A CONTINUOUS VARIATION OF ROUGHNESS SCALING CHARACTERISTICS ACROSS FRACTAL AND NON-FRACTAL PROFILES

Abstract

In this study, the scaling characteristics of root-mean-squared roughness ([Formula: see text]) was investigated for both fractal and non-fractal profiles by using roughness scaling extraction (RSE) method proposed in our previous work. The artificial profiles generated through Weierstrass–Mandelbrot (W–M) function and the actual profiles, including surface contours of silver thin films and electroencephalography signals, were analyzed. Based on the relationship curves between [Formula: see text] and scale, it was found that there was a continuous variation of the dimension value calculated with RSE method ([Formula: see text]) across the fractal and non-fractal profiles. In the range of fractal region, [Formula: see text] could accurately match with the ideal fractal dimension ([Formula: see text]) input for W–M function. In the non-fractal region, [Formula: see text] values could characterize the complexity of the profiles, similar to the functionality of [Formula: see text] value for fractal profiles, thus enabling the detection of certain incidents in signals such as an epileptic seizure. Moreover, the traditional methods (Box-Counting and Higuchi) of [Formula: see text] calculation failed to reflect the complexity variation of non-fractal profiles, because their [Formula: see text] was generally 1. The feasibility of abnormal implementation of W–M function and the capability of RSE method were discussed according to the analysis on the properties of W–M function, which would be promising to make more understandings of the nonlinear behaviors of both theoretical and practical features.