Fractal Time

Fractal Time

In his latest book, former senior computer systems designer and bestselling author Gregg Braden merges these ancient and modern world views into a powerful new model of time. Marrying the modern laws of fractal patterns to the ancient concept of cycles, he demonstrates how everything from the war and peace between nations to our most joyous relationships and personal crises are the returning patterns of our past. As each pattern returns, it carries the same conditions of previous cycles —fractal patterns that can be known, measured and predicted!

Fractal Time

Why a Watched Kettle Never Boils

Fractal Time

This book provides an interdisciplinary introduction to the notion of fractal time, starting from scratch with a philosophical and perceptual puzzle. How subjective duration varies, depending on the way we embed current content into contexts, is explained. The complexity of our temporal perspective depends on the number of nestings performed, i.e. on the number of contexts taken into account. This temporal contextualization is described against the background of the notion of fractal time. Our temporal interface, the Now, is portrayed as a fractal structure which arises from the distribution of content and contexts in two dimensions: the length and the depth of time. The leitmotif of the book is the notion of simultaneity, which determines the temporal structure of our interfaces. Recent research results are described which present and discuss a number of distorted temporal perspectives. It is suggested that dynamical diseases arise from unsuccessful nesting attempts, i.e. from failed contextualization. Successful nesting, by contrast, manifests itself in a "win-win handshake" between the observer-participant and his chosen context. The answer as to why a watched kettle never boils has repercussions in many a discipline. It would be of immense interest to anyone who works in the fields of cognitive and complexity sciences, psychology and the neurosciences, social medicine, philosophy and the arts.

Fractal Space-time and Microphysics

Towards a Theory of Scale Relativity

Fractal Space-time and Microphysics

This is the first detailed account of a new approach to microphysics based on two leading ideas: (i) the explicit dependence of physical laws on scale encountered in quantum physics, is the manifestation of a fundamental principle of nature, scale relativity. This generalizes Einstein's principle of (motion) relativity to scale transformations; (ii) the mathematical achievement of this principle needs the introduction of a nondifferentiable space-time varying with resolution, i.e. characterized by its fractal properties.The author discusses in detail reactualization of the principle of relativity and its application to scale transformations, physical laws which are explicitly scale dependent, and fractals as a new geometric description of space-time.

Fractals of Brain, Fractals of Mind

In Search of a Symmetry Bond

Fractals of Brain, Fractals of Mind

This collective volume is the first to discuss systematically what are the possibilities to model different aspects of brain and mind functioning with the formal means of fractal geometry and deterministic chaos. At stake here is not an approximation to the way of actual performance, but the possibility of brain and mind to implement nonlinear dynamic patterns in their functioning. The contributions discuss the following topics (among others): the edge-of-chaos dynamics in recursively organized neural systems and in intersensory interaction, the fractal timing of the neural functioning on different scales of brain networking, aspects of fractal neurodynamics and quantum chaos in novel biophysics, the fractal maximum-power evolution of brain and mind, the chaotic dynamics in the development of consciousness, etc. It is suggested that the margins of our capacity for phenomenal experience, are fractal-limit phenomena . Here the possibilities to prove the plausibility of fractal modeling with appropriate experimentation and rational reconstruction are also discussed. A conjecture is made that the brain vs. mind differentiation becomes possible, most probably, only with the imposition of appropriate symmetry groups implementing a flowing interface of features of local vs. global brain dynamics. (Series B)

Fractal Geometry

Mathematical Methods, Algorithms, Applications

Fractal Geometry

International authorities from Canada, Denmark, England, Germany, Russia and South Africa focus on research on fractal geometry and the best practices in software, theoretical mathematical algorithms, and analysis. They address the rich panoply of manifold applications of fractal geometry available for study and research in science and industry: i.e., remote sensing, mapping, texture creations, pattern recognition, image compression, aeromechanical systems, cryptography and financial analysis. Economically priced, this important and authoritative reference source for research and study cites over 230 references to the literature, copiously illustrated with over 320 diagrams and photographs. The book is published for The Institute of Mathematics and its Applications, co-sponsored with The Institute of Physics and The Institution of Electrical Engineers. Outlines research on fractal geometry and the best practices in software, theoretical mathematical algorithms, and analysis International authorities from around the world address the rich panoply of manifold applications of fractal geometry available for study and research in science and industry Addresses applications in key research fields of remote sensing, mapping, texture creations, pattern recognition, image compression, aeromechanical systems, cryptography and financial analysis

Fractals in Molecular Biophysics

Fractals in Molecular Biophysics

Historically, science has sought to reduce complex problems to their simplest components, but more recently it has recognized the merit of studying complex phenomena in situ. Fractal geometry is one such appealing approach, and this book discusses its application to complex problems in molecular biophysics. The book provides a detailed, unified treatment of fractal aspects of protein and structure dynamics, fractal reaction kinetics in biochemical systems, sequence correlations in DNA and proteins, and descriptors of chaos in enzymatic systems. In an area that has been slow to acknowledge the use of fractals, this is an important addition to the literature, offering a glimpse of the wealth of possible applications to complex problems.

Fractal Market Analysis

Applying Chaos Theory to Investment and Economics

Fractal Market Analysis

A leading pioneer in the field offers practical applications of this innovative science. Peters describes complex concepts in an easy-to-follow manner for the non-mathematician. He uses fractals, rescaled range analysis and nonlinear dynamical models to explain behavior and understand price movements. These are specific tools employed by chaos scientists to map and measure physical and now, economic phenomena.

Computational Structural Engineering

Proceedings of the International Symposium on Computational Structural Engineering, held in Shanghai, China, June 22–24, 2009

Computational Structural Engineering

Following the great progress made in computing technology, both in computer and programming technology, computation has become one of the most powerful tools for researchers and practicing engineers. It has led to tremendous achievements in computer-based structural engineering and there is evidence that current devel- ments will even accelerate in the near future. To acknowledge this trend, Tongji University, Vienna University of Technology, and Chinese Academy of Engine- ing, co-organized the International Symposium on Computational Structural En- neering 2009 in Shanghai (CSE’09). CSE’09 aimed at providing a forum for presentation and discussion of sta- of-the-art development in scientific computing applied to engineering sciences. Emphasis was given to basic methodologies, scientific development and engine- ing applications. Therefore, it became a central academic activity of the Inter- tional Association for Computational Mechanics (IACM), the European Com- nity on Computational Methods in Applied Sciences (ECCOMAS), The Chinese Society of Theoretical and Applied Mechanic, the China Civil Engineering So- ety, and the Architectural Society of China. A total of 10 invited papers, and around 140 contributed papers were p- sented in the proceedings of the symposium. Contributors of papers came from 20 countries around the world and covered a wide spectrum related to the compu- tional structural engineering.

Fractal Speech Processing

Fractal Speech Processing

Although widely employed in image processing, the use of fractal techniques and the fractal dimension for speech characterisation and recognition is a relatively new concept which is now receiving serious attention. This book represents the fruit of research carried out to develop novel fractal-based techniques for speech and audio signal processing. Much of this work is finding its way into practical commercial applications with Nokia Communications and other key organisations. The book starts with an introduction to speech processing and fractal geometry, setting the scene for the heart of the book where fractal techniques are described in detail with numerous applications and examples, and concluding with a chapter summing up the advantages and potential of these new techniques over conventional processing methods. A valuable reference for researchers, academics and practising engineers working in the field of audio signal processing and communications.