Tetrahedral tile pasting systems

Tile pasting system is a parallel generating model which glues two square tiles at their edges to create intricate tiling patterns. It is extended by using three dimensional objects namely tetrahedral tiles and the patterns generated are used to decorate floors and walls. In the literature k-Tabled Tetrahedral Tile Pasting System (k-TTTPS) and Tetrahedral Tile Pasting P System (TetTPPS) were introduced to generate tetrahedral picture patterns. In this paper, Controlled Tabled Tetrahedral Tile Pasting System (CTTTPS) is proposed to generate tetrahedral picture patterns and CTTTPS is compared with k-TTTPS and TetTPPS in terms of generative powers. It is proved that CTTTPS has more generative power than the generative powers of k-TTTPS and TetTPPS. Extended Tetrahedral Tile Pasting System (ETTPS) and Extended Tetrahedral Tile Pasting P System (ETTPPS) are also proposed in this paper and are compared with CTTTPS in terms of their generative powers. This study has connections with pattern recognition and image analysis with applications in tiling of tetrahedral patterns.