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Approximating Polygons for Space-Filling Curves Generated with P Systems

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Enjoying Natural Computing

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11270))

Abstract

In the novel area of membrane computing, the bio-inspired computing models with the generic name of P systems have turned out to be a convenient framework for handling different kinds of problems and for developing suitable solutions. One such problem area is generation of geometric patterns of approximations of space-filling curves encoded as words over appropriate chain code symbols. Parallel chain code P systems with rewriting in parallel of words in the regions using context-free rules have been shown to generate the languages of chain code words representing the finite approximation patterns of the well-known space-filling Peano and Hilbert curves. Here we consider the approximating polygons that converge to the space-filling curves of Hilbert and construct a parallel chain code P system generating these approximating polygons. We also construct a parallel chain code P system for generating the approximating polygons corresponding to another space-filling curve, known as Lebesgue’s curve, which is almost everywhere differentiable unlike any other space-filling curve.

K. G. Subramanian—Honorary Visiting Professor.

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Acknowledgements

We thank the anonymous referees for their valuable suggestions and comments which greatly helped to improve the paper.

The first author wishes to thank Mario for a long lasting friendship and a fruitful working relationship.

All the authors join in saying: Happy Birthday, Mario!

Author information

Authors and Affiliations

  1. Faculty of Mathematics and Computer Science, University of Bucharest, 14 Academiei St., 010014, Bucharest, Romania

    Rodica Ceterchi

  2. Faculty of Science, Liverpool Hope University, Hope Park, Liverpool, L16 9JD, UK

    Atulya K. Nagar & K. G. Subramanian

Authors
  1. Rodica Ceterchi
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  2. Atulya K. Nagar
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  3. K. G. Subramanian
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Corresponding author

Correspondence to Rodica Ceterchi .

Editor information

Editors and Affiliations

  1. University of Seville, Sevilla, Spain

    Carmen Graciani

  2. University of Seville, Sevilla, Spain

    Agustín Riscos-Núñez

  3. Romanian Academy, Bucharest, Romania

    Gheorghe Păun

  4. Leiden University, Leiden, The Netherlands

    Grzegorz Rozenberg

  5. Turku Centre for Computer Science, Turku, Finland

    Arto Salomaa

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Ceterchi, R., Nagar, A.K., Subramanian, K.G. (2018). 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. Lecture Notes in Computer Science(), vol 11270. Springer, Cham. https://doi.org/10.1007/978-3-030-00265-7_5

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  • DOI: https://doi.org/10.1007/978-3-030-00265-7_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-00264-0

  • Online ISBN: 978-3-030-00265-7

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