Fractal Analysis and Chaos in Geosciences

The fractal analysis is becoming a very convenient tool to process obtained data from chaotic systems in geosciences. It can be used to resolve many ambiguities in this field. Fractal analysis is an up-to-date method of applying nontraditional mathematics to patterns that defy understanding with traditional Euclidean concepts. Fractal analysis is measuring fractal characteristics of data. It entails several methods to assign a fractal dimension and other fractal characteristics to a dataset which may be a theoretical dataset or a pattern or signal extracted from phenomena including natural geometric objects, sound, market fluctuations, heart rates, digital images, molecular motion, networks, etc. Fractal analysis is now widely used in all areas of science. An important limitation of fractal analysis is that arriving at an empirically determined fractal dimension does not necessarily prove that a pattern is fractal; rather, other essential characteristics have to be considered. Fractals are not necessarily physical forms -- they can be spatial or temporal patterns, as well. In general, fractals can be any type of infinitely scaled and repeated pattern. In this regard, it is important to be aware that theoretical fractals are abstractions, but the subjects of fractal analysis, such as digital images limited by screen resolution, are generally not true fractals in the strictest sense. Similarly, the so-called fractals typically found in nature are not substantially scaled, thus, like finite computer generated patterns, are generally only approximations to fractals in the strictest sense. This book places emphasis on recent applications of the fractal/mutifractal analysis in geosciences and will be an immense valuable tool for researchers and students from universities. The book relates fractals and chaos to assortment of geological and geophysical applications and presents the essential concepts of fractal geometry and chaotic dynamics.