Fractal Simulation and Classification of Folds

Abstract: The method of fractal simulation and classification of folds is firstly studied here to describe various types of complex fold patterns in quantitative analysis. Based on the characteristics of natural folds with a fractal pattern, the fold patterns are simulated to describe various types of folds quantitatively by means of fractal interpolation. The major factors affecting the fold pattern are elucidated in fractal simulation of folds, i.e. positions of interpolation points (x, y) and the disturbance coefficient d of folds (‐1<d<1). The bigger the value d for a fold simulation is, the more complex or disturbed the folds are and the better developed the relative secondary folds are. If d>0, folds are upconvex. IF d<0, they are down‐convex. |d|=0, |d|=0.25 and |d|=0.5 represent three conspicuous turning states. If |d|=0, the points will be joined by a straight line. If |d|=0.25, the points will be joined smoothly. If |d|<0.25, there will be complex secondary folds between the points. If |d| >0.5, there will be more complex secondary folds between the points. The complex degrees of the fold pattern, therefore, can be classified by the disturbance coefficient d and by the discongruent degree Δ d. In nature, most folds are self‐affine fractal folds.