Symbolic dynamics of glider guns for some one-dimensional cellular automata

摘要

By exploiting the characteristic function, Lameray diagram, and forward time- map of one-dimensional cellular automata (1D CAs), an empirical observation of long-term time-asymptotic behaviors of glider guns is achieved. Based on this qualitative property, the mathematical definition of glider gun for 1D CAs is proposed from the viewpoint of symbolic dynamics. Moreover, its underlying asymptotic dynamics is characterized in subtle detail, demonstrating that the dynamic evolution of glider gun converges to the limit cycle. This conclusion holds for all general 1D CAs, which is an extended discovery in both CAs and nonlinear dynamics. Meanwhile, chaotic dynamics of gliders is excavated to illustrate rich and complicated dynamical behaviors of guns. For the examples, glider guns of rules 54 and 110 are offered to present the constructive procedures described in this paper.