How Does the Neighborhood Affect the Global Behavior of Cellular Automata?

摘要

The neighborhood is a fundamental constituent of the cellular automaton (CA) and has been investigated in its own right by H.Nishio, M.Margenstern and F.von Haeseler(2004,2005). In this paper we ask a new question how the neighborhood affects the global behavior of CA and particularly gives some instances of CA where the global behavior does not depend on the neighborhood. We also discuss the conjectures that the injectivity is generally preserved from changing the neighborhood but the surjectivity is not.