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Grammatical Picture Generation: A Tree-Based Approach

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This book introduces the reader to the notions, the techniques, and the theory of grammatical picture generation, a research field focusing on formal systems that describe sets of pictures by means of syntactic rules. The book presents important types of picture generators, using a tree-based approach to stress their common algorithmic basis, the treatment influenced by the theory of computation, and the theory of formal languages in particular. It guides the reader through the basics of the tree-based approach on to dedicated chapters on line-drawing languages, collage grammars, iterated function systems, grid picture languages, languages of fractals, and languages of coloured collages, while presenting results about (un)decidable, NP-complete, or efficiently solvable problems, normal forms, hierarchies of language classes, and related phenomena. In support, the book contains detailed exercises throughout, and the software on the enclosed CD allows the reader to experiment with the picture generators explained in the text. The book is of interest to researchers and graduate students in computer science and mathematics who are engaged with the theory and practice of picture-generating systems.

Pictures are important, in everyday life as well as in art, engineering, and most branches of the natural and social sciences. About three decades ago, the observation that simple geometric processes often yield very complex geometric objects (i.e., pictures) gave rise to new branches of mathematics whose purpose was to study such processes and the resulting pictures: fractal geometry, dynamic systems, and chaos theory. More or less in parallel with this development, the increasing availability of computer desktop systems and other graphical output devices made computer scientists think about formal systems to describe sets of pictures. This led to the development of various types of picture-generating devices. This book is about such picture generators, including some of the most basic devices studied in fractal geometry.

In the computer science literature, the first devices for picture generation were proposed in the late 1960s and early 1970s, most notably the array grammars of Rosenfeld, Siromoney, and others, and the shape grammars of Gips and Stiny. About a decade later, picture generators based on string grammars were proposed, using either the chain-code interpretation of Freeman or the turtle geometry known from the Logo programming language. Each of these lines of research has been continued ever since, and various other approaches have been proposed.
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