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Space-filling curves and infinite graphs

  • Rani Siromoney
  • K. G. Subramanian
Conference paper
Part of the Lecture Notes in Computer Science book series (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.

Keywords

Geometric Pattern Label Graph Curve Pattern Rectangular Array Hilbert Curve 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Rani Siromoney
    • 1
  • K. G. Subramanian
    • 1
  1. 1.Department of MathematicsMadras Christian CollegeTambaram, Madras

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