Periodic Nature in General System and Cellular Automata

Introduction: In this research paper we have discussed the various periodic points in general systems and established relation among them by adopting strong conditions to them so we can relate smoothly. Additionally, we developed the relationship with the dynamical systems and derived periodic points in Tent maps and circular maps in general systems. We established the fundamental characteristics of cellular automata in general systems, such as continuity. Furthermore, we covered periodic points in additive CAs with radius zero and the inverse of a periodic point in additive cellular automata. Objectives: To be familiar with the relationships between different periodic points in a general system, general system examples, and the contrast between the periodic behavior of a dynamical system and a new system. Explaining periodic nature in additive form and defining cellular automata in a new framework. Methods: We employed fundamental notions of dynamical systems and the definition of cellular automata in a new system. Results and Conclusion: The relationships between different periodic points in a general system, periodic points in a new system, the periodic nature of additive cellular automata in the new system, and its basic characteristics were all revealed to us.