This first practical book on fractals for Windows with accompanying software brings to life the dazzling world of fractals--impossibly intricate, endlessly fascinating visual patterns generated by computers according to mathematical laws of pure randomness. Includes 3-D glasses, a disk containing the revolutionary new Winfract program, and a spectacular fold-out, color poster.
This book provides a thorough investigation of the application of chaos theory and fractal analysis to computer vision. The field of chaos theory has been studied in dynamical physical systems, and has been very successful in providing computational models for very complex problems ranging from weather systems to neural pathway signal propagation. Computer vision researchers have derived motivation for their algorithms from biology and physics for many years as witnessed by the optical flow algorithm, the oscillator model underlying graphical cuts and of course neural networks. These algorithms are very helpful for a broad range of computer vision problems like motion segmentation, texture analysis and change detection. The contents of this book include chapters in biological vision systems, foundations of chaos and fractals, behavior of images and image sequences in phase space, mathematical measures for analyzing phase space, applications to pre-attentive vision and applications to post-attentive vision. This book is intended for graduate students, upper division undergraduates, researchers and practitioners in image processing and computer vision. The readers will develop a solid understanding of the concepts of chaos theory and their application to computer vision. Readers will be introduced to a new way of thinking about computer vision problems from the perspective of complex dynamical systems. This new approach will provide them a deeper understanding of the various phenomena present in complex image scenes.
The Desktop Fractal Design Handbook is a four-chapter introductory text to fractal geometry. The underlying algorithms are derived from mathematics, which is reflected in the images they produce. Chapter 1 provides an overview of the products of the desktop fractal design system. Chapter 2 describes the installation and operation of hardware and operating system of the design system, along with its maintenance. Chapter 3 outlines the use of the desktop fractal design system, specifically on hot to design fractals on the fractal design screen, maps, paintings, and help screens. Chapter 4 focuses on the many practical applications of fractals. This book will be of value to mathematicians, engineers, graphic artists, teachers, and students.
This book deals with the visualization and exploration of invariant sets (fractals, strange attractors, resonance structures, patterns etc.) for various kinds of nonlinear dynamical systems. The authors have created a special Windows 95 application called WInSet, which allows one to visualize the invariant sets. A WInSet installation disk is enclosed with the book.The book consists of two parts. Part I contains a description of WInSet and a list of the built-in invariant sets which can be plotted using the program. This part is intended for a wide audience with interests ranging from dynamical systems to computer design.In Part II, the invariant sets presented in Part I are investigated from the theoretical perspective. The invariant sets of dynamical systems with one, one-and-a-half and two degrees of freedom, as well as those of two-dimensional maps, are discussed. The basic models of the diffusion equations are also considered. This part of the book is intended for a more advanced reader, with at least a BSc in Mathematics.
A book for beginning Windows programmers who want to have fun learning the ropes, and for Windows experts who want to unlock the promise of fractals. The book includes a 16-page color insert of dazzling windows fractals color plates, plus 3D glasses. The disk includes over 200 full-color, modifiable example fractals and bonus programs with working C source code.
Up-to-date text focuses on how fractal geometry can be used to model real objects in the physical world, with an emphasis on fractal applications. Includes solutions, hints, and a bonus CD.
Fractals are intricate geometrical forms that contain miniature copies of themselves on ever smaller scales. This colorful book describes methods for producing an endless variety of fractal art using a computer program that searches through millions of equations looking for those few that can produce images having aesthetic appeal. Over a hundred examples of such images are included with a link to the software that produced these images, and can also produce many more similar fractals. The underlying mathematics of the process is also explained in detail.Other books by the author that could be of interest to the reader are Elegant Chaos: Algebraically Simple Chaotic Flows (J C Sprott, 2010) and Elegant Circuits: Simple Chaotic Oscillators (J C Sprott and W J Thio, 2020).
This book/disk package presents over a dozen programs to enable DOS, Windows, and OS/2 users to create their own colorful fractal graphics. An introductory chapter explains the fundamental of fractals; subsequent chapters show readers how to use the accompanying programs.
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.
