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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© 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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