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\centerline{\twelveb AN ANNOTATED BIBLIOGRAPHY}
\vskip 4pt
\centerline{\twelveb OF PLANT MODELING AND GROWTH SIMULATION}
\vskip 16pt
\centerline{\it Aristid Lindenmayer}
\vskip 8pt
\centerline{\rm Theoretical Biology Group}
\centerline{\rm University of Utrecht}
\centerline{\rm Padualaan 8, 3584 CH Utrecht}
\centerline{\rm The Netherlands}
\vskip 8pt
\centerline{\csc and}
\vskip 8pt
\centerline{\it Przemyslaw Prusinkiewicz}
\vskip 8pt
\centerline{\rm Department of Computer Science}
\centerline{\rm University of Regina}
\centerline{\rm Regina, Saskatchewan S4S 0A2}
\centerline{\rm Canada}
\vskip 16pt
\centerline{\rm February 28, 1988}
\vskip 16pt

{\twelveb CONTENTS}
\vskip 8pt
\item{1.}  General
\item{2.}  Surveys
\item{3.}  Theory of L-systems
\itemitem{3.1.}  Books
\itemitem{3.2.}  Bibliographies
\itemitem{3.3.}	 Papers
\item{4.}  Geometrical interpretation of L-systems
\item{5.}  L-systems in developmental analysis
\item{6.}  Multidimensional L-systems
\item{7.}  Synthesis of realistic plant images
\itemitem{7.1.}  Synthesis methods based on L-systems
\itemitem{7.2.}  Other synthesis methods
\itemitem{7.3.}  Organ models
\item{8.}  Related botanical papers
\itemitem{8.1.}  Plant architecture
\itemitem{8.2.}  Phylotaxis
\itemitem{8.3.}  Inflorescences
\itemitem{8.4.}  Leaves
\itemitem{8.5.}  Population dynamics and modular organisms.
{\parindent=0pt\parskip=10pt\pretolerance=400
\vskip 8pt

{\twelveb 1.  GENERAL}

\Hpar
{\csc Jean, R.~V. [1984]:}
{\sl Mathematical approach to pattern and form in plant growth.}
John Wiley and Sons, New York.

\Hpar
{\csc Lindenmayer, A. [1977]:}
``Theories and observations of developmental biology.''
In: R. E. Butts and J. Hintikka (Eds.):
{\sl Foundational problems in special sciences}.
D. Reidel Publ. Co., Dordrecht-Holland, pp. 103--118.

\Cpar
{\coms On the role of mathematical theories in biology.}

\Hpar
{\csc Mandelbrot, B. B. [1982]:}
{\sl The fractal geometry of nature.}
W.~H.~Freeman, San Francisco.

\Hpar
{\csc Stevens, P. S. [1974]:}
{\sl Patterns in nature}.
Little, Brown and Co., Boston.

\Hpar
{\csc Thompson, d'Arcy [1952]:}
{\sl On growth and form}.
At the University Press, Cambridge.
\vskip 8pt

{\twelveb 2.  SURVEYS}

\Hpar
{\csc Smith, A.~R. [1987]:} ``Formal geometric languages for natural
phenomena.''  In:
{\sl SIGGRAPH '87 Course Notes on the Modeling of Natural Phenomena\/}.

\Cpar
{\coms Personal reflections on the role of rewriting concepts in geometry,
specifically as applied to the modeling of plants.  Emphasizes the
role of L-systems.  Contains details on
programs Gene and mktree, and an annotated graftal bibliography.}

\Hpar
{\csc Fournier, A. [1987]:} ``Prolegomenon.''  In: 
{\sl SIGGRAPH '87 Course Notes on the Modeling of Natural Phenomena\/}.

\Cpar
{\coms A general introduction to the field of natural phenomena modeling,
with an emphasis on fractals
and the modeling of biological structures.}

{\comb The following papers survey the development of ideas
related to the L-systems in the biological context.}

\Hpar
{\csc Lindenmayer, A. [1975]:}
``Developmental algorithms for multicellular organisms: a survey of
L-systems.''
{\sl Journal of Theoretical Biology} {\bf 54}, pp. 3-22.

\Hpar
{\csc Lindenmayer, A. [1978]:}
``Algorithms for plant morphogenesis.''  In:
R. Sattler (Ed.): {\sl Theoretical plant morphology\/}, Leiden
University Press, The Hague, pp. 37--81.

\Hpar
{\csc Lindenmayer, A. [1982]:}
``Developmental algorithms: Lineage versus interactive control
mechanisms.''  In:  S. Subtelny and P.~B. Green:
{\sl Developmental order: Its origin and regulation},
Alan R. Liss, Inc., New York, pp. 219--245.

\Hpar
{\csc Lindenmayer, A. [1987]:}  ``Models for multicellular development: 
characterization, inference and complexity of L-systems.''  In:
A. Kelmenov\'a and J.Kelmen (Eds.): {\sl Trends, techniques and
problems in theoretical computer science\/}.  Lecture Notes
in Computer Science {\bf 281}, pp.~138--168, Springer-Verlag,
Berlin.

{\csc Macdonald, N. [1983]:}
{\sl Trees and networks in biological models.} J. Wiley, New York.

\Cpar
{\coms Chapters 18 and 19 present a good introduction to L-systems from the
biological perspective.}
\vskip 8pt

{\twelveb 3.  THEORY OF L-SYSTEMS}

{\twelveb 3.1.  Books.}

\Hpar
{\csc Herman, G.~T.~{\rm and} Rozenberg, G.  [1975]:}  {\sl Developmental
systems and languages.}  North-Holland,  Amsterdam.

\Cpar
{\coms The first and a very useful textbook on L-systems.}

\Hpar
{\csc Lindenmayer, A. {\rm and} Rozenberg, G. {\rm (Eds.)} [1976]:}
{\sl Automata, languages, development.}
North-Holland, Amsterdam.

\Hpar
{\csc Rozenberg, G., and Salomaa, A. [1980]:} {\sl The mathematical theory
of L-systems.}  Academic Press, New York.

\Cpar
{\coms A more recent monograph of L-systems.
Emphasis is put on 0L-systems.}

\Hpar
{\csc Rozenberg, G. {\rm and} Salomaa, A. {\rm (Eds.)} [1986]:}
{\sl The Book of L.}
Springer-Verlag, Berlin.

\Hpar
{\csc Salomaa, A. [1973]:} {\sl Formal languages.} 
Academic Press, New York.

\Cpar
{\coms Contains a very lucid introduction to L-systems.}

\Hpar
{\csc Vit\'anyi, P. M. B. [1980]:} {\sl Lindenmayer systems: structure,
languages and growth functions.} Mathematical Centre, Amsterdam.

{\twelveb 3.2.  Bibliographies.}

\Hpar
{\csc Rozenberg, G., Penttonen, M. {\rm and} Salomaa, A. [1977]:}
``Bibliography of L systems.'' {\sl Theoretical Computer Science}
{\bf 5}, pp. 339--354.

\Hpar
{\csc Rozenberg, G., M\"aenp\"a\"a, J. {\rm and} Salomaa, A. [1981]:}
``Supplementary bibliography of L~systems.''  {\sl Bull. Europ. Assoc.
Theor. Comp. Sci. (Leiden)} {\bf 13}, pp. 64--79.

{\twelveb 3.3.  Papers.}

\Hpar
{\csc Lindenmayer, A. [1968]:}
``Mathematical models for cellular interaction in development, Parts I and II.''
{\sl  Journal of Theoretical Biology} {\bf 18}, pp.~280--315.

\Cpar
{\coms The original paper on L-systems.}

\Hpar
{\csc Eichhorst, P. {\rm and} Savitch, W.~J. [1980]:}
``Growth functions of stochastic Lindenmayer systems.'' 
{\sl Information and Control} {\bf 45}, pp.~217--228.

\Hpar
{\csc Yokomori, T. [1980]:}  
``Stochastic characterizations of E0L languages.''
{\sl Information and Control} {\bf 45}, pp.~26--33.

\Cpar
{\coms The above two papers introduce a definition of stochastic L-systems which
is useful when adding specimen-to-specimen
variation to models
(cf. Nishida [1980], Prusinkiewicz [1987]):}

\Hpar
{\csc J\"urgensen, H. {\rm and} Lindenmayer, A. [1987]:}
``Inference algorithms for developmental systems with cell
lineages.''
{\sl Bulletin of Mathematical Biology} {\bf 49}, Nr. 1, pp. 93--123.

\Cpar
{\coms The problem is to find a D0L-system generating an observed sequence
of tree structures.}

\Hpar
{\csc Wood, D. [1975]:}
``Time-delayed 0L languages and sequences.''
{\sl Information Sciences} {\bf 8}, pp. 271--281.

\Hpar
{\csc Wood, D. [1977]:}
``Generalized time-delayed 0L languages.''
{\sl Information Sciences} {\bf 12}, pp. 151--155.

\Hpar
{\csc Culik, K. II {\rm and} Wood, D. [1978]:}
``Speed-varying 0L systems.''
{\sl Information Sciences} {\bf 14}, pp. 161--170.

\Cpar
{\coms The above three papers introduce the concept of {\it time-delayed
L-systems}.  It may be worthwhile to look at them again in the light
of simulation of continuous growth.}

\Hpar
{\csc Jones, N. D. {\rm and} Skyum, S. [1979]:} ``Complexity
of some problems concerning L-systems.'' {\sl Mathematical Systems
Theory} {\bf 13}, pp. 29-43.

\Cpar
{\coms A review of results on computation and complexity of L-systems.}

\Hpar
{\csc Vit\'anyi, P.~M.~B. [1986]:}
``Development, growth and time.''
In G. Rozenberg and A. Salomaa [Eds.]:
{\sl The Book of L},
Springer-Verlag, Berlin, pp.~431--444.

\Cpar
{\coms An attempt to obtain the sigmoidal growth curve using L-systems;
the concept of slowing down the progress of time
at a certain age seems artificial.}
\vskip 8 pt

{\twelveb 4.  GEOMETRICAL INTERPRETATIONS OF L-SYSTEMS}

{\comb L-systems were conceived for the purpose of describing development
of plants, but originally this description was confined to
the topological level.  
In order to present simulated plant development using computer-generated
images it is necessary to specify a geometrical interpretation of L-systems
as well. The first approaches --- by Hogeweg and Hesper [1974], and 
Frijters and Lindenmayer [1974] ---
used the same branching angle throughout the entire
structure.  More flexible approaches are listed below.}

\Hpar
{\csc Szilard, A.~L. {\rm and} Quinton, R.~E. [1979]:}
``An interpretation for DOL systems by computer graphics.''
{\sl The Science Terrapin} {\bf 4}, pp.~8--13.

\Cpar
{\coms The original paper introducing the
concept of using the symbols generated by an L-system to specify 
directions and angles between line segments.}

\Hpar
{\csc Siromoney, R. {\rm and} Subramanian, K.~G. [1983]:}
``Space-filling curves and infinite graphs.''
In H. Ehrig, M. Nagl and G. Rozenberg (Eds.): 
{\sl Graph grammars and their application to computer
science; Second International Workshop\/}.
Lecture Notes in Computer Science {\bf 153}, 
Springer-Verlag, Berlin, pp. 380-391.

\Cpar
{\coms Chain coding is used to graphically interpret strings
generated by L-systems.}

\Hpar
{\csc Freeman H. [1961]:}
``On encoding arbitrary geometric configurations.''
{\sl IRE Trans.  Electron.  Comput.} {\bf  10}, pp.~260--268.

\Cpar
{\coms The classic paper on chain coding.}

\Hpar
{\csc Prusinkiewicz, P. [1986]:}
``Graphical applications of L-systems.''
{\sl Proceedings of Graphics Interface '86 --- Vision Interface '86},
pp.~247--253.

\Cpar
{\coms
Turtle geometry is used as the basis for interpreting strings generated
by L-systems.
In contrast to chain coding which relies on absolute directions,
in turtle geometry directions are specified
relative to the previous ones.}

\Hpar
{\csc Abelson, H. {\rm and} diSessa, A.~A. [1982]:}
{\sl Turtle geometry}.
M.I.T.  Press, Cambridge.

\Cpar
{\coms The fundamental book on turtle geometry.}

\Hpar
{\csc Maurer, H.~A., Rozenberg, G. {\rm and} Welzl, E. [1982]:}
``Using string languages to describe picture languages.''
{\sl Information and Control} {\bf 54}, pp.~155--185.

\Hpar
{\csc Sudborough, I.~H. {\rm and} Welzl, E. [1985]:}
``Complexity and decidability for chain code picture languages.''
{\sl Theoretical Computer Science} {\bf 36}, pp.~173--202.

\Cpar
{\coms The above two papers formally analyze the properties of
pictures generated by Chomsky grammars under the chain interpretation.
It would be interesting to apply a similar approach to L-systems.}

\Hpar
{\csc Dekking, F.~M. [1982]:}
{\sl Recurrent sets: A fractal formalism.}
Delft University of Technology, Report 82-32.

{\csc Dekking, F.~M. [1982]:}
``Recurrent sets.'' 
{\sl Advances in Mathematics} 
{\bf 44}, Nr. 1, pp. 78--104.

\Cpar
{\coms Two papers on generating fractals using string languages; 
a fairly formal approach.}

\Hpar
{\csc Smith, A.~R. [1984]:}
{\sl Graftal formalism notes.}
Technical Memo Nr. 114, Lucasfilm Computer Division, San Rafael, CA.
\vskip 8pt

{\twelveb 5.  L-SYSTEMS IN DEVELOPMENTAL ANALYSIS}

{\comb The subsequent papers present a progression of L-system-based
techniques from a simple model of a context-free linear structure
(blue-green bacteria) to a complex context-sensitive branching
structure ({\it Mycelis muralis\/}).}

\Hpar
{\csc Baker, R. {\rm and} Herman, G.~T. [1972]:}
``Simulation of organisms using a developmental model, Parts I and II.''
{\sl Int. J. of Bio-Medical Computing} {\bf 3}, pp.~201--215 and 251--267.

\Hpar
{\csc Herman, G.~T. {\rm and} Liu, W.~H. [1973]:}
``The daughter of CELIA, the French flag, and the firing squad.''
{\sl Simulation} {\bf 21}, pp.~33--41.

\Hpar
{\csc Lindenmayer, A. [1974]:}
``Adding continuous components to L-systems.''  In:
G. Rozenberg and A. Salomaa (Eds.):
{\sl L Systems}, Lecture Notes in Computer Science {\bf 15}, 
Springer-Verlag, Berlin, pp. 53-68.

\Cpar
{\coms The above three 
papers present details of the first program for simulating
plant development with L-systems, called CELIA.}

\Hpar
{\csc Frijters, D. {\rm and} Lindenmayer, A. [1974]:}
``A model for the growth and flowering of {\it Aster novae-angliae}
on the basis of table (1, 0) L-systems.''
In: G. Rozenberg and A. Salomaa (Eds.): {\sl L Systems},
Lecture Notes in Computer Science {\bf 15}, Springer-Verlag, Berlin, pp.~24--52.

\Cpar
{\coms One of the first papers including computer-generated plots
of plants generated using L-systems.}

\Hpar
{\csc Frijters, D. [1978a]:}
``Principles of simulation of inflorescence development.''
{\sl Annals of Botany} {\bf 42}, pp.~549--560.

\Cpar
{\coms Delays, sequences of stages, developmental switches
implemented using table 0L-systems and CELIA-style
numerical attributes of segments are discussed, but all 
models presented are interactionless.}

\Hpar
{\csc Frijters, D. [1978b]:}
``Mechanisms of developmental integration of {\it Aster
novae-angliae} L. and {\it Hieracium murorum} L.''
{\sl Annals of Botany} {\bf 42}, pp.~561--575.

\Cpar
{\coms This paper discusses mechanisms which control plant development,
including delays, interaction and developmental switches, but does
not specify them in the form of ready-to-use L-systems.  However, many
mathematical
relationships between parts of the analyzed plants are given.}

\Hpar
{\csc Lindenmayer, A. [1984]:}
``Positional and temporal control mechanisms
in inflorescence development.''
In: P.~W.~Barlow and D.~J.~Carr (Eds.):
{\sl Positional controls in plant development},
University Press, Cambridge.

\Hpar
{\csc Janssen, J.~M. {\rm and} Lindenmayer, A. [1987]:}
``Models for the control of branch positions and flowering sequences of
capitula in {\it Mycelis muralis} (L.) Dumont (Compositae).''
{\sl New Phytologist} {\bf 105}, pp.~191--220.

\Cpar
{\coms The second paper is a refinement of the first one; both use
{\it Mycelis muralis} as an example.}

{\comb Some other papers using L-systems to analyze biological development
are listed below.}

\Hpar
{\csc Frijters, D. {\rm and} Lindenmayer, A. [1976]:}
``Developmental descriptions of
branching patterns with paracladial relationships.''
In: A. Lindenmayer and G.  Rozenberg (Eds.):
{\sl Automata, languages, development},  North-Holland,
Amsterdam, pp.~57--73.

\Cpar
{\coms Paracladial relations describe self-similarities in branching structures
on the topological level.  It would be interesting to investigate the 
relationship between paracladial relations and geometric self-similarity
as found in fractals.}

\Hpar
{\csc Lindenmayer, A. [1977]:}
``Paracladial relationships in leaves.''
{\sl Ber. Deutsch Bot. Ges. Bd.} {\bf 90}, pp. 287--301.

\Cpar
{\coms Self-similarity of leaf structures is described in terms of
D0L-systems.  A simple L-system describing leaf topology of {\it Delphinium
ajacis} is given, but addition of geometry is not a trivial
problem in this case.}

\Hpar
{\csc Nishida, T. [1980]:}
``KOL-systems simulating almost but not exactly
the same development --- the case of Japanese cypress.''
{\sl Memoirs Fac. Sci., Kyoto University, Ser. Bio.} {\bf 8}, pp.~97--122.

\Cpar
{\coms Development of shoots of Japanese cypress is expressed in
terms of stochastic L-systems, directly applicable to the production of
realistic computer-generated images.}

\Hpar
{\csc Robinson, D.~F. [1986]:}
``A notation for the growth of inflorescences.''
{\sl New Phytologist} {\bf 103}, pp. 587-596.

\Cpar
{\coms The proposed notation is not the same as L-systems, but
a translation between the two is straightforward.  Out of several
detailed examples, only {\it Lychnis coronaria} has been modeled
by us using computer graphics so far.}
\vskip 8pt

{\twelveb 6.  MULTIDIMENSIONAL L-SYSTEMS}

\Hpar
{\csc Habel, A. {\rm and} Kreowski, H.-J. [1983]:}
``On context-free graph languages generated by edge replacement.''
In: H. Ehrig, M. Nagl and G. Rozenberg (Eds.):
{\sl Graph grammars and their application to computer
science; Second International Workshop\/},
Lecture Notes in Computer Science {\bf 153}, 
Springer-Verlag, Berlin, pp.~143--158.

\Cpar
{\coms Graph-rewriting systems can be divided into two categories,
those which replace nodes and those which replace edges.  Edge-rewriting
systems have direct biological applications.  This paper surveys
the theoretical background of edge rewriting.}

{\comb Two approaches to parallel graph rewriting
are known as {\it map L-systems} and {\it double-wall L-systems}.  The following
papers describe map L-systems or ideas leading to them.}

\Hpar
{\csc Culik, K. II {\rm and} Lindenmayer, A. [1976]:}
``Parallel graph generating and graph recurrence systems for multicellular
development.''
{\sl Int. J. General Systems} {\bf 3}, pp. 53--66.

\Hpar
{\csc Lindenmayer, A. {\rm and} Culik, K. II [1979]:}
``Growing cellular systems: generation of graphs by parallel rewriting.''
{\sl Int. J. General Systems} {\bf 5}, pp. 45--55.

\Hpar
{\csc Culik, K. II {\rm and} Wood, D. [1979]:}
``A mathematical investigation of propagating graph 0L-systems.''
{\sl Information and Control} {\bf 43}, pp.~50--82.

\Cpar
{\coms Three papers on parallel graph generation which precede
the concept of map L-systems.}

\Hpar
{\csc Lindenmayer, A. {\rm and} Rozenberg, G. [1979]:}
``Parallel generation of maps:  Developmental systems for cell layers.''
In: V. Claus, H. Ehrig and G. Rozenberg (Eds.):
{\sl Graph grammars and their application to computer
science; First International Workshop\/},
Lecture Notes in Computer Science {\bf 73},
Springer-Verlag, Berlin, pp.~301--316.

\Cpar
{\coms The original paper on map L-systems.}

\Hpar
{\csc Siero, P.~L.~J., Rozenberg, G. {\rm and} Lindenmayer, A. [1982]:}
``Cell division patterns: syntactical description and implementation.''
{\sl Computer Graphics and Image Processing} {\bf 18}, pp. 329--346.

\Hpar
{\csc Lindenmayer, A. {\rm and} de Does, M. [1983]:}
``Algorithms for the generation and drawing of maps representing cell clones.''
In: H. Ehrig, M. Nagl and G. Rozenberg (Eds.):
{\sl Graph grammars and their application to computer
science; Second International Workshop\/},
Lecture Notes in Computer Science {\bf 153},
Springer-Verlag, Berlin, pp.~39--57.

\Cpar
{\coms The above papers contain detailed examples of how map L-systems work.
There also introduce graphical interpretations of maps.}

\Hpar
{\csc Lindenmayer, A. [1984]:}
``Models for plant tissue development with cell division orientation
regulated by preprophase bands of microtubules.''
{\sl Differentiation} {\bf 26}, pp. 1-10.

\Cpar
{\coms Example of a three-dimensional L-system, or {\it cellwork}.
Includes a calculation of edge lengths after subdivision.}

\Hpar
{\csc Lindenmayer, A. [1987]:}
``An introduction to parallel map generating systems.''
In: H. Ehrig, M. Nagl, A. Rosenfeld and G. Rozenberg (Eds.):
{\sl Graph grammars and their application to computer
science; Third International Workshop\/},
Lecture Notes in Computer Science {\bf 291},
Springer-Verlag, Berlin, pp. 27--40.

{\comb A different approach to define cellular structures was
developed by J. L\"uck and H.~B. L\"uck under the name of
double-wall L-systems.}

\Hpar
{\csc L\"uck, J. {\rm and} L\"uck, H.~B. [1981]:}
``Proposition d'une typologie de
l'organisation cellulaire des tissus v\'eg\'etaux.''
In: Herv\'e Le Guardier and Thiebut Moulin (Eds.):
{\sl Actes du premier s\'eminaire de l'Ecole de
Biologie Th\'eorique du CNRS},
Ecole Nationale Superieure de Techniques
Avanc\'ees, Paris, pp.~335--371.

\Hpar
{\csc L\"uck, J. {\rm and} L\"uck, H.~B. [1982]:}
``Sur la structure de
l'organisation tissulaire et son incidence sur la morphogen\`ese.''
In: Herv\'e Le Guardier (Ed.):
{\sl Actes du deuxi\`eme s\'eminaire de l'Ecole de Biologie
Th\'eorique du CNRS}, Publications de l'Universit\'e de Rouen, Abbaye de
Solignac, pp.~385--397.

\Hpar
{\csc L\"uck, J. {\rm and} L\"uck, H. [1983]:}
``Generation of 3-dimensional plant
bodies by double wall map and stereomap systems.''
In: H. Ehrig, M. Nagl and G. Rozenberg (Eds.):
{\sl Graph-Grammars and Their Application to
Computer Science; Second International Workshop\/},
Lecture Notes in Computer Science {\bf 153},
Springer-Verlag, Berlin, pp.~219--231.

\Hpar
{\csc L\"uck, J. {\rm and} L\"uck, H.~B. [1985]:}
``Comparative plant
morphogenesis founded on map and stereomap generating systems.''
In: J.  Demongeot, E. Goles and M. Tchuente (Eds.):
{\sl Dynamical systems and
cellular automata},  Academic Press, London, pp.~111--121.

\Hpar
{\csc L\"uck, J. {\rm and} L\"uck, H.~B. [1985]:} 
``Un m\'ecanisme g\'en\'erateur d'h\'elices
phyllotaxiques.''  In: G. Benchetrit and J. Demongeot (Eds.):
{\sl Actes du IVe s\'eminaire de l'Ecole de Biologie
Th\'eorique\/}, Editions du CNRS, Paris, pp.~317--330.

\Hpar
{\csc L\"uck, H.~B. {\rm and} L\"uck, J. [1986]:}
``Unconventional leaves (An application of map 0L-systems to biology).''
In: G. Rozenberg and A.  Salomaa (Eds.):
{\sl The book of L}.  Springer-Verlag, Berlin - Heidelberg -
New York - Tokyo, pp.~275--289.

\Hpar
{\csc L\"uck, J. {\rm and} L\"uck, H.~B. [1987]:}
``From 0L and IL map systems to indeterminate and determinate growth
in plant morphogenesis.''
In: H. Ehrig, M. Nagl, A. Rosenfeld and
G. Rozenberg (Eds.):
{\sl Graph grammars and their application to computer
science; Third International Workshop\/},
Lecture Notes in Computer Science {\bf 291},
Springer-Verlag, Berlin, pp. 393--410.

\Hpar
{\csc L\"uck, J., Lindenmayer, A. {\rm and} L\"uck, H.~B. [1988]:}
``Models for cell tetrads and clones in meristematic cell layers.''
{\sl Botanical Gazette}, in press.
\vskip 8pt

{\twelveb 7.  SYNTHESIS OF REALISTIC PLANT IMAGES} 

{\twelveb 7.1. Synthesis methods based on L-systems.}

\Hpar
{\csc Hogeweg, P. {\rm and} Hesper, B.  [1974]:}
``A model study on biomorphological description.''
{\sl Pattern Recognition} {\bf 6}, pp.~165--179.

\Cpar 
{\coms The techniques of A.~R. Smith were inspired by this paper.}

\Hpar
{\csc Smith, A. R. [1978]:}
``About the cover: Reconfigurable machines.''
{\sl Computer} {\bf 11}, Nr.~7, pp.~3--4.

\Cpar
{\coms The first realistic images of computer-generated plants.}

\Hpar
{\csc Smith, A. R. [1984]:}
``Plants, fractals, and formal languages.''
{\sl Computer Graphics} {\bf 8}, Nr. 3, pp.~1--10.

\Cpar
{\coms A classic; the first paper to recognize the role of formal
languages in computer graphics.  Coins
the term ``database amplification''.  Contains many
realistic plant images.}

\Hpar
{\csc Smith, A. R. [1985]:}
{\sl Grammars for generating the complexity of reality.}
Video tape, Lucasfilm/PIXAR.

\Cpar
{\coms A video illustration of the above paper.}

\Hpar
{\csc Prusinkiewicz, P. [1987]:}
``Applications of L-systems to computer imagery.''
In: H. Ehrig, M. Nagl, A. Rosenfeld and
G. Rozenberg (Eds.):
{\sl Graph grammars and their application to computer
science; Third International Workshop\/},
Lecture Notes in Computer Science {\bf 291},
Springer-Verlag, Berlin, pp.~534--548.

\Cpar
{\coms The turtle interpretation of L-systems is generalized to three
dimensions. Stochastic L-systems are used to model specimen-to-specimen
variation within a species, and bicubic patches are integrated with the
L-system-based model.  L-systems generating several plant images are 
specified in detail.}

\Hpar
{\csc Beyer, T. {\rm and} Friedell, M. [1987]:}
``Generative scene modelling.'' 
{\sl Proceedings of EUROGRAPHICS '87}, pp.~151--158 and 571.

\Cpar
{\coms The authors claim to have invented a ``new theory of scene modelling''
while ignoring previous work in the field, including the 1984 paper by
A.~R. Smith.  The extension of L-systems to graphs with
cycles seems to be different from the map L-systems of Lindenmayer
and the double-wall L-systems of the L\"ucks, although the description is
too superficial to determine, what was really done.}

{\twelveb 7.2. Other synthesis methods.}

\Hpar
{\csc Aono, M. {\rm and} Kunii, T.~L. [1984]:}
``Botanical tree image generation.''
{\sl IEEE Computer Graphics and Applications}
{\bf 4}, Nr.~5, pp.~10--34.

\Cpar
{\coms Topology is defined by recursive algorithms; variation between
trees is achieved primarily by manipulating branching angles.
Based on the analysis of tree architecture by Honda.}

\Hpar
{\csc Aono, M. {\rm and} Kunii, T.~L. [1985]:}
{\sl Botanical tree image generation},
Video tape, IBM Japan, Tokyo.

\Hpar
{\csc Bloomenthal, J. [1985]:}
``Modeling the Mighty Maple.''
{\sl Computer Graphics} {\bf 19}, Nr.~3, pp.~305--311.

\Cpar
{\coms An exercise in realism; uses splines to model branches, carefully models
branching points, and texture-maps leaves and bark.} 

\Hpar
{\csc Bloomenthal, J. [1987]:} {\sl Polygonization of implicit surfaces.}
Report CSL-87-2, Xerox Corporation, Palo Alto, CA.

\Cpar
{\coms A method for modeling branching points in trees with wide branches.}

\Hpar
{\csc Eyrolles, G. [1986]:}
{\sl Synth\`ese d'images figuratives d'arbres par des
m\'ethodes combinatoires.}
Ph.~D. Thesis, Universit\'e de Bordeaux I.

\Cpar
{\coms 
Realistic two-dimensional tree silhouettes are 
generated using a stochastic
technique based on Horton-Strahler analysis (a classic method for analysing
river systems.)}

\Hpar
{\csc Kawagushi, Y. [1982]:}
``A morphological study of the form of nature.'' 
{\sl Computer Graphics} {\bf 16}, Nr.~3, pp.~223--232.

\Cpar
{\coms Generation of abstract branching structures.} 

\Hpar
{\csc Oppenheimer, P. [1986]:}
``Real time design and animation of fractal plants and trees.''
{\sl Computer Graphics} {\bf 20}, Nr.~4, pp.~55--64.

\Hpar
{\csc Reeves, W.~T. {\rm and} Blau, R. [1985]:}
``Approximate and probabilistic algorithms
for shading and rendering structured particle systems.''
{\sl Computer Graphics} {\bf 19}, Nr.~3, pp.~313--322.

{\twelveb 7.3. Organ models.}

\Hpar
{\csc Lienhardt, P. [1987]:}
{\sl Mod\'elisation et \'evolution de surfaces libres.}
Ph.~D. Thesis, Universit\'e Louis Pasteur, Strasbourg.

\Hpar
{\csc Lienhardt, P. {\rm and} Francon, J. [1987]:}
{\sl Synth\`ese d'images de feuilles v\'eg\'etales.}
Technical Report R-87-1, D\'epartement d'informatique, Universit\'e
Louis Pasteur, Strasbourg.
\vskip 8pt

{\twelveb 8.  RELATED BOTANICAL PAPERS}

{\twelveb 8.1. Plant architecture.}

{\comb Two fundamental books on trees.}

\Hpar
{\csc Hall\'e, F.,  Oldeman, R.~A.~A. {\rm and} Tomlinson, P.~B. [1978]:}
{\sl Tropical trees and forests: an architectural analysis.}
Springer-Verlag, Berlin.

\Hpar
{\csc Zimmerman, M.~H., {\rm and} Brown, C.~L. [1971]:}
{\sl Trees --- structure and function.} 
Springer-Verlag, Berlin.

{\comb The series of papers authored or co-authored by Honda provides
increasingly refined models of trees.  While the approach based on L-systems
starts from the topology of branching structures and complements
it with geometrical details, Honda starts from the branching geometry.
However, as both models get increasingly accurate, the same
types of problems, such as interaction and growth control mechanisms,
are addressed.}

\Hpar
{\csc Honda, H. [1971]:}
``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 shape of the
tree-like body.''
{\sl J. Theoretical Biology} {\bf 31}, pp. 331--338.

\Cpar
{\coms Tree structures are defined by simple recursive algorithms.
Emphasis is put on geometry.  Special attention is given to the definition
of branching angles.}

\Hpar
{\csc Fisher, J.~B. {\rm and} Honda, H. [1977]:}
``Computer simulation of branching pattern and geometry in {\it Terminalia}
(Combretaceae), a tropical tree.''
{\sl Botanical Gazette} {\bf 138}, Nr. 4, pp. 377--384.

\Hpar
{\csc Honda, H., Tomlinson, P.~B. {\rm and} Fisher, J.~B. [1982]:}
``Two geometrical models of branching of botanical trees.''
{\sl Annals of Botany} {\bf 49}, pp. 1--11.

\Cpar
{\coms Extensions and improvements of the previous paper.}

\Hpar
{\csc Honda, H. {\rm and} Fisher, J.~B. [1978]:}
``Tree branch angle: Maximizing effective leaf area.''
{\sl Science} {\bf 199}, pp. 888--890.

\Cpar
{\coms Observed branch angles in {\it Terminalia} are shown to be similar
to theoretically optimal values that produce the maximum effective leaf area.}

\Hpar
{\csc Honda, H. {\rm and} Fisher, J.~B. [1979]:}
``Ratio of tree branch lengths: The equitable distribution of leaf
clusters on branches.''
{\sl Proceedings of the National Academy of Sciences USA} {\bf 76}, Nr. 8,
pp. 3875--3879.

\Cpar
{\coms Continuation of the previous paper; observed branch angles in 
{\it Terminalia} also produce the most equitable distribution of leaf
clusters.}

\Hpar
{\csc Honda, H,. Tomlinson, P.~B. {\rm and} Fisher, J.~B. [1981]:}
``Computer simulation of branch interaction and regulation by unequal flow
rates in botanical trees.''
{\sl Amer. J. Botany} {\bf 68}, pp. 569--585. 

\Hpar
{\csc Borchert, R. {\rm and} Honda, H. [1984]:}
``Control of development in the bifurcating branch system of
{\it Tabebuia rosea}: A computer simulation.''
{\sl Botanical Gazette} {\bf 145}, Nr. 2, pp. 184--195.

\Cpar
{\coms Branch interaction is applied to control the number of branches
of various orders.  Yet another specification of branching geometry is
introduced.  The conclusion states: {\it Our results suggest that any
realistic simulation of the development of the branch system in botanical
trees requires at least four sets of rules addressing (1) geometry
of the branch system, (2) reduction of branch numbers at higher orders through
reduction of branching in lateral branches, (3) the establishment of
apical control through branch interaction, and (4) control of growth of
the branch system as a whole by a sigmoid growth function.}
It would be very interesting to express these results in 
terms of L-systems, and compare them with the {\it Mycelis} model.}

{\comb There are also other papers which analyze plant architecture
in a quantitative way, thus providing useful data for simulation.}

\Hpar
{\csc Bell, A.~D., Roberts, D. {\rm and } Smith, A. [1979]:}
``Branching patterns: the simulation of plant architecture.''
{\sl Journal of Theoretical Biology} {\bf 81}, pp. 351--375.

\Cpar
{\coms Simulation of two-dimensional branching patterns of rhizomatous plants.}

\Hpar
{\csc Descoings, B. [1975]:}
``Les types morphologiques et biomorphologiques des especes graminoides
dans les formations herbeuses tropicales.''
{\sl Naturalia Monspeliensia, s\'er. Bot} {\bf 25}, pp. 23--25.

\Hpar
{\csc Ford, H. [1987]:} ``Investigating the ecological and evolutionary
significance of plant growth form using stochastic simulation.''
{\sl Annals of Botany} {\bf 59}, pp. 487--494.

\Hpar
{\csc Remphery, W.~R., Neal, B.~R. {\rm and} Steeves, T.~A. [1983]:}
``The morphology and growth of {\it Arctostaphylos uva-ursi} (bearberry):
An architectural analysis''.
{\sl Canadian Journal of Botany} {\bf 61}, Nr. 9, pp. 2430-2450.

\Hpar
{\csc Remphery, W.~R., Neal, B.~R. {\rm and} Steeves, T.~A. [1983]:}
``The morphology and growth of {\it Arctostaphylos uva-ursi} (bearberry):
An architectural model simulating colonizing growth''.
{\sl Canadian Journal of Botany} {\bf 61}, Nr. 9, pp. 2451-2458.

\Hpar
{\csc Renshaw, E. [1985]:} ``Computer simulation of Sitka spruce:
Spatial branching models for canopy growth and root structure.''
{\sl IMA J. of Math. Applied in Medicine and Biology} {\bf 2},
pp.~183--200.

\Hpar
{\csc Smith, B.~H. [1984]:}
``The optimal design of a herbaceous body.''
{\sl The American Naturalist} {\bf 123}, pp. 197--211.

\Hpar
{\csc Yu, O {\rm and} Gnonot, M. [1981, 1982]:} ``Recherches sur le
tallage chez le dactyle ({\it Dactylis glomerata} L.). I. Etude
experimentale de l'effet de l'azote sur le tallage.  II. R\'eflexions
sur la formalisation et la mod\'elisation des processus de tallage.''
{\sl Acta Oecologica, Oecol. Plantarum} {\bf 2}, pp. 351--365, and
{\bf 3}, pp. 39--47.

{\comb The following papers analyze mechanical properties of tree structures.}

\Hpar
{\csc Murray, C.~D. [1927]:}
``A relationship between circumference and weight in trees and its
bearing on branching angles.''
{\sl Journal of General Physiology} {\bf 10}, pp. 725-739.

\Hpar
{\csc McMahon, T.~A. [1975]:}
``The mechanical design of trees.''
{\sl Scientific American}, pp. 93-102.

\Hpar
{\csc McMahon, T.~A., {\bf and} Kronauer, R.~E. [1976]:}
``Tree structures: deducing the principle of mechanical design.''
{\sl Journal of Theoretical Biology} {\bf 59}, pp.~443--466.

\Hpar
{\csc Armstrong, W.~W. [1986]:}
``The dynamics of tree linkages with a fixed root
link and limited range of rotation.''
{\sl Actes du Colloque Internationale
l'Imaginaire Num\'erique '86}, pp. 16-21.

{\twelveb 8.2. Phyllotaxis.}

\Hpar
{\csc Erickson, R.~O. [1973]:}
``Tubular packing of spheres in biological fine structure.''
{\sl Science} {\bf 181}, pp. 705-716.

\Hpar
{\csc Erickson, R.~O.~[1983]:}
``The geometry of phyllotaxis.''
In: J. E. Dale and F. L. Milthrope (Eds.):
{\sl The growth and functioning of leaves},
University Press, Cambridge, pp.~53--88.

\Cpar
{\coms An important comprehensive reference.}

\Hpar
{\csc Hellendoorn, P.~H. {\rm and} Lindenmayer, A. [1974]:}
``Phyllotaxis in {\it Bryophyllum tubiflorum}: Morphogenetic
studies and computer simulations.''
{\sl Acta Biol. Neerl.} {\bf 23}, Nr. 4, pp. 473--492.

\Hpar
{\csc Veen, A.~H. {\rm and} Lindenmayer, A. [1977]:}
``Diffusion mechanism for phyllotaxis: Theoretical physico-chemical
and computer study.''
{\sl Plant Physiol.} {\bf 60}, pp. 127--139.

\Hpar
{\csc Kilmer, W.~L. [1971]:}
``On growing pine cones and other Fibonacci fruits --- McCulloch's
Localized algorithm.''
{\sl Mathematical Biosciences} {\bf 11}, pp. 53-57.

\Hpar
{\csc Mathai, A.~M. {\rm and} Davis, T.~A. [1974]:}
``Constructing the sunflower head.''
{\sl Mathematical biosciences} {\bf 20}, pp. 117-133.

\Cpar
{\coms Some nice flower models
are produced, but the underlying mathematical reasoning is not clear.}

\Hpar
{\csc Mitchison, G.~J. [1977:} ``Phyllotaxis and the Fibonacci series.''
{\sl Science} {\bf 196}, pp.~270--275.

\Hpar
{\csc Richards, F.~J. [1959]:} ``Phyllotaxis: its quantitative expression
and relation to growth in the apex.'' {\sl Philos. Trans. Royal Society
London}, Ser. B, {\bf 235}, pp. 509--564.

{\twelveb 8.3. Inflorescences.}

{\comb The first group of publications is devoted to the description and
classification of inflorescences.}

\Hpar
{\csc Troll, W. [1964]:}
{\sl Die Infloreszenzen}, Vol. I.  Gustav Fischer Verlag,
Stuttgart.

\Hpar
{\csc M\"uller-Doblies D. {\rm and} M\"uller-Doblies U. [1987]:}
``Cautious improvement of a descriptive terminology of inflorescences.''
{\sl Monocot newsletter} {\bf 4},
Institut f\"ur Biologie, Technical University of Berlin (West), 13 pp.

\Hpar
{\csc Weberling, F. [1965]:}
``Typology of inflorescences.''
{\sl J. Linn. Soc. (Bot.)} {\bf 59}, Nr. 378, pp. 215--222.

{\comb The second group of interest focuses on mechanisms which
control inflorescence development and flowering sequences.}

\Hpar
{\csc Raju, M.~V.~S., Jones, G.~J. {\rm and} Ledingham, G.~F. [1984]:}
`` Floret anthesis and pollination in wild oats {\it (Avena fatua)}.''
{\sl Canadian Journal of Botany} {\bf 63}, pp. 2187-2195.

\Cpar
{\coms Contains data on the flowering sequence of the wild oats.}

\Hpar
{\csc Sell, Y. [1980]:}
``Action de l'apex caulinaire et maturation florale dans le cadre de la
floraison descendante.''
{\sl Flora} {\bf 169}, pp. 15-22.

\Cpar
{\coms The role of apical dominance in inflorescence development.}

\Hpar
{\csc Sell, Y. [1980]:}
``Physiological and phylogenetic significance of the direction of flowering
in inflorescence complexes.''
{\sl Flora} {\bf 169}, pp. 282-294.

\Cpar
{\coms From the summary: {\it Downward flowering of the lateral shoots
of a herbaceous plant is here suggested to be the expression of antagonistic
long-range interactions between various organs.}}

{\twelveb 8.4. Leaves.}

\Hpar
{\csc Silk, W.~K. {\rm and} Erickson, R.~O. [1979]:}
``Kinematics of plant growth.''
{\sl Journal of Theoretical Biology} {\bf 76}, pp. 481-501.

\Hpar
{\csc Erickson, R.~O. {\rm and} Silk, W.~K. [1980]:}
``The Kinematics of plant growth.''
{\sl Scientific American} {\bf 242}, Nr. 5, pp. 134--151.

\Hpar
{\csc Scholten, H. {\rm and} Lindenmayer, A. [1981]:}
``A mathematical model for the laminar development of simple leaves.''
In: W. van Cotthem (Ed.):
{\sl Morphologie --- Anatomie und Systematik der Pflanzen, 5. Symposium},
Verlag Waegeman, Ninove, Belgium, pp. 29--37.

\Cpar
{\coms An analytical description of growth is expressed in terms of
{\it growth fields} and applied to leaf blades.}

\Hpar
{\csc Jeune, B. [1978]:}
``Sur le d\'eterminisme de la forme de feuilles de dicotyl\'edones.''
{\sl Adansonia} {\bf 2}, pp. 83--94.

\Hpar
{\csc Jeune, B. [1986]:}
``Mod\`ele de d\'eveloppement pour des feuilles basip\`etes de
Dicotyl\'edons.''
{\sl Adansonia} {\bf 8}, pp. 301--323.

\Cpar
{\coms A case study of the development of very young leaves.}

\Hpar
{\csc K\"urbs, S. [1973]:}
``Vergleichend-entwicklungsgeschichtliche Studien an
Ranunculaceen-Fiederbl\"attern.'' Part I and II.
{\sl Bot. Jahrb. Syst.} {\bf 93} Nr. 1, pp. 130--167 and Nr. 3, pp. 325-371.

\Cpar
{\coms Analyzes leaves of the dissected and divided type.}

{\comb The following papers contain detailed pictures and discussion
of venation patterns.}

\Hpar
{\csc Bougnon, F., Dulieu, H. {\rm and} Turlier, M.-F. [1969]:}
``Morphologie v\'eg\'etale --- Rapports entre les directions
fondamentales de croissance dans l'\'ebauche et la nervation
foliaires.''
{\sl C. R. Acad. Sc. Paris, S\'er. D} {\bf 268}, pp. 48--50.

\Hpar
{\csc Lersten, N. [1965]:}
``Histogenesis of leaf venation in {\it Trifolium Wormskioldii}
(Leguminosae)''
{\sl American Journal of Botany} {\bf 52}, Nr. 8, pp. 767--774.

\Hpar
{\csc Philpott, J. [1956]:}
``Blade tissue organization of foliage leaves of some Carolina shrub-bog
species as compared with their Appalachian mountain affinities.''
{\sl The Botanical Gazette} {\bf 118}, Nr. 2.

\Hpar
{\csc Pray, T.~R. [1954--1955]:}
``Foliar venation of angiosperms, Part I -- IV.''
{\sl American Journal of Botany} {\bf 41}, pp. 663--670;
{\bf 42}, pp. 18--27, 611--618 and 698--706.

{\twelveb 8.5. Population dynamics and modular organisms.}

\Hpar
{\csc Bazzaz, F.~A. {\rm and} Harper, J.~L. [1977]:}
``Demographic analysis of the growth of {\it Linum usitaissimum.''}
{\sl New Phytologist} {\bf 78}, pp. 193--207.

\Hpar
{\csc Bell, A.~D. [1986]:} ``The simulation of branching patterns in modular
organisms.'' {\sl Philos. Trans. Royal Society London} Ser. B, {\bf 313},
pp.~143--169.

\Hpar
{\csc Hall\'e, F. [1986]:} ``Modular growth in seed plants.''
{\sl Philos. Trans. Royal Society London} Ser. B, {\bf 313},
pp.~77--87.

\Hpar
{\csc Harper, J.~L. {\rm and} Bell, A. D. [1979]:} ``The population
dynamics of growth form in organisms with modular growth.''
In: R.~M. Anderson, B.~O. Turner and L.~R. Taylor (Eds.):
{\sl Population dynamics}, Blackwell, Oxford, pp.~29--52.

\Hpar
{\csc Maillette, L. [1982]:} ``Structural dynamics of silver birch.
I. The fates of buds.  II.  A matrix model of the bud population.''
{\sl J. Appl. Ecol.} {\bf 19}, pp.~203--218 and 219--238.

\Hpar
{\csc Porter, J.~R. [1983]:} ``A modular approach to analysis of plant
growth. I. Theory and principles.  II. Methods and results.''
{\sl New Phytologist} {\bf 94}, pp.~183--190 and 191--200.
}
\bye