L-systems: from the Theory to Visual Models of Plants

In 1968, Aristid Lindenmayer introduced a formalism for simulating the development of multicellular organisms, subsequently named L-systems [18]. This formalism was closely related to abstract automata and formal languages, and attracted the immediate interest of theoretical computer scientists. The vigorous development of the mathematical theory of L-systems was followed by its applications to the modeling of plants. These applications gained momentum after 1984, when Smith introduced state-of-the art computer graphics techniques to visualize the structures and processes being modeled [52]. Smith also attracted attention to the phenomenon of data-base amplification, or the possibility of generating complex structures from compact data sets, which is inherent in L-systems and forms the cornerstone of L-system applications to image synthesis. Subsequent developments (presented here from our personal perspective, without covering the fast-growing array of contributions from many other researchers) included:

[1]  Alvy Ray Smith,et al.  Plants, fractals, and formal languages , 1984, SIGGRAPH.

[2]  Brian W. Kernighan,et al.  The C Programming Language, Second Edition , 1988 .

[3]  Przemyslaw Prusinkiewicz,et al.  Developmental Models of Multicellular Organisms: A Computer Graphics Perspective , 1987, ALIFE.

[4]  P. Prusinkiewicz,et al.  A model for cellular development in morphogenetic fields , 1992 .

[5]  S. Subtelny,et al.  Developmental order, its origin and regulation , 1982 .

[6]  H. Honda,et al.  Control of Development in the Bifurcating Branch System of Tabebuia rosea: A Computer Simulation , 1984, Botanical Gazette.

[7]  Przemyslaw Prusinkiewicz,et al.  Animation of the development of multicellular structures , 1990 .

[8]  P. Prusinkiewicz,et al.  Virtual plants: new perspectives for ecologists, pathologists and agricultural scientists , 1996 .

[9]  Radomír Mech,et al.  Visual Models of Plant Development , 1997, Handbook of Formal Languages.

[10]  Aristid Lindenmayer,et al.  A Model for the Growth and Flowering of Aster Novae-Angliae on the Basis of Table < 1, 0 > L-Systems , 1974, L Systems.

[11]  A. Lindenmayer,et al.  Models for the control of branch positions and flowering sequences of capitula in mycelis muralis (l , 1987 .

[12]  Przemyslaw Prusinkiewicz,et al.  Applications of L-systems to computer imagery , 1986, Graph-Grammars and Their Application to Computer Science.

[13]  Przemyslaw Prusinkiewicz,et al.  Graphical applications of L-systems , 1986 .

[14]  Brian W. Kernighan,et al.  The C Programming Language , 1978 .

[15]  A. Lindenmayer Developmental systems without cellular interactions, their languages and grammars. , 1971, Journal of theoretical biology.

[16]  David M. Raup,et al.  Geometric analysis of shell coiling; general problems , 1966 .

[17]  J. Hanan,et al.  Module and metamer dynamics and virtual plants , 1994 .

[18]  Mark James,et al.  Synthetic topiary , 1994, SIGGRAPH.

[19]  A. Lindenmayer,et al.  Grammars of Development: Discrete-State Models for Growth, Differentiation, and Gene Expression in Modular Organisms , 1992 .

[20]  A. Lindenmayer,et al.  Developmental algorithms for multicellular organisms: a survey of L-systems. , 1975, Journal of theoretical biology.

[21]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[22]  Manfred Nagl,et al.  Graph-Grammars and Their Application to Computer Science , 1986, Lecture Notes in Computer Science.

[23]  D M Raup,et al.  Theoretical Morphology of the Coiled Shell , 1965, Science.

[24]  Przemyslaw Prusinkiewicz,et al.  The Algorithmic Beauty of Plants , 1990, The Virtual Laboratory.

[25]  Aristid Lindenmayer,et al.  Models for multicellular development: Characterization, inference and complexity of L-systems , 1986, IMYCS.

[26]  H. Honda Description of the form of trees by the parameters of the tree-like body: effects of the branching angle and the branch length on the sample of the tree-like body. , 1971, Journal of theoretical biology.

[27]  A. Bell,et al.  Plant Form: An Illustrated Guide to Flowering Plant Morphology , 1991 .

[28]  Przemyslaw Prusinkiewicz,et al.  L-systems: from formalism to programming languages , 1992 .

[29]  Przemyslaw Prusinkiewicz,et al.  Parametric l-systems and their application to the modelling and visualization of plants , 1992 .

[30]  James D. Foley,et al.  Fundamentals of interactive computer graphics , 1982 .

[31]  Jim Hanan,et al.  The Artificial Life of Plants , 1995 .

[32]  H. B. Lück,et al.  A comprehensive model for acrotonic, mesotonic and basitonic branchings in plants , 1990 .

[33]  Przemyslaw Prusinkiewicz,et al.  Visualization of botanical structures and processes using parametric L-systems , 1990 .

[34]  Przemyslaw Prusinkiewicz,et al.  Subapical Bracketed L-Systems , 1994, TAGT.

[35]  Seymour Papert,et al.  Mindstorms: Children, Computers, and Powerful Ideas , 1981 .

[36]  H. V. Koch Une méthode géométrique élémentaire pour l’étude de certaines questions de la théorie des courbes planes , 1906 .

[37]  Harold Abelson,et al.  Turtle geometry : the computer as a medium for exploring mathematics , 1983 .

[38]  Grzegorz Rozenberg,et al.  The mathematical theory of L systems , 1980 .

[39]  Radomír Mech,et al.  Visual models of plants interacting with their environment , 1996, SIGGRAPH.

[40]  A. Lindenmayer Mathematical models for cellular interactions in development. II. Simple and branching filaments with two-sided inputs. , 1968, Journal of theoretical biology.

[41]  P. Prusinkiewicz,et al.  Modeling the architecture of expanding Fraxinus pennsylvanica shoots using L-systems , 1994 .

[42]  Peter C. Chapin Formal languages I , 1973, CSC '73.

[43]  Grzegorz Rozenberg,et al.  Developmental systems and languages , 1972, STOC.

[44]  Przemyslaw Prusinkiewicz,et al.  Visual Models of Morphogenesis , 1993, Artificial Life.

[45]  James Hanan,et al.  Plantworks: A software system for realistic plant modelling , 1988 .