APPLICATIONS OF VARIANCE FRACTAL DIMENSION: A SURVEY

Abstract

Chaotic dynamical systems are pervasive in nature and can be shown to be deterministic through fractal analysis. There are numerous methods that can be used to estimate the fractal dimension. Among the usual fractal estimation methods, variance fractal dimension (VFD) is one of the most significant fractal analysis methods that can be implemented for real-time systems. The basic concept and theory of VFD are presented. Recent research and the development of several applications based on VFD are reviewed and explained in detail, such as biomedical signal processing and pattern recognition, speech communication, geophysical signal analysis, power systems and communication systems. The important parameters that need to be considered in computing the VFD are discussed, including the window size and the window increment of the feature, and the step size of the VFD. Directions for future research of VFD are also briefly outlined.