Leonardo

COMPUTERS AND THE IMAGINATION: VISUAL ADVENTURES BEYOND THE EDGE by Clifford A. Pickover. St. Martin's Press, New York, NY, U.S.A., 1991. 444 pp., iIlus. Trade, $29.95. ISBN: 0-312-06131-5. Reviewed l7y Dawn Friedman, Department ofChemistry, Harvard University, 12 Oxford Street, Cambridge, JIM 02138, U.S.A. This unique collection of computergraphics explorations may overwhelm the unwary reader with its intensity, richness and breadth. The common thread linking its 60-odd chapter topics is the dynamic effect of computers on human imagination. Throughout are dazzling, evocative images and intellectual puzzles that range from the intriguing to the mind-boggling. Pickovcr's book can be approached on different levels by people of diverse backgrounds and interests. It is a broad-spectrum conversationstarter ; left on a desk or coffee table, it will attract artists, mathematicians, researchers and computer addicts. If one begins by simply leafing through the book at random, a startling image or provocative heading will soon catch the eye. Topics are highly selfcontained ; the concepts behind each attention-grabber are outlined in a page or two of text, so that many readers will be eager to explore further. The next level provides an array of thought-provoking questions and challenging variations on each topic. Pseudocode algorithms are provided for those who want to create images, run simulations and solve puzzles using their own computers. References and suggestions for further reading allow topics to serve asjumping-off points for reader exploration, artistic experimentation or original research. The author has organized this cornucopia of computer adventures into sections. In the first section, "Simulation ", the reader can learn how to generate butterfly curves, design spider webs or simulate mutations. This section makes a good introduction to the book, especially for those interested in programming the pseudocode examples. The "Speculation" section poses debate-provoking questions such as, "What if humankind , in the year 1900, had been given a modern personal computer?" and surveys some answers. "Visualiza386 Current Media tion" includes computer-graphics experiments on the growth of seashells and the practical uses of the moire effect . Under "Exploration" appear mathematical diversions such as prime plaids, million-point sculptures and cakemorphic integers. "Invention " includes speculative creations such as the disconcerting speechsynthesis grenade, while "Imagination" presents bizarre computer-generated poetry. Some of the author's strangest ideas animate the stories collected under "Fiction". The Appendices are well worth reading: a sort of catchment basin for the exuberant overflow of ideas from the book proper, they include a series of "Exercises for the Mind and Eye" and an extensive and valuable bibliography of computer resources in many media for artists , scientists, educators and interested amateurs. DIFFERENTIAL AND DIFFERENCE EQUATIONS THROUGH COMPUTER EXPERIMENTS PHASER:AN ANIMATOR/SIMULATOR FOR DYNAMICAL SYSTEMS FOR IBM PERSONAL COMPUTERS by Huseyn Kocak, Springer-Verlag, New York, NY, U.S.A., 1986.224 pp. ISBN: 0-387-96239-5. Reviewed l7y Michele Emmer, Via Santa Maria della Speranza 5, 00139 Rome, Italy. Differential and Difference Equations through. Computer Experiments is a manual for readers learning how to use PHASER, the software program on the accompanying diskette. It is also an illustrated guide to the world of experimental and theoretical dynamics; it presents a dozen concrete examples ranging from the most rudimentary, appropriate for beginning students, to the highly complex, suitable for research mathematicians. It is not by chance that this software was rated the best mathematics software of 1989 by the judges at the third annual EDUCOM/NCRIPTAL. I have personally used PHASER for several years with students in mathematics, physics and biology. Because it only uses menus, it requires no computerprogramming knowledge, and it is easy to use. Lecturers can use PHASER to supplement beginning and advanced courses in differentialldifference equations. As Marvin S. Margolis wrote in Notices ofthe AMS: I also like the program because it motivates the study of dynamical systems. When I first tried PHASER it displayed 'phase portraits' for differential equations that I found puzzling. As a result I began reading the reference literature on differential equations and dynamical systems. As I studied the references, I began to understand dynamical systems better than I ever had in the past. Without the program I doubt...