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Fractals are the geometry of the natural world. They're about the broken, wrinkled, wiggly world- the uneven shapes of nature, unlike the idealised forms of Euclidean geometry. We see fractals everywhere; indeed, we are fractals ourselves. Fractal geometry is an extension of classical geometry which can make precise models of physical structures, from ferns to galaxies. It can describe the shape of a cloud as precisely as an architect can describe a house. Introducing Fractals traces the historical development of this mathematical discipline, explores its descriptive powers in the natural world, and then looks at the applications and the implications of the discoveries it has made. As John Archibald Wheeler, protégé of Niels Bohr, friend of Albert Einstein and mentor of Richard Feynman has said, 'No one will be considered scientifically literate tomorrow, who is not familiar with fractals.'
Many are familiar with the beauty and ubiquity of fractal forms within nature. Unlike the study of smooth forms such as spheres, fractal geometry describes more familiar shapes and patterns, such as the complex contours of coastlines, the outlines of clouds, and the branching of trees. In this Very Short Introduction, Kenneth Falconer looks at the roots of the 'fractal revolution' that occurred in mathematics in the 20th century, presents the 'new geometry' of fractals, explains the basic concepts, and explores the wide range of applications in science, and in aspects of economics. This is essential introductory reading for students of mathematics and science, and those interested in popular science and mathematics. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
Author : David P. Feldman
ISBN : 9780199566433
Genre : Mathematics
File Size : 80.30 MB
Format : PDF
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For students with a background in elementary algebra, this book provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia Sets and the Mandelbrot Set, power laws, and cellular automata. The book includes over 200 end-of-chapter exercises.
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.
Author : William G. Brozo
ISBN : 9780807772485
Genre : Education
File Size : 35.71 MB
Format : PDF, Kindle
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Graphic novels are an excellent medium to motivate today’s youth to become independent learners and thinkers. This practical guide shows secondary school teachers how to incorporate graphic novels into content area instruction as a tool for meeting the needs of diverse learners and achieving the goals of the Common Core State Standards. The authors provide instructional guidelines with classroom examples that demonstrate how graphic novels can be used to expand content knowledge and literacy in science, social studies, math, and English/language arts. Teachers will appreciate the book’s specific suggestions for selecting graphic novels and for employing responsive practices that will build students’ reading, writing, speaking, listening, and media competencies. “The range and complexity of graphic novels being published right now is simply amazing to me. . . . They are part of what should be a balanced array of texts that all can read, enjoy, and learn from. In this volume, the authors point to this proliferation, as well as the educative potential of graphic novels. After reading its pages, I feel others will agree with me that they have done an excellent job pointing out how graphic novel creators such as Jim Ottaviani and Larry Gonick communicate much about history, science, and mathematics while also making connections to comprehension and thinking skills that accompany both literacy and content-specific learning.” —From the Foreword by Stergios Botzakis, assistant professor of adolescent literacy in the Theory and Practice in Teacher Education Department at The University of Tennessee, Knoxville “The authors have set forth on a task I feel long is overdu—connecting the literacy potential of graphic novels to the content areas. This book is a wonderful contribution to the field of content area literacy studies.” —Michael D. Boatright, assistant professor, Department of English, Western Carolina University Book Features: Advice for selecting and evaluating graphic novels. Teaching strategies for each of the four major content domains. Guidance for aligning instruction with the Common Core State Standards. A list of educational graphic novels organized by content area. Study group questions.And more! William G. Brozo is a professor of literacy in the Graduate School of Education at George Mason University in Fairfax, Virginia, and author of RTI and the Adolescent Reader. Gary Moorman is professor emeritus at Appalachian State University in Boone, North Carolina. Carla K. Meyer is an assistant professor in the Reading Education and Special Education Department at Appalachian State University.
Author : Giorgio Franceschetti
ISBN : 9780080469010
Genre : Technology & Engineering
File Size : 53.80 MB
Format : PDF, ePub, Mobi
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Scattering, Natural Surfaces, and Fractals provides a comprehensive overview of electromagnetic scattering from natural surfaces, ranging from the classical to the more recent (fractal) approach. As remote sensing applications become increasingly important, this text provides readers with a solid background in interpretation, classification and thematization of microwave images. The “scattering problem is discussed in detail with emphasis on its application to electromagnetic wave propagation, remote sensing, radar detection, and electromagnetic diagnostics. Natural surface and fractals complete this treatise focusing on how the fractal model represents our natural environment and other planets in our solar system, most recently as used to research the planet Venus and Titan, one of the moons of Saturn. An example of how scattering, fractals, and natural surfaces are of great importance is the following: Natural oil slicks in the ocean have been found to be fractal while man-made ones (generated by illegal washing of oil carrying ships) are not. Processing of an ocean image from space may detect the latter by means of a fractal analysis. An elegant and clear treatment of a rigorous topic with informative prose and realistic illustrations of scattering Provides readers with a solid background in interpretation, classification, and thematization of microwave images The only book available on fractal models and their application to scattering
