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基本説明
Compilation of the "Chaos and Fractals" section of the journal Computers & Graphics. Provides visual demonstrations of complicated and beautiful structures that can arise in systems, based on simple rules.
Full Description
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.
Contents
Abbreviated contents. Introduction. Part 1. Geometry and Nature. Chaos game visualization of sequences (H.J. Jeffrey). Tumor growth simulation (W. Duchting). Computer simulation of the morphology and development of several species of seaweed using Lindenmayer systems (J.D. Corbit, D.J. Garbary). Part II. Attractors. Automatic generation of strange attractors (J.C. Sprott). Attractors with dueling symmetry (C.A. Reiter). A new feature in Henon's map (M. Michelitsch, O.E. Roessler). Part III. Cellular Automata, Gaskets, and Koch Curves. Sensitivity in cellular automata: some examples (M. Frame). One tub, eight blocks, twelve blinkers and other views of life (J.E. Pulsifer, C.A. Reiter). Scouts in hyperspace (S. Shepard, A. Simoson). Part IV. Mandelbrot, Julia and Other Complex Maps. A tutorial on efficient computer graphics representations of the Mandelbrot set (R. Rojas). Julia sets in the quaternions (A. Norton). Self-similar sequences and chaos from Gauss sums (A. Lakhtakia, R. Messier). Part V. Iterated Function Systems. Some nonlinear iterated function systems (M. Frame, M. Angers). Balancing order and chaos in image generation (K. Culik II, S. Dube). Estimating the spatial extent of attractors of iterated function systems (D. Canright). Automatic generation of iterated function systems (J.C. Sprott). Modelling and rendering of nonlinear iterated function systems (E. Groeller). Part VI. Computer Art. Automatic parallel generation of aeolian fractals on the IBM power visualization system (C.A. Pickover). Julia set art and fractals in the complex plane (I.D. Entwistle). Methods of displaying the behaviour of the mapping z? z2 + &mgr; (I.D. Entwistle). AUTUMN - a recipe for artistic fractal images (J.E. Loyless). Author index. Subject index.
