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An introduction to parallel map generating systems

  • Aristid Lindenmayer
Part I Tutorial Introductions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 291)

Abstract

Map grammars are discussed first of all in their relationships to graph grammars. Maps are more strictly specified and better implementable structures than planar graphs. While graphs consist of vertices and edges, maps can be defined as sets of vertices, edges and regions. After the original introduction of sequential map grammars, most of the recent work has been on parallel map generating systems. The main types of these are: (1) binary fission/fusion systems with labeling and interactions of the regions, (2) the map interpretations of parallel graph grammars (such as propagating graph OL-systems) with node (region) labeling, and (3) the edgelabel-controlled binary propagating map OL-systems (BPMOL-systems). Of the latter systems various classes are defined: with single or double edge labels, and with edge insertion controlled by cicular words or by markers. Properties and applicability to cell division patterns of these families of systems are compared.

Key words

Maps planar graphs map grammars parallel rewriting systems edge-label-control fission/fusion systems PGOL-systems BPMOL-systems OL-systems 

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References

  1. 1.
    W.T. Tutte, Graph Theory. Addison-Wesley Publ. Co., Reading, Mass., 1984.Google Scholar
  2. 2.
    A. Nakamura, A. Lindenmayer & K. Aizawa, Map OL systems with markers. In this volume.Google Scholar
  3. 3.
    A. Lindenmayer, Developmental algorithms: lineage versus interactive control mechanisms. In: Developmental Order: Its Origin and Regulation, 40th Symp. of Soc. for Dev. Biol., edited by S. Subtelny & P.B. Green, Alan R. Liss, Inc., New York, pp. 219–245, 1982.Google Scholar
  4. 4.
    K. Culik II & A. Lindenmayer, Parallel graph generating and graph recurrence systems for multicellular development. Int.J.Gen.Syst., 3: 53–66, 1976.Google Scholar
  5. 5.
    A. Lindenmayer & K. Culik II, Growing cellular systems: generation of graphs by parallel rewriting. Int.J.Gen.Syst., 5: 45–55, 1979.Google Scholar
  6. 6.
    K. Culik II & D. Wood, A mathematical investigation of propagating graph OL-systems. Information and Control, 43: 50–82, 1979.CrossRefGoogle Scholar
  7. 7.
    H.-J. Kreowski, Graph grammar derivations: is parallelism already concurrency? In this volume.Google Scholar
  8. 8.
    A. Rosenfeld & J.P. Strong, A grammar for maps. In: Software Engineering, edited by J. Tau, Academic Press, New York, Vol.2, pp. 227–239, 1971.Google Scholar
  9. 9.
    B.H. Mayoh, Mułtidimensional Lindenmayer organisms. In: L Systems, edited by G. Rozenberg & A. Salomaa, Lect. Notes in Comp. Sci., 15: 302–326, 1974.Google Scholar
  10. 10.
    B.H. Mayoh, Another model for the development of multidimensional organisms. In: Automata, Languages, Development, edited by A. Lindenmayer & G. Rozenberg, North-Holland Publ. Co., Amsterdam, pp. 469–485, 1976.Google Scholar
  11. 11.
    J.W. Carlyle, S.A. Greibach & A. Paz, A two-dimensional generating system modeling growth by binary cell division. In: Proceedings, 15th Annual Symp. on Switching and Automata Theory, IEEE Computer Soc., Long Beach, Calif., pp. 1–12, 1974.Google Scholar
  12. 12.
    J.W. Carlyle, S.A. Greibach & A. Paz, Planar map generation by parallel binary fission/fusion grammars. In: The Book of L, edited by G. Rozenberg & A. Salomaa, Springer-Verlag, Berlin, pp. 29–43, 1986.Google Scholar
  13. 13.
    M. Nagl, Graph-Grammatiken, Theorie, Implementierung, Anwendungen. Vieweg, Braunschweig, 375 pp., 1979.Google Scholar
  14. 14.
    A. Lindenmayer & G. Rozenberg, Parallel generation of maps: developmental systems for cell layers. In: Graph. Grammars and their Application to Computer Science and Biology, edited by V. Claus et al., Lect. Notes in Comp. Sci., 73: 301–316, 1979.Google Scholar
  15. 15.
    A. Nakamura, A. Lindenmayer & K. Aizawa, Some systems for map generation. In: The Book of L, edited by G. Rozenberg & A. Salomaa, Springer-Verlag, Berlin, pp. 323–332, 1986.Google Scholar
  16. 16.
    M.J.M. de Boer & A. Lindenmayer, Map OL-systems with edge label control: comparison of marker and cyclic systems. In this volume.Google Scholar
  17. 17.
    M. de Does & A. Lindenmayer, Algorithms for the generation and drawing of maps representing cell clones. In: Graph Grammars and their Applications to Computer Science, 2nd Int. Workshop, edited by H. Ehrig et al., Lect. Notes in Comp. Sci., 153: 39–57, 1983.Google Scholar
  18. 18.
    J. Lück & H.B. Lück, Proposition d'une typologie de l'organisation cellulaire des tissus végétaux. In: Actes du ler Séminaire de l'Ecole de Biologie théorique du C.N.R.S., edited by H. Le Guyader & Th. Moulin, E.N.S.T.A., Paris, pp. 335–371, 1981.Google Scholar
  19. 19.
    J. Lück & H.B. Lück, Generation of 3-dimensional plant bodies by double wall map and stereomap systems. In: Graph Grammars and Their Applications to Computer Science, 2nd Int. Workshop, edited by H. Ehrig et al., Lect. Notes in Comp. Sci., 153: 219–231, 1983.Google Scholar
  20. 20.
    J. Lück & H.B. Lück, Sur la structure de l'organisation tissulaire et son incidence sur la morphogénèse. In: Actes du 2ème Séminaire de l'Ecole de Biologie théorique du C.N.R.S., edited by H. Le Guyader, Univ. de Rouen, pp. 385–397, 1982.Google Scholar
  21. 21.
    J. Lück, A. Lindenmayer & H.B. Lück, Analysis of cell tetrads and clones in meristematic cell layers. Botanical Gazette, in press.Google Scholar
  22. 22.
    A. Lindenmayer, Models of spatial orientation and temporal regulation of cell divisions in meristems. In: Actes du 5ème Séminaire de l'Ecole de Biologie théorique du C.N.R.S., edited by H.B. Lück, Editions du C.N.R.S., Paris, in press.Google Scholar
  23. 23.
    A. Paz & Y. Raz, Complexity of pattern generation by map-L systems. In: Graph-Grammars and Their Application to Computer Science and Biology, edited by V. Claus et al., Lect. Notes in Comp. Sci., 73: 367–378, 1979.Google Scholar
  24. 24.
    P.L.J. Siero, G. Rozenberg & A. Lindenmayer, Cell division patterns: syntactical description and implementation. Computer Graphics and Image Proc., 18:329–346,1982.Google Scholar
  25. 25.
    A. Paz, Geometry versus topology in map grammars. In: Graph Grammars and Their Application to Computer Science, 2nd Int. Workshop, edited by H. Ehrig et al., Lect. Notes in Comp. Sci., 153: 288–296, 1983.Google Scholar
  26. 26.
    R.W. Korn, The changing shapes of plant cells: transformations during cell proliferation. Annals of Botany, 46: 649–666, 1980.Google Scholar
  27. 27.
    P. Prusinkiewicz, Applications of L-systems to computer imagery. In this volume.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Aristid Lindenmayer
    • 1
  1. 1.Theoretical Biology GroupUniversity of UtrechtUtrechtThe Netherlands

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