Skip to main content

Relational Growth Grammars – A Parallel Graph Transformation Approach with Applications in Biology and Architecture

  • Conference paper
Applications of Graph Transformations with Industrial Relevance (AGTIVE 2007)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 5088))

Abstract

We present the formalism of relational growth grammars. They are a variant of graph grammars with a principal application for plant modelling, where they extend the well-established, but limited formalism of L-systems. The main property is the application of rules in parallel, motivated by the fact that life is fundamentally parallel. A further speciality is the dynamic creation of right-hand sides on rule application. Relational growth grammars have been successfully used not only for plant modelling, but also to model general 3D structures or systems of Artificial Life. We illustrate these applications at several examples, all being implemented using our programming language XL which extends Java and provides an implementation of relational growth grammars.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

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. Baresi, L., Heckel, R.: Tutorial introduction to graph transformation: A software engineering perspective. In: [43], pp. 431–433

    Google Scholar 

  2. Buck-Sorlin, G., Kniemeyer, O., Kurth, W.: Barley morphology, genetics and hormonal regulation of internode elongation modelled by a relational growth grammar. New Phytologist 166(3), 859–867 (2005)

    Article  Google Scholar 

  3. Giavitto, J.L., Michel, O.: MGS: a rule-based programming language for complex objects and collections. Electronic Notes in Theoretical Computer Science 59(4) (2001)

    Google Scholar 

  4. Kurth, W., Kniemeyer, O., Buck-Sorlin, G.: Relational growth grammars – a graph rewriting approach to dynamical systems with a dynamical structure. In: Banâtre, J.-P., Fradet, P., Giavitto, J.-L., Michel, O. (eds.) UPP 2004. LNCS, vol. 3566, pp. 56–72. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  5. Prusinkiewicz, P., Lindenmayer, A.: The Algorithmic Beauty of Plants. Springer, New York (1990)

    Book  MATH  Google Scholar 

  6. Kurth, W.: Growth grammar interpreter GROGRA 2.4 – a software tool for the 3-dimensional interpretation of stochastic, sensitive growth grammars in the context of plant modelling. Introduction and reference manual. Berichte des Forschungszentrums Waldökosysteme, B 38, Göttingen (1994)

    Google Scholar 

  7. Barczi, J.F., de Reffye, P., Caraglio, Y.: Essai sur l’identification et la mise en oeuvre des paramètres nécessaires à la simulation d’une architecture végétale. Le logiciel AMAPSIM. In: Bouchon, J., de Reffye, P., Barthélémy, D. (eds.) Modélisation et Simulation de l’Architecture des Végétaux, pp. 205–254. Science Update, INRA, Paris (1997)

    Google Scholar 

  8. Maillette, L.: The value of meristem states, as estimated by a discrete-time Markov chain. Oikos 59, 235–240 (1990)

    Article  Google Scholar 

  9. Renton, M., Guédon, Y., Godin, C., Costes, E.: Similarities and gradients in growth-unit branching patterns during ontogeny in fuji apple trees: A stochastic approach. Journal of Experimental Botany 57(12), 3131–3143 (2006)

    Article  Google Scholar 

  10. Sonntag, M.: Effect of morphological plasticity on leaf area distribution, single tree, and forest stand dynamics. Bayreuther Forum Ökologie 52, 205–222 (1998)

    Google Scholar 

  11. Breckling, B.: An individual based model for the study of pattern and process in plant ecology: An application of object oriented programming. EcoSys. 4, 241–254 (1996)

    Google Scholar 

  12. Perttunen, J., Sievänen, R., Nikinmaa, E., Salminen, H., Saarenmaa, H., Väkevä, J.: Lignum: A tree model based on simple structural units. Annals of Botany 77, 87–98 (1996)

    Article  Google Scholar 

  13. Eschenbach, C.: Emergent properties modelled with the functional structural tree growth model ALMIS: Computer experiments on resource gain and use. Ecological Modelling 186, 470–488 (2005)

    Article  Google Scholar 

  14. Prusinkiewicz, P., Karwowski, R., Lane, B.: The L+C plant modelling language. In: [47], 27–42

    Google Scholar 

  15. Françon, J.: Sur la modélisation informatique de l’architecture et du développement des végétaux. Document R90/12, Université Louis Pasteur, Strasbourg, Département d’Informatique (1990)

    Google Scholar 

  16. Kniemeyer, O., Buck-Sorlin, G., Kurth, W.: GroIMP as a platform for functional-structural modelling of plants. In: [47], 43–52

    Google Scholar 

  17. Abelson, H., diSessa, A.: Turtle Geometry. MIT Press, Cambridge (1982)

    MATH  Google Scholar 

  18. Lindenmayer, A., Rozenberg, G. (eds.): Automata, Languages, Development. North Holland, Amsterdam (1976)

    MATH  Google Scholar 

  19. Godin, C., Caraglio, Y.: A multiscale model of plant topological structures. Journal of Theoretical Biology 191, 1–46 (1998)

    Article  Google Scholar 

  20. Renton, M., Thornby, D., Hanan, J.: Canonical modelling. In: [47], 151–164

    Google Scholar 

  21. Ehrig, H., Heckel, R., Korff, M., Löwe, M., Ribeiro, L., Wagner, A., Corradini, A.: Algebraic approaches to graph transformation II: Single pushout approach and comparison with double pushout approach. In: [46], ch. 4, pp. 247–312

    Google Scholar 

  22. Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. Springer, New York (2006)

    MATH  Google Scholar 

  23. Parisi-Presicce, F., Ehrig, H., Montanari, U.: Graph rewriting with unification and composition. In: Ehrig, H., Nagl, M., Rosenfeld, A., Rozenberg, G. (eds.) Graph Grammars 1986. LNCS, vol. 291, pp. 496–514. Springer, Heidelberg (1987)

    Chapter  Google Scholar 

  24. Kniemeyer, O.: Design and Implementation of a Graph Grammar Based Language for Functional-Structural Plant Modelling. PhD thesis, BTU Cottbus (forthcoming, 2008)

    Google Scholar 

  25. Chien, T.W., Jürgensen, H.: Parameterized L systems for modelling: Potential and limitations. In: Rozenberg, G., Salomaa, A. (eds.) Lindenmayer Systems, pp. 213–229. Springer, Berlin (1992)

    Chapter  Google Scholar 

  26. Nagl, M.: On a generalization of Lindenmayer-systems to labelled graphs. In: [18], pp. 487–508

    Google Scholar 

  27. Nagl, M.: Graph-Grammatiken: Theorie, Anwendungen, Implementierungen. Vieweg, Braunschweig (1979)

    Google Scholar 

  28. Rozenberg, G.: T0L systems and languages. Information and Control 23(4), 357–381 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  29. Schürr, A.: Programmed graph replacement systems. In: [46], ch. 7, pp. 479–546

    Google Scholar 

  30. Taentzer, G., Biermann, E., Bisztray, D., Bohnet, B., Boneva, I., Boronat, A., Geiger, L., Geiß, R., Horvath, Á., Kniemeyer, O., Mens, T., Ness, B., Plump, D., Vajk, T.: Generation of Sierpinski triangles: A case study for graph transformation tools. In: Schürr, A., Nagl, M., Zündorf, A. (eds.) AGTIVE 2007. LNCS, vol. 5088. Springer, Heidelberg (2008)

    Google Scholar 

  31. Batz, G.V., Kroll, M., Geiß, R.: A first experimental evaluation of search plan driven graph pattern matching. In: [45], pp. 468–483

    Google Scholar 

  32. Smith, C., Prusinkiewicz, P., Samavati, F.F.: Local specification of surface subdivision algorithms. In: [48], pp. 313–327

    Google Scholar 

  33. Kniemeyer, O., Kurth, W.: The modelling platform GroIMP and the programming language XL. In: Schürr, A., Nagl, M., Zündorf, A. (eds.) AGTIVE 2007. LNCS, vol. 5088. Springer, Heidelberg (2008)

    Google Scholar 

  34. Gardner, M.: Mathematical Games: The fantastic combinations of John Conway’s new solitaire game Life. Scientific American 223(4), 120–123 (1970)

    Article  Google Scholar 

  35. Kniemeyer, O.: Rule-based modelling with the XL/GroIMP software. In: Schaub, H., Detje, F., Brüggemann, U. (eds.) GWAL-6, pp. 56–65. Akademische Verlagsgesellschaft, Berlin (2004)

    Google Scholar 

  36. Kniemeyer, O., Buck-Sorlin, G., Kurth, W.: Representation of genotype and phenotype in a coherent framework based on extended L-systems. In: Banzhaf, W., Ziegler, J., Christaller, T., Dittrich, P., Kim, J.T. (eds.) ECAL 2003. LNCS (LNAI), vol. 2801, pp. 625–634. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  37. Kniemeyer, O., Buck-Sorlin, G., Kurth, W.: A graph-grammar approach to artificial life. Artificial Life 10, 413–431 (2004)

    Article  Google Scholar 

  38. Kurth, W.: Die Simulation der Baumarchitektur mit Wachstumsgrammatiken. Wissenschaftlicher Verlag, Berlin (1999)

    Google Scholar 

  39. Buck-Sorlin, G., Hemmerling, R., Kniemeyer, O., Burema, B., Kurth, W.: A rule-based model of barley morphogenesis, with special respect to shading and gibberellic acid signal transduction. Annals of Botany (in press, 2008)

    Google Scholar 

  40. Kim, J.T.: transsys: A generic formalism for modelling regulatory networks in morphogenesis. In: Kelemen, J., Sosík, P. (eds.) ECAL 2001. LNCS (LNAI), vol. 2159, pp. 242–251. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  41. Szuba, J., Ozimek, A., Schürr, A.: On graphs in conceptual engineering design. In: [48], pp. 75–89

    Google Scholar 

  42. Heer, T., Retkowitz, D., Kraft, B.: Algorithm and tool for ontology integration based on graph rewriting. In: [45], pp. 484–490

    Google Scholar 

  43. Ehrig, H., Engels, G., Parisi-Presicce, F., Rozenberg, G. (eds.): ICGT 2004. LNCS, vol. 3256. Springer, Heidelberg (2004)

    MATH  Google Scholar 

  44. Schürr, A., Nagl, M., Zündorf, A. (eds.): AGTIVE 2007. LNCS, vol. 5088. Springer, Heidelberg (2008)

    MATH  Google Scholar 

  45. Schürr, A., Nagl, M., Zündorf, A. (eds.): Proceedings of the International Workshop on Applications of Graph Transformations with Industrial Relevance, October 10-12, 2007. University of Kassel, Kassel (2007)

    Google Scholar 

  46. Rozenberg, G. (ed.): Handbook on Graph Grammars and Computing by Graph Transformation. Foundations, vol. I. World Scientific, Singapore (1997)

    MATH  Google Scholar 

  47. Vos, J., Marcelis, L.F.M., de Visser, P.H.B., Struik, P.C., Evers, J.B. (eds.): Functional-Structural Plant Modelling in Crop Production, International Workshop. Wageningen UR Frontis Series, vol. 22. Springer, Heidelberg (2007)

    Google Scholar 

  48. Pfaltz, J.L., Nagl, M., Böhlen, B. (eds.): AGTIVE 2003. LNCS, vol. 3062. Springer, Heidelberg (2004)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Kniemeyer, O., Barczik, G., Hemmerling, R., Kurth, W. (2008). Relational Growth Grammars – A Parallel Graph Transformation Approach with Applications in Biology and Architecture. In: Schürr, A., Nagl, M., Zündorf, A. (eds) Applications of Graph Transformations with Industrial Relevance. AGTIVE 2007. Lecture Notes in Computer Science, vol 5088. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89020-1_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-89020-1_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89019-5

  • Online ISBN: 978-3-540-89020-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics