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.

Table of Contents

Introduction. Part 1. Geometry and Nature. Chaos game visualization of sequences (H. J. Jeffrey). Tumor growth simulation (W. Düchting). Computer simulation of the morphology and development of several species of seaweed using Lindenmayer systems (J.D. Corbit, D.J. Garbary). Generating fractals from Voronoi diagrams (K.W. Shirriff). Circles with kiss: a note on osculatory packing (C.A. Pickover). Graphical identification of spatio-temporal chaos (A.V. Holden, A.V. Panfilov). Manifolds and control of chaotic systems (H. Qammari, A. Venkatesan). A vacation on Mars - an artist's journey in a computer graphics world (C.A. Pickover). Part II. Attractors. Automatic generation of strange attractors (J.C. Sprott). Attractors with dueling symmetry (C.A. Reiter). A new feature in Hénon's map (M. Michelitsch, O.E. Rössler). Lyapunov exponents of the logistics map with periodic forcing (M. Markus, B. Hess). Toward a better understanding of fractality in nature (M. Klein, O.E. Rössler, J. Parisi, J. Peinke, G. Baier, C. Khalert, J.L. Hudson). On the dynamics of real polynomials on the plane (A.O. Lopes). Phase portraits for parametrically excited pendula: an exercise in multidimensional data visualisation (D. Pottinger, S. Todd, I. Rodrigues, T. Mullin, A. Skeldon). Self-reference and paradox in two and three dimensions (P. Grim, G. Mar, M. Neiger, P. St. Denis). Visualizing the effects of filtering chaotic signals (M.T. Rosenstein, J.J. Collins). Oscillating iteration paths in neural networks learning (R. Rojas). The crying of fractal batrachion 1,489 (C.A. Pickover). Evaluating pseudo-random number generators (R.L. Bowman). 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). Sierpinski fractals a


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© 1998
Elsevier Science
Print ISBN:
Electronic ISBN:

About the author

C.A. Pickover

Affiliations and Expertise

IBM T.J. Watson Research Center, Yorktown Heights, New York, NY, USA;


@from:John de Rivaz @qu:...appears to be aimed to those who have not read any of Dr Pickover's books before and who want to use the power of a modern desktop computer to emulate and possibly advance on ideas in chaos theory that appeared in the late 1980s and the 1990s. If that is your purpose, then buying this one book may well be a very good move... @source:Fractal Report @from:K.J. Falconer @qu:...this collection of articles will appeal especially to programmers, professional and amateur alike. It will also catch the eye of scientists and mathematicians along with interested lay people. This book has substantial academic content, but it can also be appreciated at the level of a coffee table book, to be dipped into for its wealth of ideas and stunning illustrations. @source:Fractals @from:R. Girvan @qu:...fascinating new book ...fractal artists and scientists will find inspiration in this excellent showcase of the relevance of chaos to the broader field of science. @source:Scientific Computing World @qu:...Although this is not a deep book, scientifically speaking, even professional mathematicians and physicist can find some inspiration in it. @source:Mathematical Reviews @qu:...This book is enhanced with numerous color illustrations, a comprehensive index, and the many computer program examples encourage reader involvement. @source:Zentralblatt fur Mathematik