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Current Literature Edited by Elizabeth Crumley I. Book Reviews Book Review Panel: George Agoston, Rudolf Amheim, John E. Bowlt, Hans Brill, Donald Brook, Patricia Butler, John Cooper, Robert Dixon, Elmer Duncan, Vic Gray, Yusuf Grillo, John G. Hanhardt, Sharon Lebell, Alan Lee, Joy Turner Luke, John Mallinckrodt, Leo Narodny, Sean O’Driscoll, David Pariser, Yehuda Safran. Shao Dazhen, Allan Shields, David Topper, Stephen Wilson. THEBEAUTYOFFRACTALS:IMAGES OFCOMPLEXDYNAMICALSYSTEMS by Heinz Otto Peitgen and Peter Richter. Springer-Verlag, Berlin, West Germany, 1986. 196pp., illus. Trade, $35.00. ISBN: 0-387-1585 1-0. Reviewedby StephenWilson,Art Department , San Francisco State University, 1600Holloway Ave., San Francisco, CA 94132, U.S.A. Fractals are perhaps best known to Leonardo readers as exotic computer graphic images generated on high resolution systems.Theseorganic-looking shapes can be rendered as either abstract or representational forms. Indeed, the commercial cinema computer graphic industryhas seized on fractalsas one way to algorithmically generate realistic-lookinglandscapes (forexample,the “Genesis” sequence in Star Trek ZZI). Many artists who use computers have become enchanted, intrigued and confused by fractals. TheBeauty ofFractaZs,a valuable book by researchers, makes the beauty and theory of fractalsavailable to a wide public. Actually fractal images are just the tip of a theoretical iceberg. These representations of structures generated by equations are used to study the behavior of dynamical chaotic systems. Many aspects of nature do not adhere to the simplified models created by scientists to illustrate basic principles. Many phenomena in nature result from the interlinked workings of predictable principles and feedback from slight imperfections-for example, weather patterns, air turbulence flows around obstructions,the growth of biological populations. A branch of mathematics called the study of chaotic systems attempts to understand and formalize the systemic regularities of these kinds of behavior. One fascinating property of these systems is self-same cyclicity. As one looks at structuresat all levels one finds repeating patterns. The example of the seashore is offered-the viewsfrom an airplane and from eyelevel are similar. The study of these systems would almost be impossible without the computer, which allowssimulation of the outcomes resulting from iterations with feedback. The computer graphic images called fractals do not magically appear from plotting the output of algorithms. The renderer must make decisions about the parameters introducedinto the equations and the method for assigning computer graphic colors to the resulting values. Changes in either will result in radically different images. And here this book raises a major issue for the future of art. Artists can play with fractals by obtaining computer routinesthat generate these images and by manipulatingthe values to see results by trial and errm. Indeed, much artist exploration of contemporary scientific concepts and tools is accomplished in this ‘playing amateur’ mode. The authors of The Beauty of Fractals have taken a higher road. They suggest that appreciation of these images can be enhanced by understanding of the underlying theory. They suggest that skill in exploring this family of images can be built by learning enough of the mathematics to understand what changing parameters mean. This book maybea modelof arthcience books of the future. The power of artworks in the future may derive not onlyfrom their sensual qualities, but also from the concepts they explore. (For elaboration of this approach, see Herbert Franke’s new edition of Computer Graphics.)Books about art in the future will need to explore both the underlying informationbase and the outward sensual manifestations. The Beauty of Fractals is a step in that direction. It is an expansion of a catalog that accompanied a touring exhibit of computer graphic fractal images called “Frontiers of Chaos”. The book offers a main chapter that explains the importance of the study of dynamics of chaos, the linkagebetweenaestheticsand science, and a littleof the underlying mathematical theory. Subsequent sections offer more detailed treatments of the mathematics and reflectionson the aesthetics, including invited contributions.Thebook is heavily illustrated with many of the figures in finely produced color. One fascinating series of illustrations illustrates cyclic self-sameness at increasing levels of magnification. Each subsequent illustration in the series is a blow-up of a section of the previous illustration. A box outline indicates the section that is blown up. The book...


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