♥ Book Title : The Fractal Geometry of Nature
☯ Full Synopsis : "Three classic fractals, tamed. Galaxies and eddies. Scaling fractals. Nonscaling fractals. Self-mapping fractals. Randomness. Stratified random fractals. Fractional brown fractals. A book-within-the-book, in color. Random tremas; texture. Miscellany. Of men and ideas."Article| Benoit B. Mandelbrot| Statement ..."
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♥ Book Title : Measure, Topology, and Fractal Geometry
☯ Full Synopsis : "Based on a course given to talented high-school students at Ohio University in 1988, this book is essentially an advanced undergraduate textbook about the mathematics of fractal geometry. It nicely bridges the gap between traditional books on topology/analysis and more specialized treatises on fractal geometry. The book treats such topics as metric spaces, measure theory, dimension theory, and even some algebraic topology. It takes into account developments in the subject matter since 1990. Sections are clear and focused. The book contains plenty of examples, exercises, and good illustrations of fractals, including 16 color plates."Article| Gerald Edgar| Statement ..."
♥ Book Title : Fractals in the Earth Sciences
☯ Full Synopsis : "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 Many of these ideas will grow and inspire further work, others will be superseded by new observations and insights, most probably with future contributions by the authors of these chapters."Article| C.C. Barton, P.R. La Pointe| Statement ..."
♥ Book Title : Fractals, Graphics, and Mathematics Education
☯ Full Synopsis : "Teaching resources for use with courses on fractal geometry, lecturers and interested readers."Article| Michael Frame, Benoit Mandelbrot| Statement ..."
♥ Book Title : Fractal Geometry in Architecture and Design
☯ Full Synopsis : "na broad sense Design Science is the grammar of a language of images Irather than of words. Modern communication techniques enable us to transmit and reconstitute images without needing to know a specific verbal sequence language such as the Morse code or Hungarian. International traffic signs use international image symbols which are not specific to any particular verbal language. An image language differs from a verbal one in that the latter uses a linear string of symbols, whereas the former is multi dimensional. Architectural renderings commonly show projections onto three mutual ly perpendicular planes, or consist of cross sections at different altitudes capa ble of being stacked and representing different floor plans. Such renderings make it difficult to imagine buildings comprising ramps and other features which disguise the separation between floors, and consequently limit the cre ative process of the architect. Analogously, we tend to analyze natural struc tures as if nature had used similar stacked renderings, rather than, for instance, a system of packed spheres, with the result that we fail to perceive the system of organization determining the form of such structures. Perception is a complex process. Our senses record; they are analogous to audio or video devices. We cannot, however, claim that such devices perceive."Article| Carl Bovill| Statement ..."
♥ Book Title : The (Mis)Behaviour of Markets
☯ Full Synopsis : "This international bestseller, which foreshadowed a market crash, explains why it could happen again if we don't act now. Fractal geometry is the mathematics of roughness: how to reduce the outline of a jagged leaf or static in a computer connection to a few simple mathematical properties. With his fractal tools, Mandelbrot has got to the bottom of how financial markets really work. He finds they have a shifting sense of time and wild behaviour that makes them volatile, dangerous - and beautiful. In his models, the complex gyrations of the FTSE 100 and exchange rates can be reduced to straightforward formulae that yield a much more accurate description of the risks involved."Article| Benoit B. Mandelbrot, Richard L. Hudson| Statement ..."
♥ Book Title : Benoit Mandelbrot
☯ Full Synopsis : "This is a collection of articles, many written by people who worked with Mandelbrot, memorializing the remarkable breadth and depth of his work in science and the arts. Contributors include mathematicians, physicists, biologists, economists, and engineers, as expected; and also artists, musicians, teachers, an historian, an architect, a filmmaker, and a comic. Some articles are quite technical, others entirely descriptive. All include stories about Benoit. Also included are chapters on fractals and music by Charles Wuorinen and by Harlan Brothers, on fractals and finance by Richard Hudson and by Christian Walter, on fractal invisibility cloaks by Nathan Cohen, and a personal reminiscence by Aliette Mandelbrot. While he is known most widely for his work in mathematics and in finance, Benoit influenced almost every field of modern intellectual activity. No other book captures the breadth of all of Benoit's accomplishments. Contents:Watching Benoit at Work (Aliette Mandelbrot)Benoit Mandelbrot: Nor Does Lightning Travel in a Straight Line (Michael Frame)Irregularities and Scaling in Signal and Image Processing: Multifractal Analysis (Patrice Abry, Stéphane Jaffard, Herwig Wendt)Three-Dimensional Fractal Homeomorphisms (Michael F Barnsley and Brendan Harding)Mandelbrot's Cascades: A Legendary Destiny (Julien Barral and Jacques Peyrière)Benoit Mandelbrot and Art (Javier Barrallo)The Nature of Fractal Music (Harlan J Brothers)Fractal Antenna and Fractal Resonator Primer (Nathan Cohen)Fractal-Based Wideband Invisibility Cloak (Nathan Cohen, Obinna Okoro, Dan Earle, Phil Salkind, Barry Unger, Sean Yen, Daniel McHugh, Stefan Polterzycki and A J Shelman-Cohen)From Fractional Brownian Motion to Multifractional and Multistable Motion (Kenneth Falconer)Watching the Markets Misbehave (Richard L Hudson)Partition Zeta Functions, multifractal Spectra, and Tapestries of Complex Dimensions (Kate E Ellis, Michel L Lapidus, Michael C Mackenzie and John A Rock)Benoit Mandelbrot, Films, and Me: A Tribute (Nigel Lesmoir-Gordon)Fractals and Humor (Demetri Martin)Multifractal Measures of Time Series: Curvature Surfaces of ƒ(α) Curves (William Martino and Michael Frame)Benoit Mandelbrot, Educator (Nial Neger and Harlan J Brothers)The Art of Roughness (Emer O'Daly)Long-Range Dependence of the Two-Dimensional Ising Model at Critical Temperature (Vladas Pipiras and Murad S Taqqu)Benoit Mandelbrot, W H Freeman, and the Launch of The Fractal Geometry of Nature (Peter Renz)Math and Physics: Lévy Flights and Drives (Michael Shlesinger)Benoit Mandelbrot in Finance (Christian Walter)How Benoit Mandelbrot Changed My Thinking about Biological Form (Ewald R Weibel)Entropic Origin of Allometry Relations (Bruce J West and Damien West)Music and Fractals (Charles Wuorinen)Stories about BenoitSome Final Thoughts (Michael Frame) Readership: People interested in the life work of Benoit Mandelbrot. While the technical articles will be accessible mainly to scientists, the range of chapters provides material of interest to a wide range of readers. The audience range from the general public for some parts, through high school and college teachers, to research scientists. Key Features:The chapters are by people who worked directly with Benoit, thus containing some personal stories about those collaborationsChapters range from technical expositions of complex fractal dimensions, through descriptions of practical applications in chemical and electrical engineering, to stories about working with Benoit on a film projectChapters on fractals in education will be of interest to mathematics teachers, the largest group of people who use fractalsKeywords:Nonlinear Science;Complex Systems"Article| Michael Frame, Nathan Cohen| Statement ..."
♥ Book Title : The Colours of Infinity
☯ Full Synopsis : "A geometry able to include mountains and clouds now exists. I put it together in 1975, but of course it incorporates numerous pieces that have been around for a very long time. Like everything in science, this new geometry has very, very deep and long roots. Benoît B. Mandelbrot Introduction This enhanced and expanded edition of THE COLOURS OF INFINITY features an additional chapter on the money markets by the fractal master himself, Professor Benoît Mandelbrot. The DVD of the film associated with this book has been re-mastered especially for this edition with exquisite new fractal animations, which will take your breath away! Driven by the curious enthusiasm that engulfs many fractalistas, in 1994, Nigel Lesmoir-Gordon overcame enormous obstacles to raise the finance for, then shoot and edit the groundbreaking TV documentary from which this book takes its name. The film has been transmitted on TV channels in over fifty countries around the world. This book is not just a celebration of the discovery of the Mandelbrot set, it also brings fractal geometry up to date with a gathering of the thoughts and enthusiasms of the foremost writers and researchers in the field. As Ian Stewart makes clear in the opening chapter, there were antecedents for fractal geometry before 1975 when Mandelbrot gave the subject its name and began to develop the underlying theory."Article| Nigel Lesmoir-Gordon| Statement ..."
♥ Book Title : Fractals
☯ Full Synopsis : "In his seminal book The Fractal Geometry of Nature, Benoit Mandelbrot wrote, "A cauliflower shows how an object can be made of many parts, each of which is like a whole, but smaller. Many plants are like that. A cloud is made of billows upon billows upon billows that look like clouds. As you come closer to a cloud you don't get something smooth, but irregularities at a smaller scale." In this collection of linked essays, William Bradley presents us with small glimpses of his larger consciousness, which is somewhat irregular itself. Reflecting on subjects as diverse as soap opera actors, superheroes, mortality, and marriage, these essays endeavor to reveal what we have in common, the connections we share that demonstrate that we are all fractals, in a sense-self-similar component parts of a larger whole."Article| William Bradley| Statement ..."
♥ Book Title : The Fractal Geometry of the Brain
☯ Full Synopsis : "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."Article| Antonio Di Ieva| Statement ..."
♥ Book Title : Thinking in Patterns
☯ Full Synopsis : "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 OCo 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: . OCo Index to Scientific & Technical Proceedings- (ISTP- / ISI Proceedings). OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Engineering & Physical Sciences.""Article| Benoit B. Mandelbrot, Miroslav Michal Novak| Statement ..."
♥ Book Title : Fractal Surfaces
☯ Full Synopsis : "The author integrates discussions of fractal geometry, surface modeling techniques, and applications to real world problems to provide a comprehensive, accessible overview of the field. His work will equip researchers with the basic tools for measurement and interpretation of data, stimulating more work on these problems and, perhaps, leading to an understanding of the reasons that Nature has adopted this geometry to shape much of our world."Article| John C. Russ| Statement ..."
♥ Book Title : Fractals: A Very Short Introduction
☯ Full Synopsis : "An essential discussion of the popular science and mathematics behind fractals reveals how fractal shapes can be found everywhere in nature from clouds to coastlines, explaining how basic concepts in fractal geometry produced a revolution in mathematical understandings of patterns in the 20th century. Original."Article| K. J. Falconer| Statement ..."