Fractals Everywhere: New Edition

Courier Corporation
Free sample

"Difficult concepts are introduced in a clear fashion with excellent diagrams and graphs." — Alan E. Wessel, Santa Clara University
"The style of writing is technically excellent, informative, and entertaining." — Robert McCarty
This new edition of a highly successful text constitutes one of the most influential books on fractal geometry. An exploration of the tools, methods, and theory of deterministic geometry, the treatment focuses on how fractal geometry can be used to model real objects in the physical world. Two sixteen-page full-color inserts contain fractal images, and a bonus CD of an IFS Generator provides an excellent software tool for designing iterated function systems codes and fractal images.
Suitable for undergraduates and graduate students of many backgrounds, the treatment starts with an introduction to basic topological ideas. Subsequent chapters examine transformations on metric spaces, dynamics on fractals, fractal dimension and interpolation, Julia sets, and parameter spaces. A final chapter introduces measures on fractals and measures in general. Problems and tools emphasize fractal applications, and an answers section contains solutions and hints.
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About the author

Michael F. Barnsley is a British mathematician, researcher, and author who holds several patents on fractal compression. He is a faculty member of the Mathematical Sciences Institute at Australian National University, and he previously taught in the United States at Georgia Tech.
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Additional Information

Publisher
Courier Corporation
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Published on
Oct 3, 2013
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Pages
560
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ISBN
9780486320342
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Language
English
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Genres
Mathematics / Geometry / General
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Content Protection
This content is DRM protected.
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Available on Android devices
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The same factors that motivated the writing of our first volume of strategic activities on fractals continued to encourage the assembly of additional activities for this second volume. Fractals provide a setting wherein students can enjoy hands-on experiences that involve important mathematical content connected to a wide range of physical and social phenomena. The striking graphic images, unexpected geometric properties, and fascinating numerical processes offer unparalleled opportunity for enthusiastic student inquiry. Students sense the vigor present in the growing and highly integrative discipline of fractal geom etry as they are introduced to mathematical developments that have occurred during the last half of the twentieth century. Few branches of mathematics and computer science offer such a contem porary portrayal of the wonderment available in careful analysis, in the amazing dialogue between numeric and geometric processes, and in the energetic interaction between mathematics and other disciplines. Fractals continue to supply an uncommon setting for animated teaching and learn ing activities that focus upon fundamental mathematical concepts, connections, problem-solving techniques, and many other major topics of elementary and advanced mathematics. It remains our hope that, through this second volume of strategic activities, readers will find their enjoyment of mathematics heightened and their appreciation for the dynamics of the world in creased. We want experiences with fractals to enliven curiosity and to stretch the imagination.
The subject of space-filling curves has fascinated mathematicians for over a century and has intrigued many generations of students of mathematics. Working in this area is like skating on the edge of reason. Unfortunately, no comprehensive treatment has ever been attempted other than the gallant effort by W. Sierpiriski in 1912. At that time, the subject was still in its infancy and the most interesting and perplexing results were still to come. Besides, Sierpiriski's paper was written in Polish and published in a journal that is not readily accessible (Sierpiriski [2]). Most of the early literature on the subject is in French, German, and Polish, providing an additional raison d'etre for a comprehensive treatment in English. While there was, understandably, some intensive research activity on this subject around the turn of the century, contributions have, nevertheless, continued up to the present and there is no end in sight, indicating that the subject is still very much alive. The recent interest in fractals has refocused interest on space filling curves, and the study of fractals has thrown some new light on this small but venerable part of mathematics. This monograph is neither a textbook nor an encyclopedic treatment of the subject nor a historical account, but it is a little of each. While it may lend structure to a seminar or pro-seminar, or be useful as a supplement in a course on topology or mathematical analysis, it is primarily intended for self-study by the aficionados of classical analysis.
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