Generative Aspects of Oxide Pictures by Oxide Tile Rewriting Grammar
P. Helen Vijitha1, Robinson Thamburaj2
1P. Helen Vijitha, Department of Mathematics Rajalakshmi Engineering College, India.
2Robinson Thamburaj, Department of Mathematics Madras Christian College, India.
Manuscript received on 5 August 2019. | Revised Manuscript received on 11 August 2019. | Manuscript published on 30 September 2019. | PP: 1537-1543 | Volume-8 Issue-3 September 2019 | Retrieval Number: C4259098319/19©BEIESP | DOI: 10.35940/ijrte.C4259.098319
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Abstract: In formal languages, picture language is generalization of string language theory to two dimensions. Pictures which may be regarded as two-dimensional objects occur in studies concerning recognition of patterns, images and various computational fields. Several studies have been done for generating and/or recognizing higher dimensional objects using formal models. Tile rewriting grammar (TRG) is yet another model introduced for generating picture languages. TRG combines isometric rewriting rules with the Giammaresi and Restivo’s Tiling system. This rewriting grammar generates spirals, square and rectangular grids. The power of generating pictures by tile rewriting grammar is more than REC .Sweety et al have generated hexagonal pictures, introducing hexagonal Tile Rewriting Grammar. Kuberalet al have introduced Triangular Tile Rewriting Grammar to generate Triangular Pictures. A special class of objects namely Oxide pictures have been of interest recently. Oxide network is a special case of Silicate network. The silicates are a complicated class of minerals made up of tetrahedral silicates. A basic silicate tetrahedron unit SiO4 is formed with Oxygen ions in the corners and a Silicate ion in the center. In a two dimensional plane a ring of tetrahedrons that are shared by Oxygen nodes forms a silicate sheet.In this paper, Oxide Tile Rewriting Grammar (OXTRG) is proposed for generating Oxide pictures. The motivation for the study is derived from the Oxide network which is obtained by deleting all the silicon nodes of a silicate network. Closure properties of OXTRG are discussed. When compared with schemes such as Oxide Tiling System and Oxide Sgraffito Automaton, OXTRG is found to be more powerful.
Keywords: Oxide Pictures, Oxide tiling systems, Oxide tile Rewriting Grammars, Oxide Sgraffito automata.
Scope of the Article: Mechanics and Materials Aspects of Advanced Construction Materials