The Algorithmic Beauty of Plants

1 Graphical modeling using L-systems.- 1.1 Rewriting systems.- 1.2 DOL-systems.- 1.3 Turtle interpretation of strings.- 1.4 Synthesis of DOL-systems.- 1.4.1 Edge rewriting.- 1.4.2 Node rewriting.- 1.4.3 Relationship between edge and node rewriting.- 1.5 Modeling in three dimensions.- 1.6 Branching structures.- 1.6.1 Axial trees.- 1.6.2 Tree OL-systems.- 1.6.3 Bracketed OL-systems.- 1.7 Stochastic L-systems.- 1.8 Context-sensitive L-systems.- 1.9 Growth functions.- 1.10 Parametric L-systems.- 1.10.1 Parametric OL-systems.- 1.10.2 Parametric 2L-systems.- 1.10.3 Turtle interpretation of parametric words.- 2 Modeling of trees.- 3 Developmental models of herbaceous plants.- 3.1 Levels of model specification.- 3.1.1 Partial L-systems.- 3.1.2 Control mechanisms in plants.- 3.1.3 Complete models.- 3.2 Branching patterns.- 3.3 Models of inflorescences.- 3.3.1 Monopodial inflorescences.- 3.3.2 Sympodial inflorescences.- 3.3.3 Polypodial inflorescences.- 3.3.4 Modified racemes.- 4 Phyllotaxis.- 4.1 The planar model.- 4.2 The cylindrical model.- 5 Models of plant organs.- 5.1 Predefined surfaces.- 5.2 Developmental surface models.- 5.3 Models of compound leaves.- 6 Animation of plant development.- 6.1 Timed DOL-systems.- 6.2 Selection of growth functions.- 6.2.1 Development of nonbranching filaments.- 6.2.2 Development of branching structures.- 7 Modeling of cellular layers.- 7.1 Map L-systems.- 7.2 Graphical interpretation of maps.- 7.3 Microsorium linguaeforme.- 7.4 Dryopteris thelypteris.- 7.5 Modeling spherical cell layers.- 7.6 Modeling 3D cellular structures.- 8 Fractal properties of plants.- 8.1 Symmetry and self-similarity.- 8.2 Plant models and iterated function systems.- Epilogue.- Appendix A Software environment for plant modeling.- A.1 A virtual laboratory in botany.- A.2 List of laboratory programs.- Appendix B About the figures.- Turtle interpretation of symbols.

[1]  G. Peano.  Sur une courbe, qui remplit toute une aire plane , 1890 .

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

[3]  Mathematische und mikroskopisch-anatomische Studien über Blattstellungen , 1907, Nature.

[4]  D'arcy W. Thompson.  On Growth and Form , 1945 .

[5]  A. Turing.  On Computable Numbers, with an Application to the Entscheidungsproblem. , 1937 .

[6]  G. Noakes,et al.  College Physics , 1945, Nature.

[7]  R. Horton.  EROSIONAL DEVELOPMENT OF STREAMS AND THEIR DRAINAGE BASINS; HYDROPHYSICAL APPROACH TO QUANTITATIVE MORPHOLOGY , 1945 .

[8]  A. Turing.  The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[9]  A. N. Strahler.  Hypsometric (area-altitude) analysis of erosional topography. , 1952 .

[10]  Noam Chomsky,et al.  Three models for the description of language , 1956, IRE Trans. Inf. Theory.

[11]  John W. Backus,et al.  The syntax and semantics of the proposed international algebraic language of the Zurich ACM-GAMM Conference , 1959, IFIP Congress.

[12]  Friedrich L. Bauer,et al.  Report on the algorithmic language ALGOL 60 , 1960, Commun. ACM.

[13]  H. Coxeter,et al.  Introduction to Geometry. , 1961 .

[14]  Herbert Freeman,et al.  On the Encoding of Arbitrary Geometric Configurations , 1961, IRE Trans. Electron. Comput..

[15]  Seymour Ginsburg,et al.  Two Families of Languages Related to ALGOL , 1962, JACM.

[16]  B. Balinsky,et al.  An introduction to embryology , 1965 .

[17]  F. Weberling.  Typology of inflorescences , 1965 .

[18]  Veva Elwell,et al.  Toxicity and Anti-Inflammatory Activity of Phenolic-Rich Extract from Nopalea cochenillifera (Cactaceae): A Preclinical Study on the Prevention of Inflammatory Bowel Diseases , 2023, Plants.

[19]  John von Neumann,et al.  Theory Of Self Reproducing Automata , 1967 .

[20]  C. H. Waddington,et al.  Cybernetics and development , 1966 .

[21]  DAN COHEN,et al.  Computer Simulation of Biological Pattern Generation Processes , 1967, Nature.

[22]  Aristid Lindenmayer,et al.  Mathematical Models for Cellular Interactions in Development , 1968 .

[23]  A. Kolmogorov.  Three approaches to the quantitative definition of information , 1968 .

[24]  Master Gardener,et al.  Mathematical games: the fantastic combinations of john conway's new solitaire game "life , 1970 .

[25]  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.

[26]  M. Zimmermann,et al.  Trees: Structure and Function. , 1972 .

[27]  H. Coxeter.  The Role of intermediate convergents in Tait's explanation for phyllotaxis , 1972 .

[28]  G. Mitchison,et al.  Rule governing Cell Division in Anabaena , 1972, Nature.

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

[30]  Franco P. Preparata,et al.  Introduction to discrete structures , 1973 .

[31]  A. Lindenmayer,et al.  PHYLLOTAXIS IN BRYOPHYLLUM TUBIFLORUM: MORPHOGENETIC STUDIES AND COMPUTER SIMULATIONS , 1974 .

[32]  Aristid Lindenmayer,et al.  Adding Continuous Components to L-Systems , 1974, L Systems.

[33]  P. Stevens.  Patterns in Nature , 1974 .

[34]  Paulien Hogeweg,et al.  A model study on biomorphological description , 1974, Pattern Recognit..

[35]  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.

[36]  A. Lindenmayer,et al.  Developmental Dscritions of Branching Patterns with Paracladial Relationships , 1975, Automata, Languages, Development.

[37]  R. Thom.  Structural stability and morphogenesis , 1977, Pattern Recognition.

[38]  P. D. Reffye.  Modélisation et simulation de la verse du caféier, à l'aide de la théorie de la résistance des matériaux , 1976 .

[39]  H. Honda,et al.  Computer Simulation of Branching Pattern and Geometry in Terminalia (Combretaceae), a Tropical Tree , 1977, Botanical Gazette.

[40]  J. A. van den Biggelaar,et al.  Development of dorsoventral polarity and mesentoblast determination in Patella vulgata , 1977, Journal of morphology.

[41]  A. Lindenmayer,et al.  Diffusion mechanism for phyllotaxis: theoretical physico-chemical and computer study. , 1977, Plant physiology.

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

[43]  J. V. D. Biggelaar,et al.  Development of dorsoventral polarity and mesentoblast determination in Patella vulgata , 1977, Journal of morphology.

[44]  D. Frijters.  Mechanisms of Developmental Integration of Aster novae-angliae L. and Hieracium murorum L. , 1978 .

[45]  Grzegorz Rozenberg,et al.  Parallel Generation of Maps: Developmental Systems for Cell Layers , 1978, Graph-Grammars and Their Application to Computer Science and Biology.

[46]  D. Frijters.  Principles of Simulation of Inflorescence Development , 1978 .

[47]  B. P. Hogeweg,et al.  About the cover: "Reconfigurable machines" , 1978, Computer.

[48]  R. Hunt.  Plant growth analysis , 1980 .

[49]  I. Aleksander.  Automata, languages, development , 1978 .

[50]  D. A. Young,et al.  On the diffusion theory of phyllotaxis. , 1978, Journal of theoretical biology.

[51]  P. Tomlinson,et al.  Tropical Trees and Forests: An Architectural Analysis , 1978 .

[52]  H. Honda,et al.  Tree Branch Angle: Maximizing Effective Leaf Area , 1978, Science.

[53]  H. Honda,et al.  BRANCH GEOMETRY AND EFFECTIVE LEAF AREA: A STUDY OF TERMINALIA‐BRANCHING PATTERN. 2. SURVEY OF REAL TREES , 1979 .

[54]  H. Vogel.  A better way to construct the sunflower head , 1979 .

[55]  H. Honda,et al.  Ratio of tree branch lengths: The equitable distribution of leaf clusters on branches. , 1979, Proceedings of the National Academy of Sciences of the United States of America.

[56]  Derick Wood,et al.  A Mathematical Investigation of Propagating Graph 0L Systems , 1979, Inf. Control..

[57]  H. Honda,et al.  BRANCH GEOMETRY AND EFFECTIVE LEAF AREA: A STUDY OF TERMINAUA‐BRANCHING PATTERN. 1. THEORETICAL TREES , 1979 .

[58]  B. G. Briggs,et al.  Evolution in the Myrtaceae--evidence from inflorescence structure , 1979 .

[59]  Takashi Yokomori,et al.  Stochastic Characterizations of EOL Languages , 1980, Inf. Control..

[60]  Walter J. Savitch,et al.  Growth Functions of Stochastic Lindenmayer Systems , 1980, Inf. Control..

[61]  B. Gunning,et al.  Microtubules and Cytomorphogenesis in a Developing Organ: The Root Primordium of Azolla pinnata , 1981 .

[62]  F. Weberling.  Morphologie der Blüten und der Blütenstände , 1981 .

[63]  H. Honda,et al.  COMPUTER SIMULATION OF BRANCH INTERACTION AND REGULATION BY UNEQUAL FLOW RATES IN BOTANICAL TREES , 1981 .

[64]  B. Barsky.  The beta-spline: a local representation based on shape parameters and fundamental geometric measures , 1981 .

[65]  H. Meinhardt.  Models of biological pattern formation , 1982 .

[66]  Jacqueline Lück,et al.  Generation of 3-dimensional plant bodies by double wall map and stereomap systems , 1982, Graph-Grammars and Their Application to Computer Science.

[67]  Annegret Habel,et al.  On context-free gragh languages generated by edge replacement , 1982, Graph-Grammars and Their Application to Computer Science.

[68]  Aristid Lindenmayer,et al.  Algorithms for the generation and drawing of maps representing cell clones , 1982, Graph-Grammars and Their Application to Computer Science.

[69]  H. Honda,et al.  Two Geometrical Models of Branching of Botanical Trees , 1982 .

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

[71]  R. Hunt.  Plant Growth Curves: The Functional Approach to Plant Growth Analysis , 1983 .

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

[73]  Manfred Nagl,et al.  Graph-Grammars and Their Application to Computer Science , 1982, Lecture Notes in Computer Science.

[74]  Grzegorz Rozenberg,et al.  Cell division patterns: Syntactical description and implementation , 1982, Comput. Graph. Image Process..

[75]  J. N. Rldley.  Computer simulation of contact pressure in capitula , 1982 .

[76]  Rani Siromoney,et al.  Space-filling curves and infinite graphs , 1982, Graph-Grammars and Their Application to Computer Science.

[77]  J. N. Ridley.  Packing efficiency in sunflower heads , 1982 .

[78]  R. J. Stevens,et al.  Manipulation and Presentation of Multidimensional Image Data Using the Peano Scan , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[79]  J. E. Dale,et al.  The Growth and Functioning of Leaves , 1984 .

[80]  N. MacDonald,et al.  Trees and networks in biological models , 1983 .

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

[82]  Tosiyasu L. Kunii,et al.  Botanical Tree Image Generation , 1984, IEEE Computer Graphics and Applications.

[83]  W. Remphrey,et al.  Crown architecture of Larix laricina saplings: quantitative analysis and modelling of (nonsylleptic) order 1 branching in relation to development of the main stem , 1984 .

[84]  Stephen Wolfram,et al.  Computer Software in Science and Mathematics. , 1984 .

[85]  W. T. Tutte.  Graph Theory , 1984 .

[86]  A. Lindenmayer.  Models for plant tissue development with cell division orientation regulated by preprophase bands of microtubules , 1984 .

[87]  Jules Bloomenthal,et al.  Modeling the mighty maple , 1985, SIGGRAPH.

[88]  Ricki Blau,et al.  Approximate and probabilistic algorithms for shading and rendering structured particle systems , 1985, SIGGRAPH.

[89]  W. Remphrey,et al.  Crown architecture of Larix laricina saplings: sylleptic branching on the main stem , 1985 .

[90]  S. Pfleeger,et al.  Introduction to discrete structures , 1985 .

[91]  Editors , 1986, Brain Research Bulletin.

[92]  Przemyslaw Prusinkiewicz.  Score Generation with L-Systems , 1986, ICMC.

[93]  Henry Lieberman,et al.  Using Prototypical Objects to Implement Shared Behavior in Object Oriented Systems , 1986, OOPSLA.

[94]  Peter Oppenheimer,et al.  Real time design and animation of fractal plants and trees , 1986, SIGGRAPH.

[95]  Akira Nakamura,et al.  Some Systems for Map Generation , 1986 .

[96]  Rani Siromoney,et al.  Rosenfeld's cycle grammars and kolam , 1986, Graph-Grammars and Their Application to Computer Science.

[97]  D. Robinson.  A notation for the growth of inflorescences , 1986 .

[98]  Aristid Lindenmayer,et al.  An introduction to parallel map generating systems , 1986, Graph-Grammars and Their Application to Computer Science.

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

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

[101]  Annegret Habel,et al.  May we introduce to you: hyperedge replacement , 1986, Graph-Grammars and Their Application to Computer Science.

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

[103]  A. Lindenmayer,et al.  Inference algorithms for developmental systems with cell lineages , 1987 .

[104]  Laurie Reuter,et al.  Rendering and magnification of fractals using iterated function systems , 1987 .

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

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

[107]  Arto Salomaa,et al.  Formal languages , 1973, Computer science classics.

[108]  M. Jaeger.  Représentation et simulation de croissance des végétaux , 1987 .

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

[110]  Przemyslaw Prusinkiewcz,et al.  Koch curves as attractors and repellers , 1988, IEEE Computer Graphics and Applications.

[111]  Heinz-Otto Peitgen,et al.  The science of fractal images , 2011 .

[112]  Marc Jaeger,et al.  Plant models faithful to botanical structure and development , 1988, SIGGRAPH.

[113]  Michael F. Barnsley,et al.  Fractals everywhere , 1988 .

[114]  Przemyslaw Prusinkiewicz,et al.  Development models of herbaceous plants for computer imagery purposes , 1988, SIGGRAPH.

[115]  E. Costes.  Analyse architecturale et modélisation du litchi (Litchi sinensis Sonn.). Contribution à l'étude de son irrégularité de production à l'île de la Réunion , 1988 .

[116]  H. B. Lück,et al.  Models of Cell Tetrads and Clones in Meristematic Cell Layers , 1988, Botanical Gazette.

[117]  Gift Siromoney,et al.  A Perspective in Theoretical Computer Science - Commemorative Volume for Gift Siromoney , 1989, A Perspective in Theoretical Computer Science.

[118]  Xavier Gérard Viennot,et al.  Combinatorial analysis of ramified patterns and computer imagery of trees , 1989, SIGGRAPH.

[119]  Ned Greene,et al.  Voxel space automata: modeling with stochastic growth processes in voxel space , 1989, SIGGRAPH.

[120]  Rani Siromoney,et al.  Kahbi Kolam and Cycle Grammars , 1989, A Perspective in Theoretical Computer Science.

[121]  René Thom,et al.  Structural stability and morphogenesis - an outline of a general theory of models , 1977, Advanced book classics.

[122]  Przemyslaw Prusinkiewicz,et al.  Application of L-Systems to Algorithmic Generation of South Indian Folk Art Patterns and Karnatic Music , 1989, A Perspective in Theoretical Computer Science.

[123]  F. Kenton Musgrave,et al.  The synthesis and rendering of eroded fractal terrains , 1989, SIGGRAPH.

[124]  M. Barnsley,et al.  Recurrent iterated function systems , 1989 .

[125]  Przemyslaw Prusinkiewicz,et al.  The concept and design of a virtual laboratory , 1990 .

[126]  Michael A. Lachance,et al.  An introduction to splines for use in computer graphics and geometric modeling , 1990 .

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

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

[129]  Przemyslaw Prusinkiewicz,et al.  Visualization of the development of multicellular structures , 1990 .

[130]  Dietmar Saupe,et al.  Rendering Methods for Iterated Function Systems , 1991 .

[131]  Appendix A Software environment for plant modeling , 2022 .