An analysis of generated fractal and measured rough surfaces in regards to their multi-scale structure and fractal dimension

摘要

This work studies the methods used to extract fractal dimensions from surface profiles and the applicability of fractals to measured surfaces. The work used generated surfaces to first evaluate these methods, and later applies the methods to measured surfaces. Two methods for generating surface profiles are used. The fractal dimension values of all generated profiles are calculated by four methods, then the results are compared. It is also found that self-similarity occurs at different fractal dimensions for the power spectrum and the Weierstrass-Mandelbrot generation methods. The analysis indicates that real measured rough surfaces are not easily represented as perfect fractals as researchers and engineers often assume.