P Systems for Patterns of Sierpi´nski Square Snowflake Curve

Abstract

Syntactic models for generating the approximating polygon patterns of space-filling curves such as the well-known Peano and Hilbert curves have been studied in the recent past. Here we consider the polygon patterns of another space-filling curve, namely, Sierpinski square snowflake ´ curve. For generating array representations of these patterns, we introduce a variant of a fairly recent and novel computing model, known as P system in the membrane computing field. We then develop a finite set of joining rules which on application, join the primitive patterns in the arrays, thereby yielding the polygon patterns of the Sierpinski square snowflake ´ curve.