G. Rozenberg A. Salomaa (Eds.) Lindenmayer Systems Impacts on Theoretical Computer Science, Computer Graphics, and Developmental Biology With 116 Figures Springer-Verlag Berlin Heidelberg GmbH
Grzegorz Rozenberg Department of Computer Science Leiden University P. O. Box 9512 2300 RA Leiden, The Netherlands Arto Salomaa The Academy of Finland Department of Mathematics University of Turku SF-20 500 Turku, Finland ISBN 978-3-642-63474-1 Library of Congress Cataloging-in-Publibation Data. Lindenmayer systems : impacts on theoretical computer science, computer graphics, and developmental biology / Grzegorz Rozenberg, Arto Salomaa [editors], p. cm. Includes bibliographical references and index. ISBN 978-3-642-63474-1 ISBN 978-3-642-58117-5 (ebook) DOI 10.1007/978-3-642-58117-5 1. Computer graphics. 2. Developmental biology. 3. L systems. I. Rozenberg, Grzegorz. II. Salomaa, Arto. T385.L558 1992 511.3-dc20 92-14822 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9,1965, in its current version, and permission for use must always be obtained from Springer- Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg 1992 Softcover reprint of the hardcover 5th edition The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera ready by authors 45/3140-5 4 3 2 1 0 - Printed on acid-free paper
Preface This is a collection of papers, mostly reporting original research, dealing with or related to L systems, which is short for Lindenmayer systems. Just as in our previous volume The Book of L (Springer-Verlag 1986), the range of contributions is large and shows the wide applicability of L systems. We would like to point out two very recent developments as examples of the strength of L systems both in theoretical and practical considerations. (i) The methods and techniques invented originally in connection with DOL systems have turned out to be applicable in various areas of automata theory and combinatorics of words not at all associated with L systems. (ii) It suffices to study the book The Algorithmic Beauty of Plants by P. Prusinkiewicz and A. Lindenmayer (Springer-Verlag 1990) to become convinced of the significance of L systems in computer graphics. We believe that this volume will be useful for quite a variegated audience. In addition to students and researchers working in L systems and in related areas of automata and language theory, as well as in combinatorics of words, the volume should be of definite interest also to people working in computer graphics and in developmental biology. Moreover, after reading the introductory contribution by Jurgensen and Lindenmayer that was originally intended to be published in the Scientific American, even a non-initiated reader should find much of the material accessible. The metatitle of this first part, In the Footsteps of L, was the working title and still is our "secret code" for the book. Aristid Lindenmayer is known to us as the father of L systems. He was convinced that for many biological phenomena, relational and set-theoretical concepts were more suitable than those from mathematical analysis. The discrete and combinatorial nature of biological structures, everywhere from the molecular to the cellular and population levels, was obvious to him. The same seems to apply to physical structures as well and, therefore, it is apparent that new tools and models are needed for practicing scientists. L systems were first visualized as everywhere expanding arrays of finite automata. Such arrays provided realistic simulations of growing cellular filaments as found in algae, mosses and fungi. The model was suitable for de-
VI scribing the global development of multicellular structures on subunits present where the growth increments are applied simultaneously in each derivation step. The first of these requirements is needed because there are natural subunits, each carrying the same genetic material, in developing organisms. The second requirement is necessary because one cannot apply local productions here and there in an asynchronous manner: time runs in the same way in every cell. Instead of arrays of finite automata, models from formal language theory turned out to be more economical, especially for computer implementations. We all know the success of L systems in computer graphics, as well as the fact that by now several books and about a thousand papers exist dealing with the mathematical aspects of the theory alone. Lindenmayer's invention has turned out to be one of the most beautiful examples of interdisciplinary science: work in one area has induced most fruitful ideas and results in other areas. It is a great pleasure for us that almost without exception the leading authorities in the field have been able to contribute to this volume. Weare pleased to have also many of the most promising young researchers in the area among the contributors. We express our gratitude to all contributors. Special thanks are due to Juha Honkala for suggesting the working title of the volume, from which the part metatitles are derived, as well as to Springer-Verlag, in particular Dr. Hans Wossner and Mrs. Ingeborg Mayer, for valuable suggestions and continuing good cooperation. It is very difficult, if not impossible, to find such a combination of a great scientist and warm, modest personality as Aristid Lindenmayer. He was always most helpful and ready to discuss also with beginners all aspects, in particular, biological implications. We dedicate this book to the memory of Aristid Lindenmayer (1925-1989). In doing so we are thinking also of his wife Jane and of her importance in creating the atmosphere for Aristid's unique work. February 1992 Grzegorz Rozenberg Arto Salomaa
Table of Contents 1. In the Footsteps of L: Exposition of L Systems Grammars of development: discrete-state models for growth, differentiation and gene expression in modular organisms A. Lindenmayer, H. Jurgensen 3 2. The Main Path Continues Further: Studies of Basic L Systems Regularity properties of L ambiguities of moiphisms J.Honkllla Iterated substitutions and locally catenative systems: a decidability result in the binary case... C. Choffrut 25 49 Alternating iteration of morphisms and the Kolakovski sequence 93 K. CuZik II, J. Karhumaki. A. Lepisto Interaction strength of DIL systems Y. Kobuchi Inductive inference of OL languages T. Yokomori A normal form for structurally equivalent EOL grammars v. Niemi Simplifications of EOL grammars.......... Th. Oumann. D. Wood The complexity of the emptiness problem for EOL systems K.-J. Lange. M. Schudy 107 115 133 149 167
VIII AOL- and CFG-size of languages A. Kelemenowi, M. Removcfkowi... 177 A comparison of two controlled rewriting mechanisms for table Lindenmayer systems............... 183 M. Pastorowi 3. Images from the Path: Computer Graphics, Pictures and Animation L-systems: from formalism to programming languages. P. Prusinkiewicz, J. Hanan 193 Parameterized L systems for modelling: potential and limitations. 213 T.W. Chien, H. Jurgensen A high-level language for L-systems and its applications N. S. Goel, I. Rozehnal On synchronized Lindenmayer picture languages... J. Dassow, J. Hromkovic Generation of random planar tessellations by hierarchical decimation....................... 263 P. Meer, A. Rosenfeld 231 253 4. Walking in the Plane: Graph Grammars and Map L Systems Parallel hyperedge replacement..... H J. Kreowski. 271 From parallel graph grammars to parallel high-level replacement systems... 283 H. Ehrig, G. Taenzer On relationships between graph L-systems and picture languages: Part II... 305 K. Aizawa, A Nakamura Map L systems with multiple markers... R. Siromoney, K.G. Subramanian, T. Robinson 319
IX 5. Enjoying Flora Along the Path: Biological Aspects and Models Locally generated colourings of hexagonal cell division patterns: application to retinal cell differentiation........ 333 Z. Tuza, A. Lindenmayer A model for cellular development in morphogenetic fields M. J. M. de Boer, F. D. Fracchia, P. Prusinkiewicz Splicing schemes and DNA......... T.Head Cellworks: an application to plant morphogenesis J. Luck, H. B. Luck 351 371 385 6. Crossroads and Branching Path: Variations and Generalizations of L Systems, Related Models Parallel communicating systems of L systems G.Paun 405 "Forgetful" L systems.......... 419 K. Krithivasan, M.V. Nagendra Prasad, M. Mahajan Skew-morphisms and systems.......... 437 M. Ito, G. Thierrin An algebraic approach to incomparable families of formal languages.................... 455 P. R. J. Asveld On the inverse neighborhoods of reversible cellular automata 477 J. Kari Templates, fragments and skins............... 497 B. Mayoh