Chain Code P System Generating a Variant of the Peano Space-Filling Curve
Conference paper
First Online:
Abstract
Generation of the finite approximations of the well-known Hilbert and Peano space-filling curves, represented as chain-code words has been studied in an earlier work. The generation was done with parallel chain code P systems with objects as chain code words and rewriting with context-free rules in parallel. Continuing this line of work, finite approximations of a variant of the Peano curve considered by Wunderlich are generated here with parallel chain code P system. We also generate approximating polygons corresponding to the Peano curve with parallel chain code P system.
Notes
Acknowledgements
We thank the anonymous referees for their valuable suggestions and comments which greatly helped to improve the paper.
References
- 1.Ceterchi, R., Mutyam, M., Pǎun, G., Subramanian, K.G.: Array - rewriting P systems. Nat. Comput. 2, 229–249 (2003)MathSciNetCrossRefGoogle Scholar
- 2.Ceterchi, R., Nagar, A.K., Subramanian, K.G.: Approximating polygons for space-filling curves generated with P systems. In: Graciani, C., Riscos-Núñez, A., Păun, G., Rozenberg, G., Salomaa, A. (eds.) Enjoying Natural Computing. LNCS, vol. 11270, pp. 57–65. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-00265-7_5CrossRefGoogle Scholar
- 3.Ceterchi, R., Subramanian, K.G., Venkat, I.: P systems with parallel rewriting for chain code picture languages. In: Beckmann, A., Mitrana, V., Soskova, M. (eds.) CiE 2015. LNCS, vol. 9136, pp. 145–155. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-20028-6_15CrossRefGoogle Scholar
- 4.Dassow, J., Habel, A., Taubenberger, S.: Chain-code pictures and collages generated by hyperedge replacement. In: Cuny, J., Ehrig, H., Engels, G., Rozenberg, G. (eds.) Graph Grammars 1994. LNCS, vol. 1073, pp. 412–427. Springer, Heidelberg (1996). https://doi.org/10.1007/3-540-61228-9_102CrossRefzbMATHGoogle Scholar
- 5.Drewes, F.: Some remarks on the generative power of collage grammars and chain-code grammars. In: Ehrig, H., Engels, G., Kreowski, H.-J., Rozenberg, G. (eds.) TAGT 1998. LNCS, vol. 1764, pp. 1–14. Springer, Heidelberg (2000). https://doi.org/10.1007/978-3-540-46464-8_1CrossRefzbMATHGoogle Scholar
- 6.Gheorghe, M., Pǎun, Gh., Pérez Jiménez, M.J., Rozenberg, G.: Research frontiers of membrane computing: open problems and research topics. Int. J. Found. Comput. Sci. 24(5), 547–624 (2013)MathSciNetCrossRefGoogle Scholar
- 7.Kitaev, S., Mansour, T., Seebold, P.: The Peano curve and counting occurrences of some patterns. J. Autom. Lang. Combin. 9(4), 439–455 (2004)MathSciNetzbMATHGoogle Scholar
- 8.Maurer, H.A., Rozenberg, G., Welzl, E.: Using string languages to describe picture languages. Inf. Control 54, 155–185 (1982)MathSciNetCrossRefGoogle Scholar
- 9.Pǎun, Gh.: Computing with membranes. J. Comput. Syst. Sci. 61, 108–143 (2000)MathSciNetCrossRefGoogle Scholar
- 10.Salomaa, A.: Formal Languages. Academic Press, London (1973)zbMATHGoogle Scholar
- 11.Sagan, H.: Space-Filling Curves. Springer, New York (1994). https://doi.org/10.1007/978-1-4612-0871-6CrossRefzbMATHGoogle Scholar
- 12.Seebold, P.: Tag system for the Hilbert curve. Discrete Math. Theor. Comput. Sci. 9, 213–226 (2007)MathSciNetzbMATHGoogle Scholar
- 13.Siromoney, R., Subramanian, K.G.: Space-filling curves and infinite graphs. In: Ehrig, H., Nagl, M., Rozenberg, G. (eds.) Graph Grammars 1982. LNCS, vol. 153, pp. 380–391. Springer, Heidelberg (1983). https://doi.org/10.1007/BFb0000120CrossRefGoogle Scholar
- 14.Subramanian, K.G.: P systems and picture languages. In: Durand-Lose, J., Margenstern, M. (eds.) MCU 2007. LNCS, vol. 4664, pp. 99–109. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-74593-8_9CrossRefGoogle Scholar
- 15.Subramanian, K.G., Venkat, I., Pan, L.: P systems generating chain code picture languages. In: Proceedings of Asian Conference on Membrane Computing, pp. 115–123 (2012)Google Scholar
- 16.Wunderlich, W.: Über Peano-Kurven. Elem. Math. 28, 1–10 (1973)MathSciNetzbMATHGoogle Scholar
Copyright information
© Springer Nature Switzerland AG 2019