Kandinsky’s Teaching at the Bauhaus: Color Theory and Analytical Drawing by Clark V. Poling (review)

Book h i mPanel:Frank Dietrich, Elmer H. Duncan, Alan Lee, RogerF. Malina, Cli&ord A. Pickover, Stephen Wilson. I. Book Reviews DOESGODPLAY DICE? (THE MATHEMATICS OF CHAOS) by Ian Stewart.Basil Blackwell, Oxford, U.K, 1989. 317 pp., illus. Trade, $19.95. ISBN: 0-631-16847-8. Reuiewed by Clvford A. Packouer,IBM Watson Research Center, Ymktown Heights, NY 10598, U.S.A. Chaos and chanceare words to desnibe phenomma o f which we are ignorant. -&en G. Carlson Ian Stewarthas done it again. Does God Play Dice?provides a detailed and expansivefollow-up to Stewart’sprevious papers on chaos for a lay audience, e.g. Ref. [11. His book details the history and concepts of chaos theory in an easy-to-follow and enjoyablemanner. Stewartapproaches the subjectwith wit and humor, giving ample illustrations and examples. Of particular interest is the skillful way with which such arcane terms as phase portraits, Hamiltonian systems,saddle points and structural stabilityare introduced-so that even a relatively new audience can begin to understand this exciting and growing scientificfield. What is chaos?Chaos theory usually involves the study of a range of phenomena exhibiting a sensitivedependence on initial conditions. From chaotic toys with randomly blinking lights to wisps and eddies of cigarette smoke,chaotic behavior is generally irregular and disorderly;other examples include weather patterns, certain neurological and cardiac activity, the stockmarket, and certain electrical networks of computers. Although chaos often seems totally ‘random’ and unpredictable, it actuallyobeys strict mathematical rules deriving from equations that can be formulated and studied. Today, there are severalscientificfields devoted to the study of how complicated behavior can arise in systems from simple rules and how minute changes in the input of nonlinear systems can lead to large differencesin the output; such fields include chaos and cellular automata theory. Compared to other famous and worthwhile books in the field such as Gleick’s [2], Stewartgoes into more detail, which is essentialfor readers who wish to participate in the search for the marvelous and complex graphical representations of chaos. Topics covered in the book include ‘Cantor Cheese’ (a circular, whole-filledo b ject of great complexity),strange attractors , bifurcation diagrams and fractals,as well as many philosophical issues concerning the significanceof chaos to scientists.The book would be improved if it provided additional equations and computer pseudocode (perhapsin an appendix). Why should artists be interested in this book? There is now a growing relationship between chaos, art and computer graphics [3,4]. In fact, one of the principal research tools for the study of chaos is computer graphics. (Readers may be interested to note that there is now an entirejournal section within Pergamon Press’sinternational journal Computersand Graphicsdevoted to computer graphics and chaos.) It is intriguing that today the break between artistic and scientificpursuits is often apparent . Whereas the earlier thinkers pursued science and art in the light of guiding principles such as harmony and proportion, today some hold the view that science stiflesthe artistic spirit. Nevertheless, the computer is capable of creating images of captivating beauty and power. On a personal note, in much of my work I have found that beauty, science and art are intertwined, and this contributes to the fascination of mathematics and chaos for both scientistsand laypeople . Mathematicalrecipes can also function as the artist’sassistant, quickly taking care of many repetitive and sometimes tedious details. B y becoming familiarwith advanced computer graphics, the computer artist can change our perception of art. Aside from artistic uses, computergraphic techniques are unmatched in their ability to convey complex scientific and mathematical information to both colleaguesand laypeople.Peter Schroeder [5] very aptly sums up this revolution in computer graphics: “Somepeople can read a musical score and in their minds hear the music-others can see, in their mind’s eye, great beauty and structure in certain mathematical functions -lesser folks,like me, need to hear music played and see numbers rendered to appreciate their structures.” References 1. I. Stewart, “TheNature of Stability”,Speculations in Sciace and Technology10, No. 4, 310-324 (1987). 2. J.Gleick, Chaos:Makinga New Science (New York Viking, 1987). 3. K. Dewdney, “ComputerRecreations”,ScimtijcAmerican 261, No. 1,120-123 (1989) 4. C. Pickover, “Symmetry,Beauty and Chaos in...