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Construction of map OL-systems for developmental sequences of plant cell layers

  • Martin J. M. de Boer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 532)

Abstract

The construction of map OL-systems for the generation of observed developmental sequences of cell patterns in plant cell layers is discussed. The aim is to construct a map OL-system which emphasizes regularities in the patterns. The indirect construction method discussed in this paper is based on the successive specification of a developmental sequence by a cell system, a double wall map OL-system (dm-system) and an mBPMOL-system (sm-system), respectively. The final sm-system is used for growth analysis and computer simulation.

Keywords

cellular layers development map L-systems construction procedure plant morphology computer simulation 

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References

  1. [1]
    Abbott, L.A. and A. Lindenmayer. 1981. Models for growth of clones in hexagonal cell arrangements: applications in Drosophila wing disc epithelia and plant epidermal tissues. J. Theor. Biol. 90: 495–514.CrossRefPubMedGoogle Scholar
  2. [2]
    Culik II, K. and D. Wood. 1979. A mathematical investigation of propagating graph-OL systems. Information and Control 43: 50–82.CrossRefGoogle Scholar
  3. [3]
    De Boer, M.J.M. 1990. The relationship between cell division pattern and global shape of young fern gametophytes II. Morphogenesis of heart-shaped thalli. Bot. Gaz. 151 (In press).Google Scholar
  4. [4]
    De Boer, M.J.M. and M. de Does. 1990. The relationship between cell division pattern and global shape of young fern gametophytes I. A model study. Bot. Gaz. 151 (In press).Google Scholar
  5. [5]
    De Boer, M.J.M., and A. Lindenmayer. 1987. Map OL-systems with edge label control: Comparison of marker and cyclic systems. Pages 378–392 in: H. Ehrig, M. Nagl, G. Rozenberg and A. Rosenfeld eds. Graph grammars and their applications to computer science. Lecture Notes in Computer Science Vol. 291. Springer-Verlag, Berlin.Google Scholar
  6. [6]
    De Does, M. and A. Lindenmayer. 1983. Algorithms for the generation and drawing of maps representing cell clones. Pages 39–57 in: H. Ehrig, M. Nagl, and G. Rozenberg, eds. Graph Grammars and their applications to computer science. Lecture Notes in Computer Science Vol. 153. Springer-Verlag, Berlin.Google Scholar
  7. [7]
    Fracchia, F.D., P. Prusinkiewicz and M.J.M. de Boer. 1990. Animation of the development of multicellular structures. Pages 3–18 in: N. Magnenat-Thalmann and D. Thalmann, eds. Springer-Verlag, Tokyo.Google Scholar
  8. [8]
    Jürgensen, H. and A. Lindenmayer. 1987. Modelling development by OL-systems: inference algorithms for developmental systems with cell lineages. Bull. Math. Biol. 49: 93–123.CrossRefGoogle Scholar
  9. [9]
    Lindenmayer, A. 1987. An introduction to parallel map generating systems. Pages 27–40 in H. Ehrig, M. Nagl, G. Rozenberg, and A. Rosenfeld, eds. Graph grammars and their application to computer science. Lecture Notes in Computer Science. Vol. 291. Springer-Verlag, Berlin.Google Scholar
  10. [10]
    Lindenmayer, A., and G. Rozenberg. 1979. Parallel generation of maps: developmental systems for cell layers. Pages 301–316 in V. Claus, H. Ehrig, and G. Rozenberg, eds. Graph grammars and their application to computer science. Lecture Notes in Computer Science Vol. 73. Springer-Verlag, Berlin.Google Scholar
  11. [11]
    Lück, J. and H.B. Lück. 1978. Automata theoretical explanation of tissue growth. Pages 974–185 in Proc. Int. Symp. Math. Topics Biol., Res. Inst. Math. Sci., Kyoto.Google Scholar
  12. [12]
    Lück, J. and H.B. Lück. 1979. Two-dimensional, differential, intercalary plant tissue growth and parallel graph generating and graph recurrence systems. Pages 301–316 in V. Claus, H. Ehrig, and G. Rozenberg, eds. Graph grammars and their application to computer science. Lecture Notes in Computer Science Vol. 73. Springer-Verlag, Berlin.Google Scholar
  13. [13]
    Lück, J. and H.B. Lück. 1982. Sur la structure de l'organisation tissulaire et son incidance sur la morphogénèse. Pages 385–397 in H. Le Guyader, ed. Actes du 2-ème séminaire de l'Ecole de Biologie théorique du C.N.R.S. Publications de l'Université de Rouen, Rouen.Google Scholar
  14. [14]
    Lück, J. and H.B. Lück. 1987. From OL and IL map systems to indeterminate and determinate growth in plant morphogenesis. Pages 393–410 in H. Ehrig, M. Nagl, G. Rozenberg, and A. Rosenfeld, eds. Graph grammars and their application to computer science. Lecture Notes in Computer Science. Vol. 291. Springer-Verlag, Berlin.Google Scholar
  15. [15]
    Lück, J., A. Lindenmayer and H.B. Lück. 1988. Models of cell tetrads and clones in meristematic cell layers. Bot. Gaz. 149: 127–141.CrossRefGoogle Scholar
  16. [16]
    Morris, V.B., K.E. Dixon and R. Cowan. 1989. The topology of cleavage patterns with examples from embryos of Nereis, Styela and Xenopus. Philos. Trans. Royal Society London Ser. B. 325: 1–36.Google Scholar
  17. [17]
    Nakamura, A., A. Lindenmayer and K. Aizawa. 1986. Some systems for map generation. Pages 323–332 in G. Rozenberg and A. Salomaa, eds. The Book of L. Springer-Verlag, Berlin.Google Scholar
  18. [18]
    Nakamura, A., A. Lindenmayer and K. Aizawa. 1987. Map OL-systems with markers. Pages 479–495 in H. Ehrig, M. Nagl, G. Rozenberg and A. Rosenfeld, eds. Graph grammars and their application to computer science. Lecture Notes in Computer Science. Vol 291. Springer-Verlag, Berlin.Google Scholar
  19. [19]
    Rozenberg, G. and A. Lindenmayer. 1973. Developmental systems with locally catenative formulas. Acta informatica 2: 214–248.CrossRefGoogle Scholar
  20. [20]
    Szilard, A.L. and R.E. Quinton. 1979. An interpretation for DOL-systems by computer graphics. The Science Terrapin, Faculty of Science, Univ. of Western Ontario, 4: 8–13.Google Scholar
  21. [21]
    Tutte, W.T. 1982. Graph Theory. Addison-Wesley Publ. Co., Reading, Mass.Google Scholar
  22. [22]
    Tuza, Z. and A. Lindenmayer. 1987. Locally generated colourings of hexagonal cell division patterns: application to retinal cell differentiation. Manuscript.Google Scholar
  23. [23]
    Zepf, E. 1952. Über die Differenzierung des Sphagnumblattes. Zeitschrift für Botanik 40: 87–118.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Martin J. M. de Boer
    • 1
  1. 1.Department of Computer ScienceUniversity of ReginaReginaCanada

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