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The goal of this paper is to show why the framework of communication complexity seems suitable for the study of cellular automata. Researchers have tackled different algorithmic problems ranging from the complexity of predicting to the…
This paper introduces a simple formalism for dealing with deterministic, non- deterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is…
In this work, the one-dimensional Cellular Automaton is extended to one that involves two sets of symbols and two global rules. As a main result, the Extended Curtis-Hedlund-Lyndon Theorem is demonstrated. Such constructions can be useful…
Cellular automata are discrete dynamical systems and a model of computation. The limit set of a cellular automaton consists of the configurations having an infinite sequence of preimages. It is well known that these always contain a…
We study the classification of cellular-automaton update rules into Wolfram's four classes. We start with the notion of the input entropy of a spatiotemporal block in the evolution of a cellular automaton, and build on it by introducing two…
Cellular automata are a discrete dynamical system which models massively parallel computation. Much attention is devoted to computations with small time complexity for which the parallelism may provide further possibilities. In this paper,…
A model for ionic and electronic grain boundary transport through thin films, scales or membranes with columnar grain structure is introduced. The grain structure is idealized as a lattice of identical hexagonal cells - a honeycomb pattern.…
A cellular automata approach using a Directed Cyclic Graph is used to model interrelationships of fluctuating time, state and space. This model predicts phenomena including a constant and maximum speed at which any moving entity can travel,…
The model of cellular automata is fascinating because very simple local rules can generate complex global behaviors. The relationship between local and global function is subject of many studies. We tackle this question by using results on…
The cellular automata discrete dynamical system is considered as the two-stage process: the majority rule for the change in the automata state and the rule for the change in topological relations between automata. The influence of changing…
A novel mechanism for cell differentiation is proposed, based on the dynamic clustering in a globally coupled chaotic system. A simple model with metabolic reaction, active transport of chemicals from media, and cell division is found to…
We introduce a general, efficient method to completely describe the topology of individual grains, bubbles, and cells in three-dimensional polycrystals, foams, and other multicellular microstructures. This approach is applied to a pair of…
The cellular automaton is a widely known model of both reversible and irreversible computations. The family of reversible second-order cellular automata considered in this work is appropriate both for construction of logic gates and…
State-of-the-art review of cellular automata, cellular automata for partial differential equations, differential equations for cellular automata and pattern formation in biology and engineering.
A general framework for the simulation of reaction-diffusion systems with probabilistic cellular automata is presented. The basic reaction probabilities of the chemical model translate directly into the transition rules of the automaton,…
We present simulations of evacuation processes using a recently introduced cellular automaton model for pedestrian dynamics. This model applies a bionics approach to describe the interaction between the pedestrians using ideas from…
A two-dimensional cellular automaton model of traffic flow with open boundaries are investigated by computer simulations. The outflow of cars from the system and the average velocity are investigated. The time sequences of the outflow and…
The situation of the metastable phase decay on the several types of heterogeneous centers is considered. The iteration procedure is formulated and with the help of the avalanche consumption property all iterations can be calculated. The…
The cellular automata (CA) approach to traffic modeling is extended to allow for spatially homogeneous steady state solutions that cover a two dimensional region in the flow-density plane. Hence these models fulfill a basic postulate of a…
The one-dimensional three-state cyclic cellular automaton is a simple spatial model with three states in a cyclic "rock-paper-scissors" prey-predator relationship. Starting from a random configuration, similar states gather in increasingly…