a unique rheological factor, but is affected by the integration of the various rheological factors. The paper simply tries to give a theoretical explanation for Ramberg's experiment.
In fact, many rheological factors affect the complexity of folds, for example, layer parallel shortening, strain softening, initial perturbation, other instabilities, preferred wavelength, non-linear material, layer anisotropy, even the bond between layer and matrix, and many other unknown factors. In the models suggested in this paper, only viscosity and thickness are assumed to affect the fractal dimensions of single-layer buckling. The fractal dimension of single-layer buckling is influenced by the coupling of viscosity and thickness in the models. In conclusion, a thicker layer with higher viscosity more easily develops more complex folds with greater fractal dimensions, filling more space than thin layer with lower viscosity. Further experiments need be done in various conditions to investigate the rheological factors which affect the complexity of folds. This opens the potential for future work in the study of complex fold rheology.