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Space-filling curves and infinite graphs

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Graph-Grammars and Their Application to Computer Science (Graph Grammars 1982)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 153))

Abstract

Two-dimensional geometric patterns in the form of the space filling curves of Peano and Hilbert are represented as a string, an array and a graph. The sequence of patterns is such that each curve is a prefix of the succeeding one and hence we get prefix preserving WDOL to generate the corresponding string representation. The limit language is generable by a CDOL system and consists of a single infinite word corresponding to the Peano curve and two infinite words for the Hilbert curve. The property that in the sequence each curve is a prefix of the succeeding one helps in the definition of the infinite arrays and infinite graphs representing the infinite curve patterns and we construct a Context-free Parentheses Kolam array grammar and a coding of a graph DOL system to generate the sequence as well as the limit.

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Authors and Affiliations

  1. Department of Mathematics, Madras Christian College, 600 059, Tambaram, Madras

    Rani Siromoney & K. G. Subramanian

Authors
  1. Rani Siromoney
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  2. K. G. Subramanian
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Hartmut Ehrig Manfred Nagl Grzegorz Rozenberg

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© 1983 Springer-Verlag Berlin Heidelberg

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Siromoney, R., Subramanian, K.G. (1983). Space-filling curves and infinite graphs. In: Ehrig, H., Nagl, M., Rozenberg, G. (eds) Graph-Grammars and Their Application to Computer Science. Graph Grammars 1982. Lecture Notes in Computer Science, vol 153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0000120

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  • DOI: https://doi.org/10.1007/BFb0000120

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12310-1

  • Online ISBN: 978-3-540-39897-4

  • eBook Packages: Springer Book Archive

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