Forma, Vol. 22 (No. 1), pp. 47-54, 2007
Original Paper

P Systems for Array Generation and Application to Kolam Patterns

K. G. Subramanian1*, R. Saravanan2 and T. Robinson3

1School of Mathematical Sciences, University Sains Malaysia, 11800 Penang, Malaysia
2Department of Mathematics, Bharath Institute of Higher Education and Research, Chennai 600073, India
3Department of Mathematics, Madras Christian College, Chennai 600059, India
*E-mail address:

(Received November 3, 2006; Accepted September 5, 2007)

Keywords: Kolam Patterns, Array Language, P-system

Abstract. In the area of membrane computing, a new computability model, now called P system was introduced by PAUN (2002) inspired from the cell structure and its functioning. One area of P systems deals with string objects and rewriting rules. Recently, array P systems with array objects and array rewriting rules were introduced. Here we introduce a new class of array P systems called sequential/parallel rectangular array P systems generating pictures of rectangular arrays. These P systems have rectangular arrays as objects in the membranes and rules in the membranes are either context-free or regular with sequential horizontal rewriting or right-linear rules with vertical rewriting in parallel as in the two-dimensional (2D) matrix grammars (SIROMONEY et al., 1972). These P systems have more generative power and accordingly, they can generate kolam patterns that cannot be handled by 2D matrix grammars.

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