Quantum Fractals
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Quantum Fractals From Heisenberg S Uncertainty To Barnsley S Fractality
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Author : Arkadiusz Jadczyk
language : en
Publisher: World Scientific
Release Date : 2014-07-23
Quantum Fractals From Heisenberg S Uncertainty To Barnsley S Fractality written by Arkadiusz Jadczyk and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-23 with Science categories.
Starting with numerical algorithms resulting in new kinds of amazing fractal patterns on the sphere, this book describes the theory underlying these phenomena and indicates possible future applications. The book also explores the following questions:
The Geometry Of Fractals A New Perspective
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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-07-07
The Geometry Of Fractals A New Perspective written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-07 with Science categories.
Embark on a captivating journey into the realm of fractals, where intricate patterns and self-similarity unveil the hidden beauty and complexity of the natural world. This comprehensive guide delves into the mathematical foundations, applications, and cultural significance of fractals, offering a fresh perspective on these fascinating geometric structures. From the delicate branching of snowflakes to the mesmerizing spirals of seashells, fractals are found in abundance in nature, revealing a level of order within apparent chaos. Botanists, geologists, and meteorologists alike have discovered the fractal patterns that govern the growth of plants, the formation of mountains, and the behavior of clouds. This book takes you on an exploration of the history of fractals, tracing their origins from early mathematical investigations to the groundbreaking work of Benoit Mandelbrot, who brought fractals to the forefront of scientific study. Discover the mathematical concepts that underlie fractal geometry, including set theory, topology, and measure theory. Beyond their mathematical elegance, fractals have found practical applications in diverse fields. Computer scientists utilize fractals to generate realistic images and animations, while engineers harness their properties for signal processing and data compression. Fractals have also inspired new forms of art and music, captivating audiences with their intricate patterns and dynamic forms. This book is not just a scientific treatise; it is an invitation to appreciate the beauty and wonder of fractals. Whether you are a mathematician, a scientist, an artist, or simply someone curious about the world around you, you will find something to engage and inspire you within these pages. **Unveil the Secrets of Fractals:** * Explore the mathematical underpinnings of fractal geometry, including set theory, topology, and measure theory. * Delve into the history of fractals, from early investigations to the groundbreaking work of Benoit Mandelbrot. * Discover the diverse applications of fractals in fields such as computer graphics, image processing, and signal processing. * Appreciate the cultural significance of fractals in art, music, and literature. * Gain a deeper understanding of the beauty and complexity of the natural world through the lens of fractals. If you like this book, write a review on google books!
Quantum Fractals
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Author : Arkadiusz Jadczyk
language : en
Publisher: World Scientific Publishing Company Incorporated
Release Date : 2014
Quantum Fractals written by Arkadiusz Jadczyk and has been published by World Scientific Publishing Company Incorporated this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Science categories.
1. Introduction -- 2. What are quantum fractals? 2.1. Cantor set. 2.2. Iterated function systems. 2.3. Cantor set throughmatrix eigenvector. 2.4. Quantum iterated function systems. 2.5. Example: The "impossible" quantum fractal. 2.6. Action on the plane. 2.7 Lorentz group, SL(2,C), and relativistic aberration -- 3. Examples. 3.1. Hyperbolic quantum fractals. 3.2. Controlling chaotic behavior and fractal dimension. 3.3. Quantum fractals on n-spheres. 3.4. Algorithms for generating hyperbolic quantum fractals -- 4. Foundational questions. 4.1. Stochastic nature of quantum measurement processes. 4.2. Are there quantum jumps? 4.3. Bohmian mechanics. 4.4. Event enhanced quantum theory. 4.5. Ghirardi-Rimini-Weber spontaneous localization. 4.6. Heisenberg's uncertainty principle and quantum fractals. 4.7. Are quantum fractals real?
Fractal Space Time And Microphysics Towards A Theory Of Scale Relativity
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Author : Laurent Nottale
language : en
Publisher: World Scientific
Release Date : 1993-04-13
Fractal Space Time And Microphysics Towards A Theory Of Scale Relativity written by Laurent Nottale and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-04-13 with Science categories.
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.
Scaling Fractals And Wavelets
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Author : Patrice Abry
language : en
Publisher: John Wiley & Sons
Release Date : 2013-03-01
Scaling Fractals And Wavelets written by Patrice Abry and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-01 with Mathematics categories.
Scaling is a mathematical transformation that enlarges or diminishes objects. The technique is used in a variety of areas, including finance and image processing. This book is organized around the notions of scaling phenomena and scale invariance. The various stochastic models commonly used to describe scaling — self-similarity, long-range dependence and multi-fractals — are introduced. These models are compared and related to one another. Next, fractional integration, a mathematical tool closely related to the notion of scale invariance, is discussed, and stochastic processes with prescribed scaling properties (self-similar processes, locally self-similar processes, fractionally filtered processes, iterated function systems) are defined. A number of applications where the scaling paradigm proved fruitful are detailed: image processing, financial and stock market fluctuations, geophysics, scale relativity, and fractal time-space.
Fractals Of Brain Fractals Of Mind
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Author : Earl Mac Cormac
language : en
Publisher: John Benjamins Publishing
Release Date : 1996-06-28
Fractals Of Brain Fractals Of Mind written by Earl Mac Cormac and has been published by John Benjamins Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-06-28 with Psychology categories.
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)
Chaos Noise And Fractals
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Author : E. Roy Pike
language : en
Publisher: CRC Press
Release Date : 2020-08-26
Chaos Noise And Fractals written by E. Roy Pike and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-26 with Mathematics categories.
The study of nonlinear dynamical systems has been gathering momentum since the late 1950s. It now constitutes one of the major research areas of modern theoretical physics. The twin themes of fractals and chaos, which are linked by attracting sets in chaotic systems that are fractal in structure, are currently generating a great deal of excitement. The degree of structure robustness in the presence of stochastic and quantum noise is thus a topic of interest. Chaos, Noise and Fractals discusses the role of fractals in quantum mechanics, the influence of phase noise in chaos and driven optical systems, and the arithmetic of chaos. The book represents a balanced overview of the field and is a worthy addition to the reading lists of researchers and students interested in any of the varied, and sometimes bizarre, aspects of this intriguing subject.
Fractal Geometry And Dynamical Systems In Pure And Applied Mathematics Ii
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Author : David Carfi
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-10-24
Fractal Geometry And Dynamical Systems In Pure And Applied Mathematics Ii written by David Carfi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-24 with Mathematics categories.
This volume contains the proceedings from three conferences: the PISRS 2011 International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics, held November 8-12, 2011 in Messina, Italy; the AMS Special Session on Fractal Geometry in Pure and Applied Mathematics, in memory of Benoît Mandelbrot, held January 4-7, 2012, in Boston, MA; and the AMS Special Session on Geometry and Analysis on Fractal Spaces, held March 3-4, 2012, in Honolulu, HI. Articles in this volume cover fractal geometry and various aspects of dynamical systems in applied mathematics and the applications to other sciences. Also included are articles discussing a variety of connections between these subjects and various areas of physics, engineering, computer science, technology, economics and finance, as well as of mathematics (including probability theory in relation with statistical physics and heat kernel estimates, geometric measure theory, partial differential equations in relation with condensed matter physics, global analysis on non-smooth spaces, the theory of billiards, harmonic analysis and spectral geometry). The companion volume (Contemporary Mathematics, Volume 600) focuses on the more mathematical aspects of fractal geometry and dynamical systems.
Russian Fractals In Indigenous Artifacts
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Author : Abdul Karim Bangura
language : en
Publisher: Vernon Press
Release Date : 2025-06-22
Russian Fractals In Indigenous Artifacts written by Abdul Karim Bangura and has been published by Vernon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-22 with Art categories.
This book is the first comprehensive work on Russian Fractals in indigenous artifacts. While existing works focus on universal phenomena, such as liquid crystal or finance, none explore the intersection between Fractals and Russia. 'Russian Fractals in Indigenous Artifacts' therefore investigates how indigenous Russian cultures have a wonderful Fractal heritage that was originally tied to socially just and ecologically sustainable social practices, including those of indigenous northern groups such as the Yakut. Fractal designs originally allowed unalienated value, both human and nonhuman, to be visible, thereby enabling just and sustainable living. This book also examines how the tsarist elite encouraged the creation of unique creative masterpieces, developing and strengthening traditional crafts and art of indigenous people—hence, Fabergé, or imperial architecture. Today, the challenge for contemporary Russia is to reestablish the relationship between the social and ecological sustainability of indigenous cultures and practices, for which we can now provide modeling and analysis. Lay attempts at this have only limited success, as they have based the attempts on a purely religious basis, which recognizes the ecological aspects but often succumbs to authoritarian nationalism. However, the freely accession of indigenous peoples to Russia for the sake of national liberation has had a positive effect on enriching them with spirituality and creativity by Fractal artifacts through friendly exchanges with one another. In 'Russian Fractals in Indigenous Artifacts,' Bangura and Zhigun express why there is a need for a forward-thinking Fractal renaissance in Russia, bringing together contemporary computational and scientific analyses with these ecologically and socially sustainable traditions.
Fractals In Engineering Theoretical Aspects And Numerical Approximations
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Author : Maria Rosaria Lancia
language : en
Publisher: Springer Nature
Release Date : 2021-03-17
Fractals In Engineering Theoretical Aspects And Numerical Approximations written by Maria Rosaria Lancia and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-17 with Mathematics categories.
Fractal structures or geometries currently play a key role in all models for natural and industrial processes that exhibit the formation of rough surfaces and interfaces. Computer simulations, analytical theories and experiments have led to significant advances in modeling these phenomena across wild media. Many problems coming from engineering, physics or biology are characterized by both the presence of different temporal and spatial scales and the presence of contacts among different components through (irregular) interfaces that often connect media with different characteristics. This work is devoted to collecting new results on fractal applications in engineering from both theoretical and numerical perspectives. The book is addressed to researchers in the field.