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

*Original Paper*

## P Systems for Array Generation and Application to Kolam Patterns

K. G. Subramanian^{1}*, R. Saravanan^{2} and T. Robinson^{3}

^{1}School of Mathematical Sciences, University Sains Malaysia, 11800 Penang, Malaysia

^{2}Department of Mathematics, Bharath Institute of Higher Education and Research, Chennai 600073, India

^{3}Department of Mathematics, Madras Christian College, Chennai 600059, India

*E-mail address: kgs@usm.my

(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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