Tetrahedral tile pasting P system for 3D patterns

Abstract

Membrane computing is a new computability model, called the P system introduced by P\v{a}un [5] inspired by the functions of living cells. Tile Pasting System is a parallel generating model proposed to generate colorful two-dimensional geometrical patterns [6]. Ceterachi et al. [1] linked the two areas of membrane computing and picture grammar and proposed array rewriting grammars. In this paper, we propose a Tetrahedral Tile Pasting system and Tetrahedral Tile pasting P system for generating three-dimensional geometrical patterns by gluing edges along the base of the tetrahedral tiles and study some of its properties.