Fractal Patterns With Matlab
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Fractal Patterns With Matlab
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Author : Santo Banerjee
language : en
Publisher: Springer Nature
Release Date : 2024-01-01
Fractal Patterns With Matlab written by Santo Banerjee and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-01 with Mathematics categories.
This book presents the iterative beauty of fractals and fractal functions graphically with the aid of MATLAB programming. The fractal images generated using the MATLAB codes provide visual delight and highly encourage the fractal lovers for creative thinking. The book compiles five cutting-edge research chapters, each with state-of-the art fractal illustrations. It starts with the fundamental theory for the construction of fractal sets via the deterministic iteration algorithm. Incorporating the theoretical base, fractal illustrations of elementary fractal sets are provided with the explicit MATLAB code. The book gives examples of MATLAB codes to present the fractal surfaces. This book is contributed to all the research beginners as well as the professionals on the field of fractal analysis. As it covers basic fractals like Sierpinski triangle to advanced fractal functions with explicit MATLAB code, the presented fractal illustrations hopefully benefit even the non-field readers. The book is a useful course to all the research beginners on the fractal and fractal-related fields.
Interplay Of Fractals And Complexity In Mathematical Modelling And Physical Patterns
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Author : Santo Banerjee
language : en
Publisher: Springer Nature
Release Date : 2025-03-07
Interplay Of Fractals And Complexity In Mathematical Modelling And Physical Patterns written by Santo Banerjee and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-07 with Science categories.
This book presents selected, peer-reviewed contributions from the International Symposium on Mathematical Analysis of Fractals and Dynamical Systems—2023 (ISMAFDS - 2023), held at the Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Tamil Nadu in India during August 24-25, 2023. It offers readers an array of captivating connections between fractal theory and nonlinear dynamics across various physics sub-domains and mathematical modeling. Fractal geometry has been developed to describe irregular natural objects that defy characterization using Euclidean geometry. Fractal techniques, such as fractal dimension and fractal functions, prove effective in mathematically modeling real-world phenomena and forecasting future consequences. The impact of fractal theory on physical sciences is widely recognized, as natural phenomena frequently exhibit fractal structures. These new concepts revolutionize our understanding of the large-scale properties of matter distribution in the universe. The book aims to familiarize readers with recent developments in common fractal patterns found in statistical physics, quantum physics, and plasma physics. Furthermore, it highlights the relationship between fractals and nonlinear dynamics through innovative approaches in mathematical modeling. This publication caters to professionals in mathematics, physics, and computer science, and also serves as a helpful resource for non-specialists seeking to comprehend fractal and nonlinear dynamics concepts. It offers valuable applications for researchers in both pure and applied backgrounds of physics and engineering.
The Fractal Geometry Of The Brain
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Author : Antonio Di Ieva
language : en
Publisher: Springer Nature
Release Date : 2024-03-12
The Fractal Geometry Of The Brain written by Antonio Di Ieva and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-03-12 with Science categories.
The new edition of the highly popular, The Fractal Geometry of the Brain, reviews the most intriguing applications of fractal analysis in neuroscience with a focus on current and future potential, limits, advantages, and disadvantages. It brings an understanding of fractals to clinicians and researchers even if they do not have a mathematical background, and it serves as a valuable tool for teaching the translational applications of computational fractal-based models to both students and scholars. As a consequence of the novel research developed at Professor Di Ieva's laboratory and other centers around the world, the second edition will explore the use of computational fractal-based analysis in many clinical disciplines and different fields of research, including neurology and neurosurgery, neuroanatomy and psychology, magnetoencephalography (MEG), eye-tracking devices (for the fractal computational characterization of “scanpaths”),deep learning in image analysis, radiomics for the characterization of brain MRIs, characterization of neuropsychological and psychiatric diseases and traits, signal complexity analysis in time series, and functional MRI, amongst others.
Exploratory Data Analysis With Matlab
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Author : Wendy L. Martinez
language : en
Publisher: CRC Press
Release Date : 2017-08-07
Exploratory Data Analysis With Matlab written by Wendy L. Martinez and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-07 with Mathematics categories.
Praise for the Second Edition: "The authors present an intuitive and easy-to-read book. ... accompanied by many examples, proposed exercises, good references, and comprehensive appendices that initiate the reader unfamiliar with MATLAB." —Adolfo Alvarez Pinto, International Statistical Review "Practitioners of EDA who use MATLAB will want a copy of this book. ... The authors have done a great service by bringing together so many EDA routines, but their main accomplishment in this dynamic text is providing the understanding and tools to do EDA. —David A Huckaby, MAA Reviews Exploratory Data Analysis (EDA) is an important part of the data analysis process. The methods presented in this text are ones that should be in the toolkit of every data scientist. As computational sophistication has increased and data sets have grown in size and complexity, EDA has become an even more important process for visualizing and summarizing data before making assumptions to generate hypotheses and models. Exploratory Data Analysis with MATLAB, Third Edition presents EDA methods from a computational perspective and uses numerous examples and applications to show how the methods are used in practice. The authors use MATLAB code, pseudo-code, and algorithm descriptions to illustrate the concepts. The MATLAB code for examples, data sets, and the EDA Toolbox are available for download on the book’s website. New to the Third Edition Random projections and estimating local intrinsic dimensionality Deep learning autoencoders and stochastic neighbor embedding Minimum spanning tree and additional cluster validity indices Kernel density estimation Plots for visualizing data distributions, such as beanplots and violin plots A chapter on visualizing categorical data
Fractal Patterns In Nonlinear Dynamics And Applications
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Author : Santo Banerjee
language : en
Publisher: CRC Press
Release Date : 2020-03-27
Fractal Patterns In Nonlinear Dynamics And Applications written by Santo Banerjee and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-27 with Mathematics categories.
Most books on fractals focus on deterministic fractals as the impact of incorporating randomness and time is almost absent. Further, most review fractals without explaining what scaling and self-similarity means. This book introduces the idea of scaling, self-similarity, scale-invariance and their role in the dimensional analysis. For the first time, fractals emphasizing mostly on stochastic fractal, and multifractals which evolves with time instead of scale-free self-similarity, are discussed. Moreover, it looks at power laws and dynamic scaling laws in some detail and provides an overview of modern statistical tools for calculating fractal dimension and multifractal spectrum.
Data Analysis In The Earth Sciences Using Matlab
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Author : Gerard V. Middleton
language : en
Publisher:
Release Date : 2000
Data Analysis In The Earth Sciences Using Matlab written by Gerard V. Middleton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Computers categories.
Exploring the application of MATLAB to the various earth sciences, this text presents an integrated, step-by-step introduction to data analysis and the use of MATLAB.
Fractal Analysis For Natural Hazards
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Author : Giuseppe Cello
language : en
Publisher: Geological Society of London
Release Date : 2006
Fractal Analysis For Natural Hazards written by Giuseppe Cello and has been published by Geological Society of London this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
In the Earth Sciences, the concept of fractals and scale invariance is well-recognized in many natural objects. However, the use of fractals for spatial and temporal analyses of natural hazards has been less used (and accepted) in the Earth Sciences. This book brings together twelve contributions that emphasize the role of fractal analyses in natural hazard research, including landslides, wildfires, floods, catastrophic rock fractures and earthquakes. A wide variety of spatial and temporal fractal-related approaches and techniques are applied to 'natural' data, experimental data, and computer simulations. These approaches include probabilistic hazard analysis, cellular-automata models, spatial analyses, temporal variability, prediction, and self-organizing behaviour. The main aims of this volume are to present current research on fractal analyses as applied to natural hazards, and to stimulate the curiosity of advanced Earth Science students and researchers in the use of fractals analyses for the better understanding of natural hazards.
Fractal Analyses Statistical And Methodological Innovations And Best Practices
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Author : John G. Holden
language : en
Publisher: Frontiers E-books
Release Date : 2013-06-03
Fractal Analyses Statistical And Methodological Innovations And Best Practices written by John G. Holden and has been published by Frontiers E-books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-03 with categories.
Many statistical and methodological developments regarding fractal analyses have appeared in the scientific literature since the publication of the seminal texts introducing Fractal Physiology. However, the lion’s share of more recent work is distributed across many outlets and disciplines, including aquatic sciences, biology, computer science, ecology, economics, geology, mathematics, medicine, neuroscience, physics, physiology, psychology, and others. The purpose of this special topic is to solicit submissions regarding fractal and nonlinear statistical techniques from experts that span a wide range of disciplines. The articles will aggregate extensive cross-discipline expertise into comprehensive and broadly applicable resources that will support the application of fractal methods to physiology and related disciplines. The articles will be organized with respect to a continuum defined by the characteristics of the empirical measurements a given analysis is intended to confront. At one end of the continuum are stochastic techniques directed at assessing scale invariant but stochastic data. The next step in the continuum concerns self-affine random fractals and methods directed at systems that entail scale-invariant or 1/f patterns or related patterns of temporal and spatial fluctuation. Analyses directed at (noisy) deterministic signals correspond to the final stage of the continuum that relates the statistical treatments of nonlinear stochastic and deterministic signals. Each section will contain introductory articles, advanced articles, and application articles so readers with any level of expertise with fractal methods will find the special topic accessible and useful. Example stochastic methods include probability density estimation for the inverse power-law, the lognormal, and related distributions. Articles describing statistical issues and tools for discriminating different classes of distributions will be included. An example issue is distinguishing power-law distributions from exponential distributions. Modeling issues and problems regarding statistical mimicking will be addressed as well. The random fractal section will present introductions to several one-dimensional monofractal time-series analysis. Introductory articles will be accompanied by advanced articles that will supply comprehensive treatments of all the key fractal time series methods such as dispersion analysis, detrended fluctuation analysis, power spectral density analysis, and wavelet techniques. Box counting and related techniques will be introduced and described for spatial analyses of two and three dimensional domains as well. Tutorial articles on the execution and interpretation of multifractal analyses will be solicited. There are several standard wavelet based and detrended fluctuation based methods for estimating a multifractal spectrum. We hope to include articles that contrast the different methods and compare their statistical performance as well. The deterministic methods section will include articles that present methods of phase space reconstruction, recurrence analysis, and cross-recurrence analysis. Recurrence methods are widely applicable, but motivated by signals that contain deterministic patterns. Nonetheless recent developments such as the analysis of recurrence interval scaling relations suggest applicability to fractal systems. Several related statistical procedures will be included in this section. Examples include average mutual information statistics and false nearest neighbor analyses.
Fractal And Multifractal Facets In The Structure And Dynamics Of Physiological Systems And Applications To Homeostatic Control Disease Diagnosis And Integrated Cyber Physical Platforms
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Author : Paul Bogdan
language : en
Publisher: Frontiers Media SA
Release Date : 2020-06-25
Fractal And Multifractal Facets In The Structure And Dynamics Of Physiological Systems And Applications To Homeostatic Control Disease Diagnosis And Integrated Cyber Physical Platforms written by Paul Bogdan and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-25 with categories.
Widespread chronic diseases (e.g., heart diseases, diabetes and its complications, stroke, cancer, brain diseases) constitute a significant cause of rising healthcare costs and pose a significant burden on quality-of-life for many individuals. Despite the increased need for smart healthcare sensing systems that monitor / measure patients’ body balance, there is no coherent theory that facilitates the modeling of human physiological processes and the design and optimization of future healthcare cyber-physical systems (HCPS). The HCPS are expected to mine the patient’s physiological state based on available continuous sensing, quantify risk indices corresponding to the onset of abnormality, signal the need for critical medical intervention in real-time by communicating patient’s medical information via a network from individual to hospital, and most importantly control (actuate) vital health signals (e.g., cardiac pacing, insulin level, blood pressure) within personalized homeostasis. To prevent health complications, maintain good health and/or avoid fatal conditions calls for a cross-disciplinary approach to HCPS design where recent statistical-physics inspired discoveries done by collaborations between physicists and physicians are shared and enriched by applied mathematicians, control theorists and bioengineers. This critical and urgent multi-disciplinary approach has to unify the current state of knowledge and address the following fundamental challenges: One fundamental challenge is represented by the need to mine and understand the complexity of the structure and dynamics of the physiological systems in healthy homeostasis and associated with a disease (such as diabetes). Along the same lines, we need rigorous mathematical techniques for identifying the interactions between integrated physiologic systems and understanding their role within the overall networking architecture of healthy dynamics. Another fundamental challenge calls for a deeper understanding of stochastic feedback and variability in biological systems and physiological processes, in particular, and for deciphering their implications not only on how to mathematically characterize homeostasis, but also on defining new control strategies that are accounting for intra- and inter-patient specificity – a truly mathematical approach to personalized medicine. Numerous recent studies have demonstrated that heart rate variability, blood glucose, neural signals and other interdependent physiological processes demonstrate fractal and non-stationary characteristics. Exploiting statistical physics concepts, numerous recent research studies demonstrated that healthy human physiological processes exhibit complex critical phenomena with deep implications for how homeostasis should be defined and how control strategies should be developed when prolonged abnormal deviations are observed. In addition, several efforts have tried to connect these fractal characteristics with new optimal control strategies that implemented in medical devices such as pacemakers and artificial pancreas could improve the efficiency of medical therapies and the quality-of-life of patients but neglecting the overall networking architecture of human physiology. Consequently, rigorously analyzing the complexity and dynamics of physiological processes (e.g., blood glucose and its associated implications and interdependencies with other physiological processes) represents a fundamental step towards providing a quantifiable (mathematical) definition of homeostasis in the context of critical phenomena, understanding the onset of chronic diseases, predicting deviations from healthy homeostasis and developing new more efficient medical therapies that carefully account for the physiological complexity, intra- and inter-patient variability, rather than ignoring it. This Research Topic aims to open a synergetic and timely effort between physicians, physicists, applied mathematicians, signal processing, bioengineering and biomedical experts to organize the state of knowledge in mining the complexity of physiological systems and their implications for constructing more accurate mathematical models and designing QoL-aware control strategies implemented in the new generation of HCPS devices. By bringing together multi-disciplinary researchers seeking to understand the many aspects of human physiology and its complexity, we aim at enabling a paradigm shift in designing future medical devices that translates mathematical characteristics in predictable mathematical models quantifying not only the degree of homeostasis, but also providing fundamentally new control strategies within the personalized medicine era.
Matlab For Engineers
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Author : Holly Moore
language : en
Publisher: Prentice Hall
Release Date : 2009
Matlab For Engineers written by Holly Moore and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Computers categories.
MATLAB for Engineers, 2eis ideal for Freshman or Introductory courses in Engineering and Computer Science. With a hands-on approach and focus on problem solving, this introduction to the powerful MATLAB computing language is designed for students with only a basic college algebra background. Numerous examples are drawn from a range of engineering disciplines, demonstrating MATLAB’s applications to a broad variety of problems. Note: This book is included in Prentice Hall’sESource series. ESource allows professors to select the content appropriate for their freshman/first-year engineering course. Professors can adopt the published manuals as is or use ESource’s websitewww.prenhall.com/esourceto view and select the chapters they need, in the sequence they want. The option to add their own material or copyrighted material from other publishers also exists.