Fundamentals Of Fractals And Chaos Theory
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| Author | : A.J. Crilly |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 278 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461230349 |
This volume is based upon the presentations made at an international conference in London on the subject of 'Fractals and Chaos'. The objective of the conference was to bring together some of the leading practitioners and exponents in the overlapping fields of fractal geometry and chaos theory, with a view to exploring some of the relationships between the two domains. Based on this initial conference and subsequent exchanges between the editors and the authors, revised and updated papers were produced. These papers are contained in the present volume. We thank all those who contributed to this effort by way of planning and organisation, and also all those who helped in the production of this volume. In particular, we wish to express our appreciation to Gerhard Rossbach, Computer Science Editor, Craig Van Dyck, Production Director, and Nancy A. Rogers, who did the typesetting. A. J. Crilly R. A. Earnshaw H. Jones 1 March 1990 Introduction Fractals and Chaos The word 'fractal' was coined by Benoit Mandelbrot in the late 1970s, but objects now defined as fractal in form have been known to artists and mathematicians for centuries. Mandelbrot's definition-"a set whose Hausdorff dimension is not an integer" -is clear in mathematical terms. In addition, related concepts are those of self-similarity and sub-divisibility. A fractal object is self-similar in that subsections of the object are similar in some sense to the whole object.
| Author | : Gary Drzewiecki |
| Publisher | : Springer Nature |
| Total Pages | : 142 |
| Release | : 2022-01-01 |
| Genre | : Technology & Engineering |
| ISBN | : 3030889688 |
This textbook serves as an introduction to nonlinear dynamics and fractals for physiological modeling. Examples and demonstrations from current research in cardiopulmonary engineering and neuro-systems engineering are provided, as well as lab and computer exercises that encourage readers to apply the course material. This is an ideal textbook for graduate students in biomedical engineering departments, researchers who analyze physiological data, and researchers interested in physiological modeling.
| Author | : M. A. Hemingway |
| Publisher | : |
| Total Pages | : |
| Release | : 1993 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Paul S. Addison |
| Publisher | : CRC Press |
| Total Pages | : 276 |
| Release | : 1997-01-01 |
| Genre | : Science |
| ISBN | : 9780849384431 |
Fractals and Chaos: An Illustrated Course provides you with a practical, elementary introduction to fractal geometry and chaotic dynamics-subjects that have attracted immense interest throughout the scientific and engineering disciplines. The book may be used in part or as a whole to form an introductory course in either or both subject areas. A prominent feature of the book is the use of many illustrations to convey the concepts required for comprehension of the subject. In addition, plenty of problems are provided to test understanding. Advanced mathematics is avoided in order to provide a concise treatment and speed the reader through the subject areas. The book can be used as a text for undergraduate courses or for self-study.
| Author | : Phillip A Laplante |
| Publisher | : World Scientific |
| Total Pages | : 217 |
| Release | : 2023-07-26 |
| Genre | : Mathematics |
| ISBN | : 981127326X |
This book offers a fun and enriching introduction to chaos theory, fractals and dynamical systems, and on the applications of fractals to computer generated graphics and image compression. Introduction to Chaos, Fractals and Dynamical Systems particularly focuses on natural and human phenomenon that can be modeled as fractals, using simple examples to explain the theory of chaos and how it affects all of us. Then, using straightforward mathematic and intuitive descriptions, computer generated graphics and photographs of natural scenes are used to illustrate the beauty of fractals and their importance in our world. Finally, the concept of Dynamical Systems, that is, time-dependent systems, the foundation of Chaos and Fractal, is introduced. Everyday examples are again used to illustrate concepts, and the importance of understanding how these vital systems affect our lives. Throughout the fascinating history of the evolution of chaos theory, fractals and dynamical systems is presented, along with brief introductions to the scientists, mathematicians and engineers who created this knowledge.Introduction to Chaos, Fractals and Dynamical Systems contains ample mathematical definitions, representations, discussions and exercises, so that this book can be used as primary or secondary source in home schooling environments.The book is suitable for homeschooling as a focused course on the subject matter or as a classroom supplement for a variety of courses at the late junior high or early high-school level. For example, in addition to a standalone course on Chaos, Fractals and Dynamical Systems (or similar title), this book could be used with the following courses:The text can also be used in conjunction with mathematics courses for undergraduates for non-science majors. The book can also be used for informal and lively family study and discussion.For each chapter, exercises and things to do are included. These activities range from simple computational tasks to more elaborate computer projects, related activities, biographical research and writing assignments.
| Author | : Manfred Schroeder |
| Publisher | : Courier Corporation |
| Total Pages | : 450 |
| Release | : 2009-08-21 |
| Genre | : Science |
| ISBN | : 0486472043 |
This fascinating book explores the connections between chaos theory, physics, biology, and mathematics. Its award-winning computer graphics, optical illusions, and games illustrate the concept of self-similarity, a typical property of fractals. The author -- hailed by Publishers Weekly as a modern Lewis Carroll -- conveys memorable insights in the form of puns and puzzles. 1992 edition.
| Author | : A.J. Crilly |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 312 |
| Release | : 2013-11-11 |
| Genre | : Computers |
| ISBN | : 3642780970 |
Applications of Fractals and Chaos presents new developments in this rapidlydeveloping subject area. The presentation is more than merely theoretical, it specifically presents particular applications in a wide range of applications areas. Under the oceans, we consider the ways in which sponges and corals grow; we look, too, at the stability of ships on their surfaces. Land itself is modelled and applications to art, medicineand camouflage are presented. Readers should find general interest in the range of areas considered and should also be able to discover methods of value for their own specific areas of interest from studying the structure of related activities.
| Author | : John Briggs |
| Publisher | : Simon and Schuster |
| Total Pages | : 196 |
| Release | : 1992 |
| Genre | : Art |
| ISBN | : 0671742175 |
Explains the significance and beauty of fractals using over 170 illustrations.
| Author | : Heinz-Otto Peitgen |
| Publisher | : Springer |
| Total Pages | : 488 |
| Release | : 1992 |
| Genre | : Mathematics |
| ISBN | : |
A broad view of chaos theory and fractal geometry and how they relate to each other, to other aspects of mathematics, and to natural phenomena. Explains fractal geometry- new language to describe complex natural forms.
| Author | : Garnett Williams |
| Publisher | : CRC Press |
| Total Pages | : 518 |
| Release | : 1997-09-09 |
| Genre | : Mathematics |
| ISBN | : 1482295415 |
This text aims to bridge the gap between non-mathematical popular treatments and the distinctly mathematical publications that non- mathematicians find so difficult to penetrate. The author provides understandable derivations or explanations of many key concepts, such as Kolmogrov-Sinai entropy, dimensions, Fourier analysis, and Lyapunov exponents.
