One-Dimensional Uniform Arrays That Wash Out Finite Islands

Both deterministic and probabilistic one-dimensional uniform systems of finite automata with local interaction are considered. A state of a deterministic system is called attracting if it is maintained in time and any finite deviation from it disappears over a finite time. Three simple examples are given of systems with a nonunique uniform attracting state. Results of computer simulations of probabilistic systems obtained by superimposing random noise on such systems are given. The simulation results indicate that the systems may be nonergodic in the case of low noise.