For almost ten years chaos and fractals have been enveloping many areas of mathematics and the natural sciences in their power, creativity and expanse. Reaching far beyond the traditional bounds of mathematics and science to the realms of popular culture, they have captured the attention and enthusiasm of a worldwide audience. The fourteen chapters of the book cover the central ideas and concepts, as well as many related topics including, the Mandelbrot Set, Julia Sets, Cellular Automata, L-Systems, Percolation and Strange Attractors, and each closes with the computer code for a central experiment. In the two appendices, Yuval Fisher discusses the details and ideas of fractal image compression, while Carl J.G. Evertsz and Benoit Mandelbrot introduce the foundations and implications of multifractals.

In this compelling exploration of life, Gregg Braden merges the modern discoveries of nature’s patterns (fractals) with the ancient view of a cyclic universe. The result is a powerful model of time—fractal time—and a realistic window into what we can expect for the mysterious year 2012 . . . and beyond. Applying fractal time to the history of the world and life, he proposes that everything from the war and peace between nations to the patterns of human relationships mirror the returning cycles of our past. As each cycle repeats, it carries a more powerful, amplified version of itself. The key: If you know where to look in the past,you know what to expect when the same conditions return in the present and future. For the first time in print, the Time Code Calculator gives you the toolto do just that! Through easy-to-understand science and step-by-step instructions, discover for yourself: • How the conditions for 2012 have occurred in the past, and what we can expect when they repeat! • The “hot dates” that hold the greatest threats of war and greatest opportunities for peace, as well as economic cycles such as the stockmarket collapse of 2008! • How Earth’s location in space triggers cycles of spiritual growth for humans! • Your personal Time Codes for the key events of business, relationships, and change in your life! • How each cycle carries a window of opportunity—a choice point—that allows us to select a new outcome for the returning pattern! • What the 1999 ice cores from Antarctica reveal about past cycles of climate, global warming, Earth’s protective magnetic fields, and what these things mean for us today!

This book will challenge how you think about time. Physics describes time as spatialized, static, and reversible, while we experience time as textured, flowing, and unidirectional. No model is better suited to capture time's quantitative and qualitative aspects than the cyclicity, creativity, and infinite depths of fractals.

This book provides a comprehensive survey of the state-of-the-art in the development of the theory of scale relativity and fractal space-time. It suggests an original solution to the disunified nature of the classical-quantum transition in physical systems, enabling quantum mechanics to be based on the principle of relativity provided this principle is extended to scale transformations of the reference system. In the framework of such a newly-generalized relativity theory (including position, orientation, motion and now scale transformations), the fundamental laws of physics may be given a general form that goes beyond and integrates the classical and the quantum regimes. A related concern of this book is the geometry of space-time, which is described as being fractal and nondifferentiable. It collects and organizes theoretical developments and applications in many fields, including physics, mathematics, astrophysics, cosmology and life sciences.

This edited volume discusses time and fractal phenomena in economics, entrepreneurship, and management. Chapters embrace a wide spectrum of topics, such as time series analysis of entrepreneurial orientation, theoretical research on the effectiveness of time management in dynamics of employee-organization relationship, the degradation of goals over time and how ambiguity and managerial cognition shape distributions of project time and cost, and fractal characteristics in energy markets and organizations. Revealing emerging aspects of time and fractals across disciplines, this volume demonstrates their significance in advancing economics, entrepreneurship, and management research. As such, this text will be useful for academics, researchers, management professionals and policy makers.

Written in a style that is accessible to a wide audience, The Fractal Geometry of Nature inspired popular interest in this emerging field. Mandelbrot's unique style, and rich illustrations will inspire readers of all backgrounds.

What are fractals? Why are they such fun? How do you make one? Why is a dripping tap not as random as it seems? What is chaos? Is the Mandelbrot Set really the most complex object in mathematics? In this beautifully illustrated book, fractal-hunter Oliver Linton takes us on a fascinating journey into the mathematics of fractals and chaos, diving into many kinds of self- similar structures to reveal some of the most recently discovered and intriguing patterns in science and nature. "e;Fascinating"e; FINANCIAL TIMES. "e;Beautiful"e; LONDON REVIEW OF BOOKS. "e;Rich and Artful"e; THE LANCET. "e;Genuinely mind-expanding"e; FORTEAN TIMES. "e;Excellent"e; NEW SCIENTIST. "e;Stunning"e; NEW YORK TIMES. Small books, big ideas.

These days computer-generated fractal patterns are everywhere, from squiggly designs on computer art posters to illustrations in the most serious of physics journals. Interest continues to grow among scientists and, rather surprisingly, artists and designers. This book provides visual demonstrations of complicated and beautiful structures that can arise in systems, based on simple rules. It also presents papers on seemingly paradoxical combinations of randomness and structure in systems of mathematical, physical, biological, electrical, chemical, and artistic interest. Topics include: iteration, cellular automata, bifurcation maps, fractals, dynamical systems, patterns of nature created through simple rules, and aesthetic graphics drawn from the universe of mathematics and art.Chaos and Fractals is divided into six parts: Geometry and Nature; Attractors; Cellular Automata, Gaskets, and Koch Curves; Mandelbrot, Julia and Other Complex Maps; Iterated Function Systems; and Computer Art.Additionally, information on the latest practical applications of fractals and on the use of fractals in commercial products such as the antennas and reaction vessels is presented. In short, fractals are increasingly finding application in practical products where computer graphics and simulations are integral to the design process. Each of the six sections has an introduction by the editor including the latest research, references, and updates in the field. This book is enhanced with numerous color illustrations, a comprehensive index, and the many computer program examples encourage reader involvement.

This lovely little book will take off and fly on its own power, but the author has asked me to write a few words, and one should not say no to a friend. Specific topics in fractal geometry and its applications have already benefited from several excellent surveys of moderate length, and gossip and preliminary drafts tell us that we shall soon see several monographic treatments of broader topics. For the teacher, however, these surveys and monographs are not enough, and an urgent need for more helpful books has been widely recognized. To write such a book is no easy task, but Jens Feder meets the challenge head on. His approach combines the old Viking's willingness to attack many difficulties at the same time, and the modern Norwegian's ability to achieve fine balance between diverging needs. lowe him special gratitude for presenting the main facts about R/ S analysis of long-run dependence; now a wide scientific public will have access to a large group of papers of mine that had until this day remained fairly confidential. Last but not least, we are all grateful to Jens for not having allowed undue personal modesty to deprive us of accounts of his own group's varied and excellent work. He did not attempt to say everything, but what he said is just fine. Benoit B. Mandelbrot Physics Department, IBM Thomas J.