Stability of Stochastic Differential Equations with Respect to Semi-martingales (X. Mao)

the algorithm that computes the orbit structure of a circular CA. This is followed by a 20 page user’s guide to the two accompanying DOS programs, and then a 150 page "atlas" of orbits structures of various CA. (In Wolfram’s terminology, these CA include the"n 3" and the"totalistic n 5" rules with number of sites L < 16; in terms of the notation of the first paragraph, n 2N + is the number of arguments for the update rule F.) The atlas consists ofgraphic representations of the orbit structures ofthese CA.The atlas software appears to be restricted to circular CA with n < 5, attribute set S {0, }, and number of sites L < 32; source code is not included. It seems to me that the audience for this book is largely limited to researchers working on these particular CA. On the one hand, a good part of the 60 pages of text describing CA is devoted to describing the algorithm employed to compute inverse images, so that the book does not serve particularly well as a broad introduction to the theory of CA. On the other hand, the software seems to be limited to the class of examples described above, and doubt that the underlying algorithm can be effectively generalized to higherdimensional CA. The foregoing remarks are not intended to belittle the possibility that the book may be valuable for researchers; the information provided by the atlas and the software may well be important in investigations of these circular CA, and may lead to insights about more general CA.