This book offers a comprehensive explanation of iterated function systems and how to use them in generation of complex objects. Discussion covers the most popular fractal models applied in the field of image synthesis; surveys iterated function system models; explores algorithms for creating and manipulating fractal objects, and techniques for implementing the algorithms, and more. The book includes both descriptive text and pseudo-code samples for the convenience of graphics application programmers.
This unique textbook emphasizes the communalities between splines and fractals in interpolation and approximation theory, with particular emphasis on fractal functions and fractal surfaces. It presents the classical theory of splines and their properties, and also gives an introduction to the burgeoning new theory of superfractals and superfractal functions.
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.
Focusing on how fractal geometry can be used to model real objects in the physical world, this up-to-date edition features two 16-page full-color inserts, problems and tools emphasizing fractal applications, and an answers section. A bonus CD of an IFS Generator provides an excellent software tool for designing iterated function systems codes and fractal images.
"FRONTIERS IN ELECTROMAGNETICS is the first all-in-one resource to bring in-depth original papers on today's major advances in long-standing electromagnetics problems. Highly regarded editors Douglas H. Werner and Raj Mittra have meticulously selected new contributed papers from preeminent researchers in the field to provide state-of-the-art discussions on emerging areas of electromagnetics. Antenna and microwave engineers and students will find key insights into current trends and techniques of electromagnetics likely to shape future directions of this increasingly important topic. Each chapter includes a comprehensive analysis and ample references on innovative subjects that range from combining electromagnetic theory with mathematical concepts to the most recent techniques in electromagnetic optimization and estimation. The contributors also present the latest developments in analytical and numerical methods for solving electromagnetics problems. With a level of expertise unmatched in the field, FRONTIERS IN ELECTROMAGNETICS provides readers with a solid foundation to understand this rapidly changing area of technology. Topics covering fast-developing applications in electromagnetics include: * Fractal electrodynamics, fractal antennas and arrays, and scattering from fractally rough surfaces * Knot electrodynamics * The role of group theory and symmetry * Fractional calculus * Lommel and multiple expansions. Professors: To request an examination copy simply e-mail [email protected]" Sponsored by: IEEE Microwave Theory and Techniques Society, IEEE Antennas and Propagation Society.
Fractal image compression technology, one of the major digital image compression techniques, has been a well kept secret for many years. While there are many books written on other technologies, such as DCT/JPEG andwavelet theory, few books touch the subject of fractal image compression. Fractal Imaging presents the logic, technology, and various uses of fractal imaging by analyzing a complete, usable fractal image representation system. This detailed work will be a must for engineers interested in building fractal imaging systems. It will also be of interest to the general public, showing how mathematics once again plays a central role in our lives, where art and science intersect. Included is a CD-ROM containing fractal images and a freeware version of Iterated Systems fractal imaging utility. Key Features * Modeling realistic images * Efficient, fractal image representation and enhancement * Data compression and coding algorithms with Sample C code * 16-page color insert * Includes Fractal Imager Software * Fractal Imager is an award-winning Windows" product that produces Fractal Image Format (FIF) files;This software helps you to create interactive Web page images that download fast and look sharp. * Put interactive images on your Web site * Give great image quality and resolution independent zoomability * Super fast Internet progressive display * More content without taking more space!
Written for researchers and developers applying Integrated Function Systems in the creation of fractal images, this book presents a modification of a widely used probabilistic algorithm for generating IFS-encoded images. The book also includes a discussion of how IFS techniques can be applied to produce animated motion pictures.
This third edition of the classic textbook in Optimization has been fully revised and updated. It comprehensively covers modern theoretical insights in this crucial computing area, and will be required reading for analysts and operations researchers in a variety of fields. The book connects the purely analytical character of an optimization problem, and the behavior of algorithms used to solve it. Now, the third edition has been completely updated with recent Optimization Methods. The book also has a new co-author, Yinyu Ye of California’s Stanford University, who has written lots of extra material including some on Interior Point Methods.
Fixed point theory is a growing and exciting branch of mathematics with a variety of wide applications in biological and mathematical sciences, proposing newer applications in discrete dynamics and super fractals. The present endeavour is to report the latest trend in metric fixed point theory, emphasising newer applications in numerical analysis, discrete dynamics and fractal graphics, besides traditional applications. The book is useful to a large class of readers interested in analysis, applicable mathematics and fractal graphics. The articles have been selected carefully so that the book is useful for sophomores up to senior researchers looking for new material and new ideas in the existence of fixed points, new applications and survey articles. A few chapters included herein are formal in nature and suggest new directions of research in this area, which are especially useful to beginners in the field. The book is divided into two parts: Part I contains surveys and existence and convergence results. In Part II (Applications), various applications of fixed point theory to initial value problems, local attractivity of certain functional integral equation solutions, fractals and super-fractals, and solving equations in numerical praxis have been discussed. The present book, which is dedicated to Professor Shyam Lal Singh, consists of articles contributed by outstanding workers all over the world. Of course, some of the articles were selected from the Symposium on Fixed Point Theory and Applications (dedicated to him) held during the 19th Annual Conference Of India (10-12 November 2016), organised by Pauri Garhwal of the Department of Mathematics, H N B Garhwal (Central) University.
Proceedings of SPIE present the original research papers presented at SPIE conferences and other high-quality conferences in the broad-ranging fields of optics and photonics. These books provide prompt access to the latest innovations in research and technology in their respective fields. Proceedings of SPIE are among the most cited references in patent literature.
The conference Convex and Fractal Geometry was held at the Stefan Banach International Mathematical Center at Bedlewo, May 21-26, 2007. ... This volume contains twelve papers related to the talks delivered at that conference.
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Felix Klein, one of the great nineteenth-century geometers, rediscovered in mathematics an idea from Eastern philosophy: the heaven of Indra contained a net of pearls, each of which was reflected in its neighbour, so that the whole Universe was mirrored in each pearl. Klein studied infinitely repeated reflections and was led to forms with multiple co-existing symmetries. For a century these ideas barely existed outside the imagination of mathematicians. However in the 1980s the authors embarked on the first computer exploration of Klein's vision, and in doing so found many further extraordinary images. Join the authors on the path from basic mathematical ideas to the simple algorithms that create the delicate fractal filigrees, most of which have never appeared in print before. Beginners can follow the step-by-step instructions for writing programs that generate the images. Others can see how the images relate to ideas at the forefront of research.