The title of this text really encapsulates what the book is about: generating pictures of patterns with linguistic grammars (typically regular and/or context-free). It facilitates implementation based on a tree data structure. The book contains 203 figures (mostly grayscale, but some in color) and an accompanying CD-ROM, which provides a system for generating pictures designed by a tree-based grammar.

The book consists of eight main chapters, two appendices, a ten-page list of references, and an extensive index to the topics and concepts covered in the book. This book introduces the reader to the notions, techniques, and theory of grammatical picture generation, a research field focusing on formal systems that describe sets of pictures by means of syntactic rules. Chapter 1 provides an introduction to picture algebra and tree structures. Chapter 2 begins the discussion with simple picture languages generated by classes of chain-code picture languages (line drawings). Chapter 3 investigates the generation of more complex pictures by incorporating a collage operator. For the purposes of this text, a collage is a finite set of geometric objects in two-dimensional space.

Chapter 4 incorporates fractal technology to produce recursive levels of detail for natural and artificial patterns from iterated function systems. Chapter 5 provides for an alternative means of recursively defining pictures in a manner that is similar to a quad-tree approach. This is based on the notion of a grid picture language. A derivation of a picture starts with an initial variable symbol (nonterminal) placed in a unit square. A production rule is applied that replaces a nonterminal symbol in the square with a subdivided grid of colors or nonterminals, each occupying a square of the grid. The process continues until no more nonterminals exist and the picture is thus formed. This chapter also presents the relevant theorems about context-free grammars and languages that relate to the generation of pictures.

Chapter 6 formalizes fractal technology for picture generation. This is accomplished by allowing for nondeterministic rules for each nonterminal, and by allowing for potentially infinite depth trees. This chapter defines the value of an infinite tree over a finite set of operations by considering a continuous mapping of trees to pictures. Chapter 7 integrates the technology of the previous chapters and extends all discussions to include color attributes. Finally, chapter 8 presents a fully developed comprehensive system to design and form color pictures based on grammar rule rewrite systems.

The two appendices are quite useful. The first appendix reviews the necessary formal language concepts for understanding the mechanics of how grammars generate languages and specifically adapt these notions to tree-based implementations and picture language grammars. The second appendix summarizes the mathematical notations used throughout the book. Their system (TREEBAG) is provided in the accompanying CD-ROM.

The author had a challenging task ahead of him in that systems based on grammars and rewrite rules tend to require rigorous mathematical theory in order to validate the approach. As such, this text does rely on mathematical notation, lemmas, theorems, and, at times, even proofs. Yet, the author does not want this text to become a theoretical treatise. His intent is to provide a comprehensive summary of the concepts and technology necessary for grammatical picture generation and to bring the reader to the level where his practical TREEBAG system is both useful and meaningful. The author should be congratulated for accomplishing an appropriate blend of the two through a text that is readable to both the research practitioner and students with appropriate backgrounds.