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Reviewer: Gregory M. Aharonian

What do you do if you are a kid with some time and a personal computer handy__?__ My use of the word “kid” is more attitudinal than chronological, that is, kids are people of all ages who still like having fun. Well, you can hack around with fractals and Tetris and other mathematical and graphical distractions for a while, but this soon becomes boring (unless you try playing Tetris with your toes). There must be more to explore in the world of mathematics, graphics, complexity, and esoterica; in fact, there should be an infinity to explore—the infinity of mathematics. Look no further. Pickover has written an entertaining book (for both reading and viewing) that collects and extends much of his work over the years on using the computer to visualize things that are relevant and fun to visualize. The book includes more than 300 illustrations (many of them computer-generated)<__?__Pub Caret> that have some connection to algorithms and complexity. The topics mentioned in the book are diverse: chaos, randomness, Cantor sets, pain-inducing patterns, cancer, buckyballs, undulating pseudofareymorphic integers, partition graphs, fractals, a self-correcting anti-dyslexia font, speech synthesis, computer-generated poetry, space-filling curves, earthworm algebra, and sociopolitics. If you ever wondered about all of those mathematical tidbits that appear in the <__?__Pub Fmt italic>New York Times<__?__Pub Fmt /italic>, <__?__Pub Fmt italic>Nature<__?__Pub Fmt /italic>, and <__?__Pub Fmt italic>New Scientist<__?__Pub Fmt /italic>, you can find many of them here. The book has 63 chapters, most about five or six pages long, that treat specific concepts. Ample quotes are provided, along with some great illustrations. The book retains much coherence across the chapters, making it an enjoyable read. Some concepts are fun (like the Gleichniszahlen-Reihe Monster), and some are thought-provoking. For example, one chapter covers what might happen if a personal computer were sent back in time to some scientists and engineers circa 1900. Another proposes a font to help people with dyslexia, an idea some of the font companies should make practical. The author provides pseudocode for many of the graphics and concepts mentioned in the book, which will help high school students and other computer novices start experimenting with concepts that, while they are lots of fun, deal with serious mathematical issues. The book does tend to use lots of mathematical jargon and not explain things in detail, which is a good incentive to go looking for ideas. All of these ideas make great seeds for science fair projects. If you like the papers Pickover has published (for example, in <__?__Pub Fmt italic>Computers in Physics<__?__Pub Fmt /italic>), you will like his book for providing lots more of this kind of material. No matter what field of science or engineering you work in, reading this book will undoubtedly spur you to think about your problems in other ways (or at least that is the excuse you can give your boss for reading it during system crashes).