Modeling Plant Development with L-Systems

Since their inception in 1968, L-systems have become a key conceptual, mathematical and software tool for modeling plant development at different levels of plant organization spanning molecular genetics, plant physiology, whole plant architecture and plant communities. The models can be descriptive, directly recapitulating observations and measurements of plants; mechanistic, explaining higher-level processes in terms of lower-level ones; or they may combine features of both classes. We present the basic idea of L-systems, motivate and outline some of their most useful extensions, and give a taste of current techniques for modeling with L-systems. The sample models progress in the scale of organization from a bacterium to a herbaceous plant to a tree, and simulate different forms of information transfer during the development, from communication between adjacent cells to bidirectional information exchange with the environment.

[1]  Radomír Mech,et al.  Self-organizing tree models for image synthesis , 2009, ACM Trans. Graph..

[2]  A. Novoplansky,et al.  TREE FORM: ARCHITECTURAL MODELS DO NOT SUFFICE , 1995 .

[3]  湯淺 太一,et al.  20世紀の名著名論:Seymour Papert: Mindstorms:Children Computers and Powerful Ideas Basic Books New York 1980 , 2005 .

[4]  Przemyslaw Prusinkiewicz,et al.  Visualization of Developmental Processes by Extrusion in Space-time , 1996, Graphics Interface.

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

[6]  Andrea A. diSessa,et al.  Turtle Geometry , 1981 .

[7]  Jim Hanan,et al.  Virtual plants - integrating architectural and physiological models , 1997 .

[8]  R. Borchert,et al.  Bifurcation Ratios and the Adaptive Geometry of Trees , 1981, Botanical Gazette.

[9]  R. Haselkorn How Cyanobacteria Count to 10 , 1998, Science.

[10]  Stéphane Douady,et al.  A Unified Model of Shoot Tropism in Plants: Photo-, Gravi- and Propio-ception , 2015, PLoS Comput. Biol..

[11]  Gerhard Buck-Sorlin,et al.  GroIMP as a platform for functional-structural modelling of plants , 2007 .

[12]  D. G. Adams,et al.  Tansley Review No. 107. Heterocyst and akinete differentiation in cyanobacteria , 1999 .

[13]  P. Prusinkiewicz,et al.  Constraints of space in plant development. , 2009, Journal of experimental botany.

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

[15]  P. Prusinkiewicz,et al.  The genetics of geometry. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[16]  G. Strang,et al.  Operator splitting , 2011 .

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

[18]  Brendan Lane,et al.  Generating Spatial Distributions for Multilevel Models of Plant Communities , 2002, Graphics Interface.

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

[20]  J. Stavans,et al.  The multicellular nature of filamentous heterocyst-forming cyanobacteria. , 2016, FEMS microbiology reviews.

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

[22]  Przemyslaw Prusinkiewicz,et al.  Design and Implementation of the L+C Modeling Language , 2003, RULE@RDP.

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

[24]  Andrew Owens,et al.  Modeling dense inflorescences , 2016, ACM Trans. Graph..

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

[26]  P. Prusinkiewicz,et al.  ART AND SCIENCE OF LIFE: DESIGNING AND GROWING VIRTUAL PLANTS WITH L-SYSTEMS , 2004 .

[27]  Przemyslaw Prusinkiewicz,et al.  Animation of plant development , 1993, SIGGRAPH.

[28]  J. Schwartz,et al.  Theory of Self-Reproducing Automata , 1967 .

[29]  Przemyslaw Prusinkiewicz,et al.  L-Py: An L-System Simulation Framework for Modeling Plant Architecture Development Based on a Dynamic Language , 2012, Front. Plant Sci..

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

[31]  G. Mitchison,et al.  Pattern formation in the blue-green alga, Anabaena. I. Basic mechanisms. , 1973, Journal of cell science.

[32]  T. Kira,et al.  A QUANTITATIVE ANALYSIS OF PLANT FORM-THE PIPE MODEL THEORY : I.BASIC ANALYSES , 1964 .

[33]  J. Huxley Problems of relative growth , 1932 .

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

[35]  H. Meinhardt,et al.  A theory of biological pattern formation , 1972, Kybernetik.

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

[37]  Olivier Michel,et al.  Computational models for integrative and developmental biology , 2002 .

[38]  G. E. Fogg GROWTH AND HETEROCYST PRODUCTION IN ANABAENA CYLINDRICA LEMM. , 1944 .

[39]  P. Klinkhamer Plant allometry: The scaling of form and process , 1995 .

[40]  K. Niklas Plant allometry: is there a grand unifying theory? , 2004, Biological reviews of the Cambridge Philosophical Society.

[41]  Stephen Wolfram,et al.  Universality and complexity in cellular automata , 1983 .

[42]  L. Mahadevan,et al.  On the growth and form of shoots , 2017, Journal of the Royal Society Interface.

[43]  O. Kniemeyer Rule-based modelling with the XL / GroIMP software , 2004 .

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

[45]  Brendan Lane,et al.  The L+C Plant-Modelling Language , 2007 .

[46]  B. Andrieu,et al.  A 3D Architectural and Process-based Model of Maize Development , 1998 .

[47]  J. Huxley Constant Differential Growth-Ratios and their Significance , 1924, Nature.

[48]  G. R. Mcghee,et al.  Theoretical Morphology: The Concept and Its Applications , 1998 .

[49]  Jacques Dumais,et al.  Beyond the sine law of plant gravitropism , 2012, Proceedings of the National Academy of Sciences.

[50]  Stanislaw M. Ulam Patterns of Growth of Figures , 1986 .

[51]  Ivan Rapaport,et al.  Modeling heterocyst pattern formation in cyanobacteria , 2009, BMC Bioinformatics.

[52]  F. E. Fritsch PRESIDENTIAL ADDRESS: The Heterocyst: A Botanical Enigma. , 1951 .

[53]  Przemyslaw Prusinkiewicz,et al.  The use of plant models in deep learning: an application to leaf counting in rosette plants , 2018, Plant Methods.

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

[55]  Colin Smith On vertex-vertex systems and their use in geometric and biological modelling , 2006 .

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

[57]  T. Bohr,et al.  Unifying model of shoot gravitropism reveals proprioception as a central feature of posture control in plants , 2012, Proceedings of the National Academy of Sciences.

[58]  R. Haselkorn,et al.  Characterization of a gene controlling heterocyst differentiation in the cyanobacterium Anabaena 7120. , 1991, Genes & development.

[59]  P. Prusinkiewicz,et al.  Generation of Spatial Patterns Through Cell Polarity Switching , 2011, Science.

[60]  P. Prusinkiewicz,et al.  Computational models of plant development and form. , 2012, The New phytologist.

[61]  H. Yoon,et al.  Heterocyst pattern formation controlled by a diffusible peptide. , 1998, Science.

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

[63]  Brendan Joseph Lane Cell Complexes: The Structure of Space and the Mathematics of Modularity , 2015 .

[64]  Gabor T. Herman,et al.  CELIA - a cellular linear iterative array simulator , 1970 .

[65]  A. Lindenmayer Mathematical models for cellular interactions in development. I. Filaments with one-sided inputs. , 1968, Journal of theoretical biology.

[66]  Brendan Lane,et al.  Modeling Morphogenesis in Multicellular Structures with Cell Complexes and L-systems , 2013 .

[67]  R. W. Baker,et al.  Simulation of organisms using a developmental model. 2. The heterocyst formation problem in blue-green algae. , 1972, International journal of bio-medical computing.

[68]  Radomír Mech,et al.  An L-System-Based Plant Modeling Language , 1999, AGTIVE.

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

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

[71]  Ludivine Taconnat,et al.  Combining laser-assisted microdissection (LAM) and RNA-seq allows to perform a comprehensive transcriptomic analysis of epidermal cells of Arabidopsis embryo , 2018, Plant Methods.

[72]  A. Lindenmayer,et al.  Discrete and continuous models for heterocyst differentiation in growing filaments of blue-green bacteria , 1987 .