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Reviewer: H. Van Dyke Parunak

The phrase “algorithmic beauty” is something of an oxymoron. Algorithms are precise, mechanical, and ruthlessly efficient, while beauty is indefinable, approximate, and ultimately inexplicable. Yet this volume earns its title, with dozens of strikingly realistic color images of flowers generated from as few as a half-dozen lines of simple mathematics. Originally a set of course notes form the SIGGRAPH conferences of 1988 and 1989, this material was first issued in hardcover in 1990 [1]; this volume is an unmodified softcover reprint. The material fully merits republication and wide distribution. Three research communities will turn to this volume. Biologists will find a fully developed methodology for using computer simulation to test and model various theories of plant development. Scholars in other natural sciences will take inspiration from this elegant mapping of computational mechanisms onto the real world. Computer artists will draw on its techniques to grow virtual plant life for their own creations. A quarter of the book is devoted to chapter 1, “Graphical Modeling Using L-Systems.” An L-system, or Lindenmayer system, is a string rewriting grammar similar to Backus-Naur form and context-free Chomsky grammars. It differs from more familiar formalisms in rewriting the entire input string at each time step, rather than processing its symbols one at a time. A given model includes an axiom (the original string) and a series of productions or rewriting rules, which include extensions for context sensitivity, stochasticity, and parameterization. The strings resulting from recursive application of these rules are mapped into geometrical shapes by interpreting their symbols as instructions to a Logo-like turtle. These instructions include movement directives, drawing instructions, and commands to push and pop the turtle's state, permitting the construction of extremely complex shapes. The computational power of the rewriting process means that an axiom and a short set of productions can generate long and complicated strings that, when subjected to turtle interpretation, produce recognizable plant forms. The approach mimics nature, growing the plant from an underlying production system (such as DNA) rather then storing the complete representation of the finished organism. The next four chapters show how this basic technology can be applied to different biological forms. Chapter 2, “Modeling of Trees,” shows how to handle branching structures and their displacement under tropisms. Chapter 3, “Developmental Models of Herbaceous Plants,” extends these methods to a much wider variety of plant shapes. Chapter 4, “Phyllotaxis,” focuses on one feature of plant structure, the regular arrangement of organs such as leaves on a plant stem, scales on a pine cone, or seeds in a sunflower. Throughout these chapters, the detailed shape of an individual leaf or flower petal is treated as a predefined data structure. Chapter 5, “Models of Plant Organs,” shows how extensions of the mechanisms used to define overall plant architecture can generate these individual components with comparable representational efficiency. Though the iterated dynamics of a production system seem well suited to generating an animation of plant growth, the ideal animation interval is often not the same as the most appropriate production step. Chapter 6, “Animation of Plant Development,” makes the two independent by introducing a time version of Lindenmayer systems. Chapter 7, “ Modeling of Cellular Layers,” shows how the same techniques that model macro-level plant structures can be applied to cellular growth. Chapter 8, “Fractal Properties of Plants,” sets L-systems in the context of the broader discussion of fractality in nature and compares L-systems to Barnsley's iterated function systems. Appendix A, “Software Environment for Plant Modeling,” describes the overall architecture of the software “virtual laboratory” within which the research agenda described in the volume is pursued. Appendix B contains technical details on the figures in the book. The volume includes a bibliography of 164 items through 1990 and an index of about 200 entries. The excellent service rendered by the publishers in reissuing this book would have been even greater if they had taken the opportunity to make some simple corrections and additions. A number of errors in the original printing have been documented for several years at the website http://www.cpsc.ucalgary.ca/projects/bmv/tabop_errata.html, but unfortunately they have not been corrected or even listed in this reprint. Also, while neither the original printing nor the reprint includes L-system software, the second volume in the “virtual laboratory” series [2] does include software, raising expectations for this volume. Pointers to a variety of L-system software for Windows, Macintosh, and Unix are available on the Web as http://www.cpsc.ucalgary.ca/projects /bmv/software.html, as is the software described in Appendix A (http://www.cpsc.ucalgary.ca/projects/bmv/vlab/). Even without the inclusion of these pointers, however, the book is a classic example of interdisciplinary research.