Right-Permutative Cellular Automata on Topological Markov Chains
نویسنده
چکیده
In this paper we consider cellular automata (G,Φ) with algebraic local rules and such that G is a topological Markov chain which has a structure compatible to this local rule. We characterize such cellular automata and study the convergence of the Cesàro mean distribution of the iterates of any probability measure with complete connections and summable decay. Subj-class: DS, PR, CO. MSC-class: Primary: 37B15, 54H20; Secondary: 28D99, 37B20.
منابع مشابه
On strong mixing property of cellular automata with respect to Markov measures
In this paper we study mixing properties of one-dimensional linear cellular automata over the ring Zm, a particular class of dynamical systems, determined by right (left) permutative local rule F with respect to the uniform Markov measure induced by doubly stochastic matrix P = p(i,j) and the probability vector π. We prove that one-dimensional linear cellular automata associated to right (resp....
متن کاملEntropy rate of higher-dimensional cellular automata
We introduce the entropy rate of multidimensional cellular automata. This number is invariant under shift–commuting isomorphisms; as opposed to the entropy of such CA, it is always finite. The invariance property and the finiteness of the entropy rate result from basic results about the entropy of partitions of multidimensional cellular automata. We prove several results that show that entropy ...
متن کاملEvolution of probability measures by cellular automata on algebraic topological Markov chains.
In this paper we review some recent results on the evolution of probability measures under cellular automata acting on a fullshift. In particular we discuss the crucial role of the attractiveness of maximal measures. We enlarge the context of the results of a previous study of topological Markov chains that are Abelian groups; the shift map is an automorphism of this group. This is carried out ...
متن کاملDetection and prediction of land use/ land cover changes using Markov chain model and Cellular Automata (CA-Markov), (Case study: Darab plain)
unprincipled changes in land use are major challenges for many countries and different regions of the world, which in turn have devastating effects on natural resources, Therefore, the study of land-use changes has a fundamental and important role for environmental studies. The purpose of this study is to detect and predicting of land use/ land cover (LULC) changes in Darab plain through the Ma...
متن کاملSimulation of Future Land Use Map of the Catchment Area, with the Integration of Cellular Automata and Markov Chain Models Based on Selection of the Best Classification Algorithm: A Case Study of Fakhrabad Basin of Mehriz, Yazd
INTRODUCTION Since the land use change affects many natural processes including soil erosion and sediment yield, floods and soil degradation and the chemical and physical properties of soil, so, different aspects of land use changes in the past and future should be considered particularly in the planning and decision-making. One of the most important applications of remote sensing is land ...
متن کامل