International Journal of Science and Research (IJSR) ISSN (Online): 2319-7064 Index Copernicus Value (2015): 78.96 | Impact Factor (2015): 6.391 Volume 6 Issue 7, July 2017 www.ijsr.net Licensed Under Creative Commons Attribution CC BY 2D-Cellular Automata: Evolution and Boundary Defects Wani Shah Jahan 1 , Fasel Qadir 2 1 Department of Electronics, S. P. College, Cluster University Srinagar, J&K, India-190001 2 PG Department of Computer Sciences, University of Kashmir, J&K, India-190006 Abstract: Cellular Automata rules producing evolution type phenomena have been used for a wide range of applications. Various models have been designed and explored for different applications. Although the strength of its parallelism has been felt by various researchers but its exploration for applications will not minimize the hardware but also maximize the optimum strength of processors. Our present study was intended to identify the additive 2D Cellular Automata linear rules on the quality of pattern evolution and the periodic parallelism utilization. We have made an analysis of 2DCA linear game of life (GOL) rule in Neumann neighborhood pattern evolution and observed pattern multiplication in the process. The results achieved will not only minimize the required hardware for parallel channel creation but also expand the microcomputer processing horizon. Keywords: Cellular Automata, Boundary Conditions, Computer Simulation, Patterns Generation; 1. Introduction Von Neumann and Stanislaw Ulam introduced cellular lattice in late 1940s as a frame work for modeling complex structures capable of self-reproduction [1]. Cellular Automata is based on a concept of dividing space into a regular lattice structure of cells where each cell can take a set of „n‟ possible values. The value of the cell change in discrete time steps by the application of rule R that depends on the neighborhood around the cell. The neighborhood can be along a line, in a plane or in space. Cellular Automata (CA) model is composed of a universe of cells in a state having neighborhood and local rule. With the advancement of time in discrete steps the cell changes its value in accordance to the state of its neighbors. Thus the rules of the system are local and uniform. There are one- dimensional, two-dimensional and three-dimensional CA models. In one- dimensional CA the cells are like a linear canvas and the values of the canvas cells change due to application of a local rule in discrete advancing time steps. In two-dimensional CA the cells form a canvas plane and the changes take place in two dimensions while as in three dimensional CA volumetric changes take place by the application of local rule with advancement of time. As image is two dimensional data matrix, here we use 2DCA model, where cells are arranged in a two dimensional canvas matrix having interaction with neighboring cells. The central space represents the target cell (cell under consideration) and all spaces around represent its eight nearest neighbors. The structure of the neighbors mostly discussed and applied include Von Neumann neighborhood and Moore neighborhood, are shown in Figure (1). In Von Neumann neighborhood, four cells are positioned at the orthogonal positions of the target cell (a i,j ) while as Moore neighborhood is extension of Neumann structure with additional four cells placed diagonally at the four corner positions. For simplicity Von Neumann neighborhood cells can be termed as orthogonal neighbors and the additional cells by Moore can be called as corner neighbors. Von Neumann Neighborhood Moore Neighborhood Figure 1 The two dimensional Cellular Automata in general are represented by the equation (I) as given below: [a i,j ] t+1 = R[ a i, j , a i, j+1 , a i+1, j , a i, j-1 , a i-1, j ] t --(I) For Additive Cellular Automata the implementation of the famous totalistic rule in Von Neumann and Moore neighbourhoods, the respective representative equations can be written as follows: [a i,j ] t+1 = XOR[ a i, j , a i, j+1 , a i+1, j , a i, j-1 , a i-1, j ] t --(II) [a i,j ] t+1 = XOR[ a i, j , a i-1, j-1 , . . . . . . , a i+1, j+1 ] t --(III) Since the exploring worksheet/canvas is practically limited, researchers [2,3,4,5] have defined some boundary conditions to facilitate the protection of data overflow outside the edges Paper ID: 20071710 1566