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The Fractal Geometry of the Brain by Antonio Di Ieva Pdf
Reviews the most intriguing applications of fractal analysis in neuroscience with a focus on current and future potential, limits, advantages, and disadvantages. Will bring an understanding of fractals to clinicians and researchers also if they do not have a mathematical background, and will serve as a good tool for teaching the translational applications of computational models to students and scholars of different disciplines. This comprehensive collection is organized in four parts: (1) Basics of fractal analysis; (2) Applications of fractals to the basic neurosciences; (3) Applications of fractals to the clinical neurosciences; (4) Analysis software, modeling and methodology.
Fractals of Brain, Fractals of Mind by Earl Mac Cormac,Maxim I. Stamenov Pdf
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)
The Fractal Brain Theory, or the Symmetry, Self Similarity and Recursivity Theory of Brain and Mind, is a Revolutionary new way of looking at the nature of intelligence and also genomics. It is the key to a powerful and new kind of Recursively Self Modifying Artificial Intelligence. Wai H. Tsang presents an exciting new synthesis of all things psychological, linguistic, neuroscientific, genomic, evolutionary, informatic, computational, complex and fractal. Dealing with the most central puzzles of mind science and AI, and weaving in some of the most fundamental concepts in mathematics such as symmetry, geometry, functions, discrete maths and formal axiomatic systems. This book presents nothing less than a seamless unified theory of Brain, Mind, Artificial Intelligence, Functional Genomics, Ontogenesis and Evolution. Also covering topics such as the quest for the Perfect & Universal Language, Recursively Self Modifying Algorithms, Super Intelligence & Technological Singularity.
Fractal Geometry in Biological Systems by Philip M. Iannaccone,Mustafa Khokha Pdf
Fractal Geometry in Biological Systems was written by the leading experts in the field of mathematics and the biological sciences together. It is intended to inform researchers in the bringing about the fundamental nature of fractals and their widespread appearance in biological systems. The chapters explain how the presence of fractal geometry can be used in an analytical way to predict outcomes in systems, to generate hypotheses, and to help design experiments. The authors make the mathematics accessible to a wide audience and do not assume prior experience in this area.
Brainfilling Curves - A Fractal Bestiary by Jeffrey Ventrella Pdf
* A lovingly-crafted visual expedition, lead by a lifelong fractal wizard with an obsession for categorizing fractal species * Hundreds of beautiful color images * An in-depth taxonomy of Koch-constructed Fractal Curves * An intuitive introduction to Koch construction * A must-read for anyone interested in fractal geometry
The Beauty of Fractals by Heinz-Otto Peitgen,Peter H. Richter Pdf
Now approaching its tenth year, this hugely successful book presents an unusual attempt to publicise the field of Complex Dynamics. The text was originally conceived as a supplemented catalogue to the exhibition "Frontiers of Chaos", seen in Europe and the United States, and describes the context and meaning of these fascinating images. A total of 184 illustrations - including 88 full-colour pictures of Julia sets - are suggestive of a coffee-table book. However, the invited contributions which round off the book lend the text the required formality. Benoit Mandelbrot gives a very personal account, in his idiosyncratic self-centred style, of his discovery of the fractals named after him and Adrien Douady explains the solved and unsolved problems relating to this amusingly complex set.
"This engaging short book is both a mathematician's reflections on grief and a mathematically-informed theory of grieving. Michael Frame retired in 2016 as a professor of mathematics at Yale University, where students fought for a place in his course on fractal geometry. Students appreciated his use of accessible examples- decalcomania paintings and illustrations of cats to explain mathematical concepts-and stories of his work and friendship with the founder of fractal geometry, Benoit Mandelbrot. In this book, he continues his work to make mathematics accessible, using his experiences with grief to give uninitiated readers insights into advanced topics in geometry. The inability to repeat an "aha moment", when you first learn something, is one type of grief that Frame examines. He connects this irreversible loss of perspective to more consequential grief-loss of a career or of a loved one-and explains ways he has thought mathematically about grieving and coping with grief. Frame is an authentic and sympathetic voice. He retired after discovering that he had an inoperable brain tumor and feeling the effects of his cancer on his teaching career. His connections and insights make this a timely and moving book in our time of personal and collective grief"--
Fractal geometry, together with the broader fields of nonlinear dynamics and complexity, represented a large segment of modern science at the end of the 20th century. Penetration of the resulting new paradigms into practically all academic disciplines has confirmed the fundamental assertion of universal formalism common to a wide range of human endeavors.This book contains an extended article by B B Mandelbrot, reviewing his contribution to fractal geometry and outlining some unsolved problems, with illustrations especially of finance and physics. It covers a range of multidisciplinary topics ? from the biology of aging, through the self-similar shape of plants, image decompression and solar magnetic fields, to sound reflection in the street. The book is a treasure trove for innovative researchers working in fields related to fractal geometry.The proceedings have been selected for coverage in: ? Index to Scientific & Technical Proceedings? (ISTP? / ISI Proceedings)? Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)? CC Proceedings ? Engineering & Physical Sciences
Struck by Genius by Jason Padgett,Maureen Seaberg Pdf
From head trauma to scientific wonder—a “deeply absorbing . . . fascinating” true story of acquired savant syndrome (Entertainment Weekly). Twelve years ago, Jason Padgett had never made it past pre-algebra. But a violent mugging forever altered the way his brain worked. It turned an ordinary math-averse student into an extraordinary young man with a unique gift to see the world as no one else does: water pours from the faucet in crystalline patterns, numbers call to mind distinct geometric shapes, and intricate fractal patterns emerge from the movement of tree branches, revealing the intrinsic mathematical designs hidden in the objects around us. As his ability to understand physics skyrocketed, the “accidental genius” developed the astonishing ability to draw the complex geometric shapes he saw everywhere. Overcoming huge setbacks and embracing his new mind, Padgett “gained a vision of the world that is as beautiful as it is challenging.” Along the way he fell in love, found joy in numbers, and spent plenty of time having his head examined (The New York Times Book Review). Illustrated with Jason’s stunning, mathematically precise artwork, his singular story reveals the wondrous potential of the human brain, and “an incredible phenomenon which points toward dormant potential—a little Rain Man perhaps—within us all” (Darold A. Treffert, MD, author of Islands of Genius: The Bountiful Mind of the Autistic, Acquired, and Sudden Savant). “A tale worthy of Ripley’s Believe It or Not! . . . This memoir sends a hopeful message to families touched by brain injury, autism, or neurological damage from strokes.” —Booklist “How extraordinary it is to contemplate the bizarre gifts that might lie within all of us.” —People
Fractals in Biology and Medicine by Gabriele A. Losa,Danilo Merlini,Theo F. Nonnenmacher,Ewald R. Weibel Pdf
In March 2000 leading scientists gathered at the Centro Seminariale Monte Verità, Ascona, Switzerland, for the Third International Symposium on "Fractals 2000 in Biology and Medicine". This interdisciplinary conference provided stimulating contributions from the very topical field Fractals in Biology and Medicine. This volume highlights the growing power and efficacy of the fractal geometry in understanding how to analyze living phenomena and complex shapes.
Evolution of the Brain, Cognition, and Emotion in Vertebrates by Shigeru Watanabe,Michel A Hofman,Toru Shimizu Pdf
This book presents a new view on the evolution of the brain, cognition, and emotion. Around a half-century ago, Professor Harry Jerison published a seminal book entitled Evolution of the Brain and Intelligence. Since then, there has been a series of dramatic methodological and conceptual changes which have led to many new insights into the understanding of brain evolution and cognition. This book is particularly focused on three significant aspects of such changes. First, taking advantage of a new integrated approach called evolutionary developmental biology or Evo/Devo, researchers have started to look into vertebrate brain evolution from the developmental perspective. Second, comparative neuroanatomists have accumulated a large amount of information about the brains of diverse animal groups to refute the old-fashioned idea that vertebrate brains evolved linearly from non-mammals to mammals. Third, comparative behavioral studies have demonstrated that sophisticated cognition and emotion are not unique to some primates but are also found in many non-primate and even non-mammalian species. This work will appeal to a wide readership in such fields as neuroscience, cognitive science, and behavioral science.
Evolution of the Primate Brain by Michel A. Hofman,Dean Falk Pdf
This volume of Progress in Brain Research provides a synthetic source of information about state-of-the-art research that has important implications for the evolution of the brain and cognition in primates, including humans. This topic requires input from a variety of fields that are developing at an unprecedented pace: genetics, developmental neurobiology, comparative and functional neuroanatomy (at gross and microanatomical levels), quantitative neurobiology related to scaling factors that constrain brain organization and evolution, primate palaeontology (including paleoneurology), paleo-anthropology, comparative psychology, and behavioural evolutionary biology. Written by internationally-renowned scientists, this timely volume will be of wide interest to students, scholars, science journalists, and a variety of experts who are interested in keeping track of the discoveries that are rapidly emerging about the evolution of the brain and cognition. Written by internationally renowned scientists, this timely volume will be of wide interest to students, scholars, science journalists, and a variety of experts who are interested in keeping track of the discoveries that are rapidly emerging about the evolution of the brain and cognition
Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems by Yeliz Karaca,Dumitru Baleanu,Yu-Dong Zhang,Osvaldo Gervasi,Majaz Moonis Pdf
Multi-Chaos, Fractal and Multi-Fractional Artificial Intelligence of Different Complex Systems addresses different uncertain processes inherent in the complex systems, attempting to provide global and robust optimized solutions distinctively through multifarious methods, technical analyses, modeling, optimization processes, numerical simulations, case studies as well as applications including theoretical aspects of complexity. Foregrounding Multi-chaos, Fractal and Multi-fractional in the era of Artificial Intelligence (AI), the edited book deals with multi- chaos, fractal, multifractional, fractional calculus, fractional operators, quantum, wavelet, entropy-based applications, artificial intelligence, mathematics-informed and data driven processes aside from the means of modelling, and simulations for the solution of multifaceted problems characterized by nonlinearity, non-regularity and self-similarity, frequently encountered in different complex systems. The fundamental interacting components underlying complexity, complexity thinking, processes and theory along with computational processes and technologies, with machine learning as the core component of AI demonstrate the enabling of complex data to augment some critical human skills. Appealing to an interdisciplinary network of scientists and researchers to disseminate the theory and application in medicine, neurology, mathematics, physics, biology, chemistry, information theory, engineering, computer science, social sciences and other far-reaching domains, the overarching aim is to empower out-of-the-box thinking through multifarious methods, directed towards paradoxical situations, uncertain processes, chaotic, transient and nonlinear dynamics of complex systems. Constructs and presents a multifarious approach for critical decision-making processes embodying paradoxes and uncertainty. Includes a combination of theory and applications with regard to multi-chaos, fractal and multi-fractional as well as AI of different complex systems and many-body systems. Provides readers with a bridge between application of advanced computational mathematical methods and AI based on comprehensive analyses and broad theories.
Fractal analysis has entered a new era. The applications to different areas of knowledge have been surprising. Benoit Mandelbrot, creator of fractal geometry, would have been surprised by the use of fractal analysis presented in this book. Here we present the use of fractal geometry, in particular, fractal analysis in two sciences: health sciences and social sciences and humanities. Part 1 is Health Science. In it, we present the latest advances in cardiovascular signs, kidney images to determine cancer growth, EEG signals, magnetoencephalography signals, and photosensitive epilepsy. We show how it is possible to produce ultrasonic lenses or even sound focusing. In Part 2, we present the use of fractal analysis in social sciences and humanities. It includes anthropology, hierarchical scaling, human settlements, language, fractal dimension of different cultures, cultural traits, and Mesoamerican complexity. And in Part 3, we present a few useful tools for fractal analysis, such as graphs and correlation, self-affine and self-similar graphs, and correlation function. It is impossible to picture today's research without fractal geometry.
