Skip to main content
SpringerLink
Log in

Integrating lineage and interaction for the visualization of cellular structures

  • Biology
  • Conference paper
  • First Online:
Graph Grammars and Their Application to Computer Science (Graph Grammars 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1073))

Abstract

This paper introduces context-sensitive cell systems as an extension of context-free cell systems for the simulation of pattern formation in two-dimensional cellular structures. The integration of interaction and lineage within the production rules allows for the modelling of division patterns that cannot solely be explained using lineage rules, such as the differentiation of epidermal leaf cells into stomata. The concept is illustrated using inhibition and reaction-diffusion models to simulate the development of a spot pattern.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. E. Bünning. Die entstehung von mustern in der entwicklung von pflanzen. Hand. Pflanzenphysiol, XV(1):383–408, 1965.

    Google Scholar 

  2. M. J. M. de Boer. Analysis and computer generation of division patterns in cell layers using developmental algorithms. PhD thesis, University of Utrecht, the Netherlands, 1989.

    Google Scholar 

  3. M. J. M. de Boer, F. D. Fracchia, and P. Prusinkiewicz. A model for cellular development in morphogenetic fields. In G. Rozenberg and A. Salomaa, editors, Lindenmayer Systems. Impacts on Theoretical Computer Science, Computer Graphics, and Developmental Biology, pages 351–370. Springer-Verlag, Berlin, 1992.

    Google Scholar 

  4. F. D. Fracchia, P. Prusinkiewicz, and M. J. M. de Boer. Visualization of the development of multicellular structures. In Proceedings of Graphics Interface '90, pages 267–277, 1990.

    Google Scholar 

  5. M. Gardner. The fantastic combinations of John Conway's new solitaire game ‘life'. Scientific American, 223(4):120–123, 1970.

    Google Scholar 

  6. R. W. Korn. A neighboring-inhibition model for stomate patterning. Dev. Biol., 88:115–120, 1981.

    Google Scholar 

  7. U. Landström. On the differentiation of perspective ectoderm to a ciliated cell pattern in embryos of Ambystoma mexicanum. J. Embryol. Exp. Morph., 41:23–32, 1977.

    Google Scholar 

  8. A. Lindenmayer and G. Rozenberg. Parallel generation of maps: Developmental systems for cell layers. In V. Claus, H. Ehrig, and G. Rozenberg, editors, Graph grammars and their application to computer science; First International Workshop, Lecture Notes in Computer Science 73, pages 301–316. Springer-Verlag, Berlin, 1979.

    Google Scholar 

  9. H. B. Lück and J. Lück. Vers une metrie des graphes evolutifs, representatifs d'ensembles cellulaires. In H. Le Guyader and T. Moulin, editors, Actes du premier seminaire de l'Ecole de Biologie Théorique du CNRS, pages 373–398. Ecole Nat. Sup. de Techn. Avanc., Paris, 1981.

    Google Scholar 

  10. J. Lück and H. B. Lück. Sur la structure de l'organisation tissulaire et son incidence sur la morphogenèse. In Hervé Le Guardier, editor, Actes du deuxième séminaire de l'Ecole de Biologie Théorique du CNRS, pages 385–397. Publications de l'Université de Rouen, Abbaye de Solignac, 1982.

    Google Scholar 

  11. H. Meinhardt. Models of biological pattern formation. Academic Press, London & New York, 1982.

    Google Scholar 

  12. A. Nakamura. A. Lindenmayer, and K. Aizawa. Some systems for map generation. In G. Rozenberg and A. Salomaa, editors, The Book of L, pages 323–332. Springer-Verlag, Berlin, 1986.

    Google Scholar 

  13. P. Prusinkiewicz and A. Lindenmayer. The Algorithmic Beauty of Plants. Springer-Verlag, New York, 1990. With J. Hanan, F. D. Fracchia, D. R. Fowler, M. J. M. de Boer and L. Mercer.

    Google Scholar 

  14. T. Sachs. Pattern formation in plant tissues. Cambridge University Press, Cambridge, 1991.

    Google Scholar 

  15. A. Turing. The chemical basis of morphogenesis. Phil. Trans. Roy. Soc. B, 237(32):5–72, 1952.

    Google Scholar 

  16. G. Turk. Generating synthetic textures on arbitrary surfaces using reaction-diffusion, 1991. Proceedings of SIGGRAPH '91 (Las Vegas, Nevada, July 28–August 2, 1991), in Computer Graphics 25,4 (July 1991), pages 289–298, ACM SIGGRAPH, New York, 1991.

    Google Scholar 

  17. A. H. Veen and A. Lindenmayer. Diffusion mechanism for phyllotaxis: Theoretical physico-chemical and computer study. Plant Physiology, 60:127–139, 1977.

    Google Scholar 

  18. V. B. Wigglesworth. Local and general factors in the development of a pattern in Rhodnius prolixus. J. Exp. Biol., 17:180–200, 1940.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graphics and Multimedia Lab, School of Computing Science Simon Fraser University, V5A 1S6, Burnaby, B.C., Canada

    F. David Fracchia

Authors
  1. F. David Fracchia
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Janice Cuny Hartmut Ehrig Gregor Engels Grzegorz Rozenberg

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Fracchia, F.D. (1996). Integrating lineage and interaction for the visualization of cellular structures. In: Cuny, J., Ehrig, H., Engels, G., Rozenberg, G. (eds) Graph Grammars and Their Application to Computer Science. Graph Grammars 1994. Lecture Notes in Computer Science, vol 1073. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61228-9_109

Download citation

  • DOI: https://doi.org/10.1007/3-540-61228-9_109

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61228-5

  • Online ISBN: 978-3-540-68388-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation