Replication in two-dimensional cellular automaton with linear rules

被引：0

作者：

Rao, U. Srinivasa ^{[1
]}

Jeganathan, L. ^{[2
]}

Mathew, Tessy ^{[3
]}

机构：

[1] School of Computer Science and Engineering, Vellore Institute of Technology, Chennai, India

[2] Research Division of Advanced Data Science, Vellore Institute of Technology, Chennai, India

[3] Department of Computer Science and Engineering, Mar Baseilos College of Engineering and Technology, Thiruvananthapuram, Kerala, India

来源：

Journal of Cellular Automata | 2020年 / 15卷 / 5-6期

关键词：

Binary images;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

A two-state, two-dimensional cellular automaton (2D CA) with uniform linear rules on 9−neighborhood renders multiple copies of any twodimensional binary image as an initial configuration. In total, there are 512 linear rules and these rules are classified into groups of nine basis of their capacities in producing the number of copies of a given image and these groups are Group-1, Group-2, · · ·, Group-9. All groups other than Group-1 have been found to be generating multiple copies for a given image at time t = 2n where n ≥ 0. A relation was derived among the size of a binary image, neighborhood and exact time for replication (two non-overlapping copies) in one-dimensional cellular automaton (1D CA). In this paper, we classify the Group-2 rules into four classes based on the directions of the translation of two copies of an image on the grid. The four classes as Horizontal rules, Vertical rules, Diagonal rules and Combination rules. We have computed the exact time for replication of a given binary image for each class separately. © 2021 Old City Publishing, Inc.

引用

页码：377 / 405