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Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and…
Cellular automaton (CA) approach is an important theoretical framework for studying complex system behavior and has been widely applied in various research field. CA traffic flow models have the advantage of flexible evolution rules and…
A stochastic cellular automata (CA) model for pedestrian dynamics is presented. Our goal is to simulate different types of pedestrian movement, from regular to panic. But here we emphasize regular situations which imply that pedestrians…
We construct a cellular automaton (CA) model that describes the movement of a particle in a disordered system. The mathematical properties of the CA model were examined by varying the configuration of grid and determining the number of…
Traffic models based on cellular automata have high computational efficiency because of their simplicity in describing unrealistic vehicular behavior and the versatility of cellular automata to be implemented on parallel processing. On the…
We show techniques of analyzing complex dynamics of cellular automata (CA) with chaotic behaviour. CA are well known computational substrates for studying emergent collective behaviour, complexity, randomness and interaction between order…
Cellular automata (CAs) are dynamical systems which exhibit complex global behavior from simple local interaction and computation. Since the inception of cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention of…
A new stochastic cellular automaton (CA) model of traffic flow, which includes slow-to-start effects and a driver's perspective, is proposed by extending the Burgers CA and the Nagel-Schreckenberg CA model. The flow-density relation of this…
Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…
The dynamics group of an asynchronous cellular automaton (ACA) relates properties of its long term dynamics to the structure of Coxeter groups. The key mathematical feature connecting these diverse fields is involutions. Group-theoretic…
In this paper we use the cellular automaton (CA) approach to model one-dimensional binary diffusion in solids. Employing a very simple state change rule we define an asynchronous CA model and take its continuum limit to obtain the governing…
A general stochastic traffic cellular automaton (CA) model, which includes slow-to-start effect and driver's perspective, is proposed in this paper. It is shown that this model includes well known traffic CA models such as…
A coarse-grained cellular automaton is proposed to simulate traffic systems. There, cells represent road sections. A cell can be in two states: jammed or passable. Numerical calculations are performed for a piece of square lattice with open…
The Cellular Automaton (CA) modeling and simulation of solid dynamics is a long-standing difficult problem. In this paper we present a new two-dimensional CA model for solid dynamics. In this model the solid body is represented by a set of…
Discretizing spacetime is often a natural step towards modelling physical systems. For quantum systems, if we also demand a strict bound on the speed of information propagation, we get quantum cellular automata (QCAs). These originally…
The proposed stochastic model for pedestrian dynamics is based on existing approaches using cellular automata, combined with substantial extensions, to compensate the deficiencies resulting of the discrete grid structure. This agent motion…
We develop a two-dimensional cellular automaton (CA) as a simple model for agents moving from origins to destinations. Each agent moves towards an empty neighbor site corresponding to the minimal distance to its destination. The…
In this paper, we give an elaborate and understandable review of traffic cellular automata (TCA) models, which are a class of computationally efficient microscopic traffic flow models. TCA models arise from the physics discipline of…
Continuum models for the spatial dynamics of growing cell populations have been widely used to investigate the mechanisms underpinning tissue development and tumour invasion. These models consist of nonlinear partial differential equations…
We study a cellular automaton model, which allows diffusion of energy (or equivalently any other physical quantities such as mass of a particular compound) at every lattice site after each timestep. Unit amount of energy is randomly added…