Author:

Keywords:

cellular automata, ergodicity, Science & Technology, Physical Sciences, Physics, Mathematical, Physics, CELLULAR AUTOMATA, ERGODICITY, 01 Mathematical Sciences, 02 Physical Sciences, Fluids & Plasmas, 49 Mathematical sciences, 51 Physical sciences

Abstract:

We study a one-dimensional cellular automaton that was originally proposed as a candidate for exhibiting nonergodic behavior under noise. We prove that the deterministic model has the eroder property for two and only two invariant states. Moreover, we give the best possible estimates for the corresponding erosion times. We then review the results we have obtained from extensive computer simulations for the stochastic model and for a "mixed" model and argue that they suggest numerical and heuristic evidence in favour of ergodic behavior for all nonzero values of the noise parameter.