Skip to main content
SpringerLink
Log in
Book cover

International Meeting of Young Computer Scientists

IMYCS 1986: Trends, Techniques, and Problems in Theoretical Computer Science pp 138–168Cite as

Models for multicellular development: Characterization, inference and complexity of L-systems

  • Chapter 3 Biologically Motivated Structures
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 281))

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. M.H. Albert & J. Lawrence, A proof of Ehrenfeucht's conjecture. Theor. Comp. Sci., 41: 121–123, 1985.

    Google Scholar 

  2. M. Aono & T.L. Kunii, Botanical tree image generation. IEEE Computer Graphies & Appls., May 1984, pp. 10–34, 1984.

    Google Scholar 

  3. R. Baker & G.T. Herman, Simulation of organisms using a developmental model. Parts I & II. Int. J. Bio-Med. Computing, 3: 203–215, 251–267, 1972.

    Google Scholar 

  4. A.D. Bell, D. Roberts & A. Smith, Branching patterns: the simulation of plant architecture. J. Theor. Biol., 81: 351–375, 1979.

    Google Scholar 

  5. M. Blattner, The unsolvability of the equality problem for the sentential forms of context-free grammars. J. Comp. & Syst. Sci., 7: 463–468, 1973.

    Google Scholar 

  6. R. Borchert & H. Honda, Control of development in the bifurcating branch system of Tabebula rosea: a computer simulation. Bot. Gaz., 145: 184–195, 1984.

    Google Scholar 

  7. J.W. Carlyle, S.A. Greibach & A. Paz, A two-dimensional generating system modeling growth by binary cell division. Proc. 15th Annual Symp. on Switching & Automata Theory, New Orleans, pp. 1–12, 1974.

    Google Scholar 

  8. 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 

  9. K. Culik II & I. Fris, The decidability of the equivalence problem for DOL systems. Inf. and Control, 35: 20–39, 1977.

    Google Scholar 

  10. K. Culik II & J. Karhumäki, A new proof for the DOL sequence equivalence problem and its implications. In: "The Book of L", edited by G. Rozenberg & A. Salomaa, Springer-Verlag, Berlin, pp. 63–74, 1986.

    Google Scholar 

  11. 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 

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

    Google Scholar 

  13. M.J.M. de Boer & A. Lindenmayer, Map OL-systems with edge label control: Comparison of marker and cyclic systems. In: "Graph Grammars and Their Applications to Computer Science, 3rd Int. Workshop", edited by H. Ehrig et al., Lect. Notes in Comp. Sci., in press.

    Google Scholar 

  14. 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 

  15. C.G. de Koster & A. Lindenmayer, Discrete and continuous models for heterocyst differentiation in growing filaments of blue-green bacteria. Manuscript, 1986.

    Google Scholar 

  16. P.G. Doucet, The syntactic inference problem for DOL-sequences. In: "L Systems", edited by G. Rozenberg & A. Salomaa, Lect. Notes in Computer Science 15: 146–161, 1974.

    Google Scholar 

  17. A. Ehrenfeucht & G. Rozenberg, A limit for sets of subwords in deterministic TOL systems. Inf. Proc. Letters 2: 70–73, 1973.

    Google Scholar 

  18. A. Ehrenfeucht & G. Rozenberg, On the subword complexity of locally catenative DOL languages. Inf. Proc. Letters 16: 7–9, 1983.

    Google Scholar 

  19. P. Eichhorst & W. Savitch, Growth functions of stochastic Lindenmayer systems. Information and Control, 45: 217–228, 1980.

    Google Scholar 

  20. J.B. Fisher & H. Honda, Computer simulation of branching pattern and geometry in Terminalia (Combretaceae), a tropical tree. Bot. Gaz., 138: 377–384, 1977.

    Google Scholar 

  21. D. Frijeters, An automata-theoretical model of the vegetative and flowering development of Hieracium murorum L. Biol. Cybernetics, 24: 1–13, 1976.

    Google Scholar 

  22. D. Frijters & A. Lindenmayer, A model for the growth and flowering of Aster novae-anagliae on the basis of table 〈1,0〉 L-systems. In: "L-Systems", edited by G. Rozenberg & A. Salomaa, Lect. Notes in Comp. Sci. 15: 24–52, 1974.

    Google Scholar 

  23. D. Frijters & A. Lindenmayer, Developmental descriptions of branching patterns with paracladial relationships. In: "Automata, Languages, Development", edited by A. Lindenmayer & G. Rozenberg, North-Holland Publ. Co., Amsterdam, pp. 57–73, 1976.

    Google Scholar 

  24. I. Gnutzmann, Zum syntaktischen Inferenzproblem bei Lindenmayer-Systemen. Dissertation, Univ. Hannover, 1979.

    Google Scholar 

  25. F. Hallé, R.A.A. Oldeman & P.B. Tomlinson, "Tropical Trees and Forests, An Architectural Analysis", Springer-Verlag, Berlin, 441 pp, 1978.

    Google Scholar 

  26. C. Harte & A. Lindenmayer, Mitotic index in growing cell populations: Mathematical models and computer simulations. Biol. Zentralblatt, 102: 509–533, 1983.

    Google Scholar 

  27. G.T. Herman & G. Rozenberg, "Developmental Systems and Languages". North-Holland Publ. Co., Amsterdam, 363 pp., 1975.

    Google Scholar 

  28. G.T. Herman & A. Walker, The syntactic inference problem as applied to biological systems. In: "Machine Intelligence", edited by B. Meltzer & D. Mitchie, Edinburgh Univ. Press, 7: 341–356, 1972.

    Google Scholar 

  29. G.T. Herman & A. Walker, Context-free languages in biological systems. Int. J. Comp. Math. 4: 369–391, 1975.

    Google Scholar 

  30. P. Hogeweg & B. Hesper, A model study of biomorphological description. Pattern Recognition, 6: 165–179, 1974.

    Google Scholar 

  31. H. Honda, Description of the form of trees by the parameters of the tree-like body: effects of the branching angle and the branch length on the shape of the tree-like body. J. Theor. Biol., 31: 331–338, 1971.

    Google Scholar 

  32. H. Honda, P.B. Tomlinson & J.B. Fisher, Two geometrical models of branching of botanical trees. Annals of Botany, 49: 1–11, 1982.

    Google Scholar 

  33. J.E. Hopcroft & J.D. Ullman, "Introduction to Automata Theory, Languages and Computation". Addison-Wesley Publ. Co., Reading, Mass. 418 pp, 1979.

    Google Scholar 

  34. J.M. Janssen & A. Lindenmayer, Models for the control of branch positions and flowering sequences of capitula in Mycelis muralis (L.) Dumont (Compositae). New Phytologist, 105: 191–220, 1987.

    Google Scholar 

  35. N.D. Jones & S. Skyum, Complexity of some problems concerning L-systems. Math. Systems Theory, 13: 29–43, 1979.

    Google Scholar 

  36. N.D. Jones & S. Skyum, A note on the complexity of general DOL membership. SIAM J. Computing, 10: 114–117, 1981.

    Google Scholar 

  37. H. Jürgensen, Probabilistic L systems. In: "Automata, Languages, Development", edited by A. Lindenmayer & G. Rozenberg, North-Holland Publ. Co., Amsterdam, pp. 211–225, 1976.

    Google Scholar 

  38. H. Jürgensen & A. Lindenmayer, Inferencealgorithms for developmental systems with cell lineages. Bulletin of Mathematical Biology, 49: 93–123, 1987.

    Google Scholar 

  39. H. Jürgensen, D.E. Matthews & D. Wood, Life and death in Markov deterministic tabled OL-systems. Inf. and Control, 48: 80–93, 1981.

    Google Scholar 

  40. J. Karhumäki, The Ehrenfeucht conjecture: a compactness claim for finitely generated free monoids. Theor. Comp. Sci., 29: 285–308, 1984.

    Google Scholar 

  41. A. Kelemenová, Levels in L-systems. Math. Slovaca, 33: 87–97, 1983.

    Google Scholar 

  42. Y. Kobuchi & S. Seki, Decision problems of locally catenative property for DIL systems. Information and Control, 43: 266–279, 1979.

    Google Scholar 

  43. A.N. Kolmogorov, Three approaches to the quantitative definition of information. Int. J. Computer Math., 2: 157–168, 1968.

    Google Scholar 

  44. A. Lindenmayer, Mathematical models of cellular interactions in development. Parts I and II. J. Theor. Biol. 18: 280–299, 300–315, 1968.

    Google Scholar 

  45. A. Lindenmayer, Developmental systems without cellular interactions, their languages and grammars. J. Theor. Biol. 30: 455–484, 1971.

    Google Scholar 

  46. A. Lindenmayer, Adding continuous components to L-systems. In: "L Systems", edited by G. Rozenberg & A. Salomaa, Lect. Notes in Computer Science 15: 53–68, 1974.

    Google Scholar 

  47. A. Lindenmayer, Developmental systems and languages in their biological context. Chapter contributed to [22], 1975 (this chapter appeared in Russian translation in Kiberneticheskii Sbornik, Nov. Ser., 17: 192–232, 1980).

    Google Scholar 

  48. A. Lindenmayer, Developmental algorithms: lineage versus interactive control mechanisms. In: "Developmental Order: Its Origin and Regulation", edited by S. Subtelny & P.B. Green, 40th Symp. Soc. Dev. Biol., Boulder, Alan R. Liss, Inc., New York, pp. 219–245, 1982.

    Google Scholar 

  49. A. Lindenmayer, Models for plant tissue development with cell division orientation regulated by preprophase bands of microtubules. Differentiation, 26: 1–10, 1984.

    Google Scholar 

  50. A. Lindenmayer, An introduction to parallel map-generating systems. In: "Graph Grammars and Their Applications to Computer Science, 3rd Int. Workshop", edited by H. Ehrig et.al., Lect. Notes in Comp. Sci., in press.

    Google Scholar 

  51. A. Lindenmayer & K. Culik II, Growing cellular systems: generation of graphs by parallel rewriting. Int. J. Gen. Systems, 5: 45–55, 1979.

    Google Scholar 

  52. 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 

  53. H.L. Liu & K.S. Fu, Cellwork topology, its network duals and some applications — three-dimensional Karnaugh map and its virtual planar representation. Information Sciences, 24: 93–109, 1981.

    Google Scholar 

  54. J. Lück & H.B. Lück, Generation of 3-dimensional plant bodies by double wall map and stereomap systems. In: "Graph Grammars and Their Application to Computer Science, 2nd Int. Workshop", edited by H. Ehrig et al., Lect. Notes in Comp. Sci. 153: 219–231, 1983.

    Google Scholar 

  55. J. Lück, A. Lindenmayer & H.B. Lück, Analysis of cell tetrads and clones in meristematic cell layers. Botanical Gazette, in press.

    Google Scholar 

  56. J. Mäenpää, G. Rozenberg & A. Salomaa, Bibliography of L-systems. Report No. 81–20, Inst. of Appl. Math. and Comp. Sci., Univ. of Leiden, 1981.

    Google Scholar 

  57. R.J. Matela & R. Ransom, A topological model of cell division: structure of the computer program. BioSystems, 18: 65–78, 1985.

    Google Scholar 

  58. N. Macdonald, "Trees and Networks in Biological Models", Wiley, New York, 1983.

    Google Scholar 

  59. B.H. Mayoh, Multidimensional Lindenmayer organisms. In: "L Systems", edited by G. Rozenberg & A. Salomaa, Lect. Notes in Comp. Sci., 15: 302–326, 1974.

    Google Scholar 

  60. G.J. Mitchison & M. Wilcox, Rule governing cell division in Anabaena. Nature, 239: 110–111, 1972.

    Google Scholar 

  61. M. Nagl, "Graph-Grammatiken, Theorie, Implementierung, Anwendungen", Vieweg, Braunschweig, 375 pp., 1979.

    Google Scholar 

  62. A. Nakamura & K. Aizawa, A relationship between graph L-systems and picture languages, Theoret. Comp. Sci., 24: 161–177, 1983

    Google Scholar 

  63. 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 

  64. A. Nakamura, A. Lindenmayer & K. Aizawa, Map OL systems with markers. In: "Graph Grammars and Their Applications to Computer Science, 3rd Int. Workshop", edited by H. Ehrig et al., Lect. Notes in Comp. Sci., in press.

    Google Scholar 

  65. J. van Neumann, "Theory of Self-Reproducing Automata", edited by A.W. Burks, Univ. of Illinois Press, Urbana, 1966.

    Google Scholar 

  66. T. Nishida, KOL-system simulating almost but not exactly the same development — the case of Japanese cypress. Memoirs Fac. Sci., Kyoto Univ., Ser. Bio., 8: 97–122, 1980.

    Google Scholar 

  67. A. Paz & A. Salomaa, Integral sequential word functions and growth equivalence of Lindenmayer systems. Inf. and Control, 23: 313–343, 1973.

    Google Scholar 

  68. P. Prusinkiewicz, Applications of L-systems to computer imagery. In: "Graph Grammars and Their Applications to Computer Science, 3rd Int. Workshop", edited by H. Ehrig et al., Lect. Notes in Comp. Sci., in press.

    Google Scholar 

  69. R. Ransom, Computer analysis of cell division in Drosophila imaginal discs: model revision and extension to simulate leg disc growth. J. Theor. Biol., 66: 361–378, 1977.

    Google Scholar 

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

    Google Scholar 

  71. A. Rosenfeld, Array and web grammars. In: "Automata, Languages, Development, edited by A. Lindenmayer & G. Rozenberg, North-Holland Publ. Co., Amsterdam, pp. 517–529, 1976.

    Google Scholar 

  72. G. Rozenberg & P.G. Doucet, On OL languages. Inf. and Control, 19: 302–318, 1971.

    Google Scholar 

  73. G. Rozenberg & A. Lindenmayer, Developmental system with locally catenative formulas. Acta Inf., 2: 214–248, 1973.

    Google Scholar 

  74. K. Ruohonen, Developmental systems with interaction and fragmentation, Inf. and Control, 28: 91–112, 1975.

    Google Scholar 

  75. G. Rozenberg & A. Salomaa, "The Mathematical Theory of L Systems", Academic Press, New York, 352 pp., 1980.

    Google Scholar 

  76. A. Salomaa & M. Soittola, Automata-Theoretical Aspects of Formal Power Series. Springer-Verlag, New York, 171 pp., 1978.

    Google Scholar 

  77. U. Schmidt, Syntaktische Inferenz von DTOL-Systemen. Diplomarbeit, T.H. Darmstadt, 1983.

    Google Scholar 

  78. A.L. Semenov & V.S. Guba, pers. commun., 1985.

    Google Scholar 

  79. 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 

  80. R. Siromoney, G. Siromoney & K. Krithivasan, Array grammars and kolam. Computer Graphics and Image Proc., 4: 63–82, 1974.

    Google Scholar 

  81. R. Siromoney, Array languages and Lindenmayer systems — a survey. In: "The Book of L", edited by G. Rozenberg & A. Salomaa, Springer-Verlag, Berlin, pp. 413–426, 1986.

    Google Scholar 

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

    Google Scholar 

  83. A.R. Smith, Plants, fractals and formal languages. Computer Graphics, 18(3): 1–10, 1984.

    Google Scholar 

  84. A.L. Szilard & R.E. Quinton, An interpretation for DOL systems by computer graphics. Science Terrapin (Univ. of West. Ont.), 4(2): 8–13, 1979.

    Google Scholar 

  85. A.H. Veen & A. Lindenmayer, Diffusion mechanism for phyllotaxis. Plant Physiol., 60: 127–139, 1977.

    Google Scholar 

  86. P.M.B. Vitanyi, "Lindenmayer Systems: Structure, Languages and Growth Functions", Mathematical Centre Tracts, No. 96, Amsterdam, 209 pp., 1980.

    Google Scholar 

  87. J. White, editor, "Studies in Plant Demography, A Festschrift for John L. Harper", Academic Press, Orlando, 393 pp., 1985.

    Google Scholar 

  88. H. Yamada & S. Amoroso, Structural and behavioural equivalences of tessellation automata. Inf. and Control, 18: 1–31, 1971.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Theoretical Biology Group, University of Utrecht, Padualaan 8, 3584 CH, Utrecht, The Netherlands

    A. Lindenmayer

Authors
  1. A. Lindenmayer
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Alica Kelemenová Jozef Kelemen

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lindenmayer, A. (1987). Models for multicellular development: Characterization, inference and complexity of L-systems. In: Kelemenová, A., Kelemen, J. (eds) Trends, Techniques, and Problems in Theoretical Computer Science. IMYCS 1986. Lecture Notes in Computer Science, vol 281. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3540185356_36

Download citation

  • DOI: https://doi.org/10.1007/3540185356_36

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18535-2

  • Online ISBN: 978-3-540-48008-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation