Exploring Discrete Dynamics. Andrew Wuensche. (2011, Luniver Press.) xxxvii + 498 pages, 290 figures, 31 tables.

Exploring Discrete Dynamics. Andrew Wuensche. (2011, Luniver Press.) xxxvii + 498 pages, 290 figures, 31 tables. Exploring Discrete Dynamics is a very extended computational and analytic exploration of discrete dynamical systems. The book makes a summary of more than 19 years of results, programming, and research by Andrew Wuensche. In 1992, at the Santa Fe Institute, Wuensche together with Mike Lesser published the celebrated book in cellular automata theory The Global Dynamics of Cellular Automata [26]. This book introduced a reverse algorithm for cellular automata, and presented an atlas of basin of attraction fields computed by means of the algorithm. Motivated by these results and Kauffmanʼs model of genetic regulatory networks [12], Wuensche subsequently developed new algorithms for random Boolean networks and discrete dynamical networks in general. His achievements have had a great influence on outstanding researchers such as Stuart Kauffman [12], Harold V. McIntosh [18], Andrew Adamatzky [1], and Christopher Langton [26], among many others; and hundreds of references in books and research articles. These results have been obtained mainly by making use of his popular open source software DDLab (Discrete Dynamics Lab, http://www.ddlab.org/), which is widely used in the scientific community and offers free access to software, code, and manual. Wuenscheʼs latest book, Exploring Discrete Dynamics, presents a very extensive description of the current features of DDLab. Successive chapters describe, in detail and in depth, every function of this tool, illustrated with numerous examples from his research. Analyses concentrate mainly on four systems of increasing generality: cellular automata (CAs), random Boolean networks (RBNs), discrete dynamical networks (DDNs), and random maps. Consequently, in this book we have a ramification that connects and relates concepts naturally derived from these main subjects: reverse algorithms, rule space, state space, basins of attraction, stability, order, chaos, complexity, networks, emergent structures, classes, filters, self-reproduction, reactiondiffusion, cryptography, and beyond [4, 7, 9, 11, 21, 24, 28, 30–33, 35–37]. Without doubt, the DDLab software is unique in its ability to study and classify discrete dynamical systems, analyze and unravel networks with the network graph, create flexible simulations where parameters can be changed on the fly, and generate basins of attraction and subtrees. In DDLab we can experiment with mutations, calculate preimages (or ancestors [10, 23]), and analyze state space configurations iterating for unlimited spans of time, including simulations in one, two, and three dimensions. In the state space implementation, we can calculate the changing input entropy and pattern density, which helps us to understand the properties of dynamical systems—applied in particular to automatically categorize CA rule space between order, complexity, and chaos. The static Z parameter, based on just the rule table, also categorizes CA rule space by predicting the indegree in subtrees to identify maximum chaos—this is applied for a method of encryption [34]. An interesting point in the book is the incorporation of a jump graph of the basin of attraction field (see p. 207). Thinking in terms of Edward Fredkinʼs finite nature hypothesis [13], the most important implication of this hypothesis is “that every volume of space-time has a finite amount of information