ABSTRACT
In this chapter, methods of determining fractal dimensions and other properties are described with emphasis on their basic/mathematical formulations and implementation steps. The methods discussed are the box counting method, triangulation prism method, Brownian motion methods with emphasis on power spectral density (PSD) function, and multifractal method. The key aspects for analysis and interpretation of surfaces for each method are explained. The specific factors affecting the accuracy of different methods are also highlighted. The methods resulting from the improvement of the existing techniques for accuracy enhancement have also been described. In addition, other applications of the multifractal method, besides the thin film surface analyses, are highlighted and relevant resources for further reading by the readers recommended. It is noted from this discussion that box counting is the most adopted technique for mono-fractal and multifractal characterization of features. The reason for its high adoption is due to its simplicity, flexibility, and improved accuracy resulting from continued research efforts which are distinctly discussed.
