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Parallel generation of maps: Developmental systems for cell layers

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 73))

Abstract

In this paper we extend parallel string generating systems (string L-systems) to parallel map generating systems(BPMOL-systems). The main distinguishing feature of of these constructs is that they generate map patterns by rewriting the graph of the map directly, and not its dual graph. These systems and their languages and sequences are illustrated in particular by applying them to the development of epidermal cell layers in which hexagonal arrays of cells are generated from previous hexagonal arrays.

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References

  1. B.H. Mayoh, Mathematical models for cellular organisms. Datalogisk Afdeling, Aarhus Univ., Report No. DAIMI PB-12, 38 pp., 1973.

    Google Scholar 

  2. B.H. Mayoh, Multidimensional Lindenmayer organisms. In: "L-systems", edited by G. Rozenberg and A. Salomaa, Lecture Notes in Computer Science 15, Springer-Verlag, Berlin-Heidelberg, pp. 302–326, 1974.

    Google Scholar 

  3. A. Rosenfeld and J.P. Strong, A grammar for maps. In: "Software Engineering", edited by J. Tou, Academic Press, New York, Vol.2, pp. 227–239, 1971.

    Google Scholar 

  4. J.W. Carlyle, S.A. Greibach, and A. Paz, A two-dimensional generating system modeling growth by binary cell division. In: 15th Annual Symp. on Switching and Automata Theory, Proceedings, New Orleans, IEEE Computer Soc., Long Beach, Calif., pp. 1–12, 1974.

    Google Scholar 

  5. B.H. Mayoh, Another model for the development of multidimensional organisms. In: "Automata, Languages, Development", edited by A. Lindenmayer and G. Rozenberg, North-Holland Publ. Co., Amsterdam, pp. 469–485, 1976.

    Google Scholar 

  6. A. Paz and Y. Raz, Complexity of pattern generation by map-L-systems. In this volume.

    Google Scholar 

  7. K. Culik II and A. Lindenmayer, Parallel rewriting on graphs and multidimensional development. Faculty of Mathematics, Univ. of Waterloo, Report No. CS-74-22, 41 pp., 1974.

    Google Scholar 

  8. M. Nagl, Graph Lindenmayer-systems and languages. Inst. für math. Maschinen und Datenverarbeitung, Univ. Erlangen-Nürnberg, Arbeitsberichte, Vol.8, No. 1, pp. 16–63, 1975.

    Google Scholar 

  9. K. Culik II and A. Lindenmayer, Parallel graph generating and graph recurrence systems for multicellular development. Int. J. General Systems, 3: 53–66, 1976.

    Google Scholar 

  10. H.B. Lück and J. Lück, Automata theoretical explanation of tissue growth. In: Proc. of the Int. Symp. on Mathematical Topics in Biology, Kyoto, pp.174–185,1978. See also paper by J. Lück and H.B. Lück in this volume.

    Google Scholar 

  11. A. Lindenmayer and K. Culik II, Growing cellular systems: Generation of graphs by parallel rewriting. Int. J. General Systems, to appear, and paper by K.Culik II and D. Wood in this volume.

    Google Scholar 

  12. H. Ehrig, Introduction to the algebraic theory of graph grammars. In this volume.

    Google Scholar 

  13. M. Nagl, A tutorial and bibliographical survey of graph grammars. In this volume.

    Google Scholar 

  14. E. Grötsch and M. Nagl, Explicit versus implicit parallel rewriting on graphs. In this volume.

    Google Scholar 

  15. A.R. Smith III, Introduction to and survey of polyautomata theory. In: "Automata, Languages, Development", edited by A. Lindenmayer and G. Rozenberg, North-Holland Publ. Co., Amsterdam, pp. 405–422, 1976.

    Google Scholar 

  16. A. Rosenfeld, Array and web grammars: An overview. Ibid., " pp. 517–529, 1976.

    Google Scholar 

  17. G.T. Herman and G. Rozenberg, "Developmental Systems and Languages" (with a contribution by A. Lindenmayer). North-Holland Publ. Co., Amsterdam, 363 pp., 1975.

    Google Scholar 

  18. G. Rozenberg and A. Salomaa, "The Mathematical Theory of L Systems". Academic Press, New York, to appear.

    Google Scholar 

  19. A. Lindenmayer, Developmental algorithms for multicellular organisms: A survey of L-systems. J. Theor. Biol., 54: 3–22, 1975.

    Google Scholar 

  20. A. Lindenmayer, Algorithms for plant morphogenesis. In: "Theoretical Plant Morphology", edited by R. Sattler, Leiden Univ. Press, The Hauge, pp. 37–81, (Supplement to Acta Biotheoretica, Vol. 27), 1978.

    Google Scholar 

  21. F.T. Lewis, The effect of cell division on the shape and size of hexagonal cells. Anatomical Record, 33: 331–355, 1926.

    Google Scholar 

  22. Lois A.B. Abbott, A biological and mathematical analysis of wing morphogenesis in Drosophila. Ph. D. Thesis, Dept. of Environmental, Population and Organismic Biology, Univ. of Colorado, Boulder, 127 pp., 1977.

    Google Scholar 

  23. R.W. Korn and R.M. Spalding, The geometry of plant epidermal cells. New Phytologist, 72: 1357–1365, 1973.

    Google Scholar 

  24. R.W. Korn, Quantitative aspects of "cell net" analysis. Manuscript, 1976.

    Google Scholar 

  25. G. Rozenberg, K. Ruohonen and A. Salomaa, Developmental systems with fragmentation. Int. J. Computer Math., 5: 177–191, 1976.

    Google Scholar 

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Volker Claus Hartmut Ehrig Grzegorz Rozenberg

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© 1979 Springer-Verlag Berlin Heidelberg

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Lindenmayer, A., Rozenberg, G. (1979). Parallel generation of maps: Developmental systems for cell layers. In: Claus, V., Ehrig, H., Rozenberg, G. (eds) Graph-Grammars and Their Application to Computer Science and Biology. Graph Grammars 1978. Lecture Notes in Computer Science, vol 73. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0025728

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  • DOI: https://doi.org/10.1007/BFb0025728

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09525-5

  • Online ISBN: 978-3-540-35091-0

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