On Two-Dimensional Cellular Automata With Rule 170

Cellular automata (CA) are special finite automata without output. They are discrete systems consisting of a regular array of cells, each of which can be assigned a value. In recent years, cellular automata have a large application on biology, physics, cryptography etc. Lots of Chinese and foreign researchers have studied the theory of CA in a variety of ways. Algebraic methods is an important branch.In this paper, we first summarized some basic knowledge about CA, for example, its origin, develop process, research direction etc. Then, we studied several kinds of two-dimensional (2D) CA with rule 170, and investigated their characters using matrix algebra. There are four parts in this paper, each part as a chapter.In chapter one, we introduced some basic knowledge, the major achievements in algebraic methods, chief concepts and notation on the theory of cellular automata. Chapter two is about the 2D CA with rule 170 on null boundary condition (rule 170N in shot). We first studied the GOE of the 2D CA with rule 170N, and summarized a formula to obtain its number of GOE. Then, we generalized the corresponding theory of 1D linear CA into 2D CA, and obtained an algorithm about the transient length and maximal cycle length of 2D CA with 170N. The following are the main results of chapter two:Theorem 2.1.2 let CAm×nbe a 2D rule 170N CA,B is a configuration of it. If there exist...