Skip to main content
SpringerLink
Log in
Book cover

International Workshop on Graph Grammars and Their Application to Computer Science

Graph Grammars 1990: Graph Grammars and Their Application to Computer Science pp 127–143Cite as

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

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((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.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  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.

    Article  PubMed  Google Scholar 

  2. Culik II, K. and D. Wood. 1979. A mathematical investigation of propagating graph-OL systems. Information and Control 43: 50–82.

    Article  Google Scholar 

  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. 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. 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. 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. 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. 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.

    Article  Google Scholar 

  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. 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. 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. 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. 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. 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. Lück, J., A. Lindenmayer and H.B. Lück. 1988. Models of cell tetrads and clones in meristematic cell layers. Bot. Gaz. 149: 127–141.

    Article  Google Scholar 

  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. 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. 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. Rozenberg, G. and A. Lindenmayer. 1973. Developmental systems with locally catenative formulas. Acta informatica 2: 214–248.

    Article  Google Scholar 

  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. Tutte, W.T. 1982. Graph Theory. Addison-Wesley Publ. Co., Reading, Mass.

    Google Scholar 

  22. Tuza, Z. and A. Lindenmayer. 1987. Locally generated colourings of hexagonal cell division patterns: application to retinal cell differentiation. Manuscript.

    Google Scholar 

  23. Zepf, E. 1952. Über die Differenzierung des Sphagnumblattes. Zeitschrift für Botanik 40: 87–118.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Regina, S4S 0A2, Regina, Saskatchewan, Canada

    Martin J. M. de Boer

Authors
  1. Martin J. M. de Boer
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Hartmut Ehrig Hans-Jörg Kreowski Grzegorz Rozenberg

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

de Boer, M.J.M. (1991). Construction of map OL-systems for developmental sequences of plant cell layers. In: Ehrig, H., Kreowski, HJ., Rozenberg, G. (eds) Graph Grammars and Their Application to Computer Science. Graph Grammars 1990. Lecture Notes in Computer Science, vol 532. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017386

Download citation

  • DOI: https://doi.org/10.1007/BFb0017386

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54478-4

  • Online ISBN: 978-3-540-38395-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation