The fractal analysis is becoming a very useful tool to process obtained data from chaotic systems in geosciences. It can be used to resolve many ambiguities in this domain. This book contains eight chapters showing the recent applications of the fractal/mutifractal analysis in geosciences. Two chapters are devoted to applications of the fractal analysis in climatology, two of them to data of cosmic and solar geomagnetic data from observatories. Four chapters of the book contain some applications of the (multi-) fractal analysis in exploration geophysics. I believe that the current book is an important source for researchers and students from universities.

The fundamental concepts of fractal geometry and chaotic dynamics, along with the related concepts of multifractals, self-similar time series, wavelets, and self-organized criticality, are introduced in this book, for a broad range of readers interested in complex natural phenomena. Now in a greatly expanded, second edition, this book relates fractals and chaos to a variety of geological and geophysical applications. All concepts are introduced at the lowest possible level of mathematics consistent with their understanding, so that the reader requires only a background in basic physics and mathematics.

This text examines the emerging field of fractals and its applications in earth sciences. Topics covered include: concepts of fractal and multifractal chaos; the application of fractals in geophysics, geology, climate studies, and earthquake seismology.

Reprint from Pure and Applied Geophysics (PAGEOPH), Volume 131 (1989), No. 1

The fractal analysis is becoming a very useful tool to process obtained data from chaotic systems in geosciences. It can be used to resolve many ambiguities in this domain. Fractals are not just complex shapes and pretty pictures generated by computers. Anything that appears random and irregular can be a fractal. Fractals permeate our lives, appearing in places as tiny as the membrane of a cell and as majestic as the solar system. Fractals have always been associated with the term chaos. The study of chaos and fractals is more than just a new field in science that unifies mathematics, theoretical physics, art, and computer science -- it is a revolution. It is the discovery of a new geometry, one that describes the boundless universe we live in; one that is in constant motion, not as static images in textbooks. Today, many scientists are trying to find applications for fractal geometry, from predicting stock market prices to making new discoveries in theoretical physics. Fractal geometry allows the description of natural patterns and the establishment and testing of models of pattern formation. In particular, it is a tool for geoscientists. This book investigates the theory and practical applications from fractal modeling to applications in the geosciences, physics, and engineering fields. It can be used to resolve many ambiguities in this domain, containing research topics showing the recent applications of the fractal/multifractal analysis in geosciences. The aim of this book is to give an overview of the applications of fractal geometry and the theory of dynamic systems in the geosciences. The state of the art is presented and the reader obtains an impression of the variety of fields for which fractal geometry is a useful tool and of the different methods of fractal geometry which can be applied. As well as specific information about new applications of fractal geometry in structural geology, physics of the solid earth, and mineralogy, proposals and ideas about how fractal geometry can be applied in the reader's field of studies will be put forward.

Fractal geometry allows the description of natural patterns and the establishment and testing of models of pattern formation. In particular, it is a tool for geoscientists. The aim of this volume is to give an overview of the applications of fractal geometry and the theory of dynamic systems in the geosciences. The state of the art is presented and the reader obtains an impression of the variety of fields for which fractal geometry is a useful tool and of the different methods of fractal geometry which can be applied. In addition to specific information about new applications of fractal geometry in structural geology, physics of the solid earth, and mineralogy, proposals and ideas about how fractal geometry can be applied in the reader's field of studies will be put forward.

Fractals have changed the way we understand and study nature. This change has been brought about mainly by the work of B. B. Mandelbrot and his book The Fractal Geometry of Nature. Now here is a book that collects articles treating fractals in the earth sciences. The themes chosen span, as is appropriate for a discourse on fractals, many orders of magnitude; including earthquakes, ocean floor topography, fractures, faults, mineral crystallinity, gold and silver deposition. There are also chapters on dynamical processes that are fractal, such as rivers, earthquakes, and a paper on self-organized criticality. Many of the chapters discuss how to estimate fractal dimensions, Hurst exponents, and other scaling exponents. This book, in a way, represents a snapshot of a field in which fractals has brought inspiration and a fresh look at familiar subjects. New ideas and attempts to quantify the world we see around us are found throughout. Many of these ideas will grow and inspire further work, others will be superseded by new observations and insights, most probably with future contributions by the authors of these chapters.

The aim of this book is to show some applications of fractal analysis in the fields of sciences. The first chapter introduces the readers to the book, while the second chapter shows the methods and challenges of fractal analysis of time-series data sets. The third chapter demonstrates fractal geometry as an attractive choice for miniaturized planar microwave filter design. The fourth chapter presents fractal antennas for wearable applications. The objective of the fifth chapter is to show some Parrondian games in discrete dynamic systems, while the last chapter reveals fractal structures of carbon nanotube system arrays.