An introduction to mathematical visualization including many fractals and using the J programming language. Designed for classroom use or individual learning. J is freely available and no prior experience with J is required. Experiments are hands on explorations that readers can duplicate. Topics include fractals, time series, iterated function systems, chaos and symmetry, cellular automata, complex dynamics, image processing, ray tracing and Open GL.
Fractals, Visualization and J is a text that uses fractals as a motivational goal for the study of visualization. The language J is introduced as needed for the topics at hand. Included are chapters: Introduction to J and Graphics, Plots, Verbs and First Fractals, Time Series and Fractals, Iterated function systems and Raster Fractals, Color, Contours and Animations, Complex Dynamics, Cellular Automata.
Fractals, Visualization and J is a text that uses fractals and chaos as motivation (among other topics) for the study of visualization. The language J is introduced as needed for the topics at hand. Included in the Fourth edition, Part 2, are chapters: Image Processing, Chaotic Attractors and Symmetry, Visualization in Three Dimensions, Ray Tracing, and Graphical User Interfaces.
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.
Biological data of all kinds is proliferating at an incredible rate. If humans attempt to read such data in the form of numbers and letters, they will take in the information at a snail's pace. If the information is rendered graphically, however, human analysts can assimilate it and gain insight at a much faster rate. The emphasis of this book is on the graphic representation of information-containing sequences such as DNA and amino acid sequences in order to help the human analyst find interesting and biologically relevant patterns. The editor's goal is to make this voyage through molecular biology, genetics and computer graphics as accessible to a broad audience as possible, with the inclusion of glossaries at the end of most chapters and program outlines where applicable. The book will be of most interest to biologists and computer scientists and the various large reference lists should be of interest to beginners and advanced students of biology, graphic art and computer science. Contributors have sought to find pattern and meaning in the cacophony of genetic and protein sequence data using unusual computer graphics and musical techniques.
"Witness the Forever Wild" is a guide to hiking in the Adirondacks designed to facilitate modern "leave no trace" hiking in this precious wilderness. The book includes descriptions of 56 hiking routes and more than 250 color nature photographs to enhance these hikes. Start coordinates are given for each hike, aiding the use GPS and/or internet direction software for locating trailheads. Distance, time par, and cumulative ascent data is given for each route. The book contains 32 color topographic maps showing 26 primary routes drawn by overlaying GPS data from the route onto the maps. Distance and time data along the route is also given. Most routes are day hikes, but there are a few hikes from interior base camps. A few routes are trail-less or include a trail-less segment. If you are new to the Adirondacks, there are hikes suitable for you. If you are an experienced Adirondack hiker, you will likely find interesting and challenging Adirondack hikes that are unusual but lovely.
Now approaching its tenth year, this hugely successful book presents an unusual attempt to publicise the field of Complex Dynamics. The text was originally conceived as a supplemented catalogue to the exhibition "Frontiers of Chaos", seen in Europe and the United States, and describes the context and meaning of these fascinating images. A total of 184 illustrations - including 88 full-colour pictures of Julia sets - are suggestive of a coffee-table book. However, the invited contributions which round off the book lend the text the required formality. Benoit Mandelbrot gives a very personal account, in his idiosyncratic self-centred style, of his discovery of the fractals named after him and Adrien Douady explains the solved and unsolved problems relating to this amusingly complex set.
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.
