Related papers: Classification of Cellular Automata based on Stati…
Correlated time series are time series that, by virtue of the underlying process to which they refer, are expected to influence each other strongly. We introduce a novel approach to handle such time series, one that models their interaction…
Cellular automata have long been celebrated for their ability to generate complex behaviors from simple, local rules, with well-known discrete models like Conway's Game of Life proven capable of universal computation. Recent advancements…
Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits…
Cellular automata (CA) are a class of computational models that exhibit rich dynamics emerging from the local interaction of cells arranged in a regular lattice. In this work we focus on a generalised version of typical CA, called graph…
In this paper we present a quantization of Cellular Automata. Our formalism is based on a lattice of qudits, and an update rule consisting of local unitary operators that commute with their own lattice translations. One purpose of this…
This study focuses on an extended model of a standard cellular automaton (CA) that includes an extra index consisting of a radius that defines a perception area for each cell in addition to the radius defined by the CA rule. Extended…
A recently introduced cellular automaton model for the description of traffic flow is investigated. It generalises asymmetric exclusion models which have attracted a lot of interest in the past. We calculate the so-called fundamental…
The control of chaotic systems implies inducing an unpredictable system to follow a desired trajectory using the smallest "force". In low-dimensional continuous systems, one method is that of reconstructing the tangent space, so that the…
We present a 2-dimensional cellular automaton model for the simulation of pedestrian dynamics. The model is extremely efficient and allows simulations of large crowds faster than real time since it includes only nearest-neighbour…
We study the set of strictly periodic points in surjective cellular automata, i.e., the set of those configurations which are temporally periodic for a given automaton but they not spatially periodic. This set turns out to be dense for…
Probabilistic cellular automata describe the dynamics of classical spin models, which, for sufficiently small temperature $T$, can serve as classical memory capable of storing information even in the presence of nonzero external magnetic…
In the present work we introduce a stochastic cellular automata model in order to simulate the dynamics of the stock market. A direct percolation method is used to create a hierarchy of clusters of active traders on a two dimensional grid.…
Cellular automata are dynamical systems defined on lattices and commuting with the Bernoulli shift. In this work, we focus on the spectral properties of D-dimensional cellular automata. We give a characterization of their spectrum from both…
We define the notion of stochastic stability, already present in the literature in the context of smooth dynamical systems, for invariant measures of cellular automata perturbed by a random noise, and the notion of strongly stochastically…
A transition from asymmetric to symmetric patterns in time-dependent extended systems is described. It is found that one dimensional cellular automata, started from fully random initial conditions, can be forced to evolve into complex…
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…
In previous works, hexagonal cellular automata (CA) have been studied as a variation of the famous Game of Life CA, mainly for spiral phenomena simulations; where the most interesting constructions are related to the Belousov-Zhabotinsky…
We propose a probabilistic cellular automata model for the spread of innovations, rumors, news, etc. in a social system. The local rule used in the model is outertotalistic, and the range of interaction can vary. When the range R of the…
Two-dimensional nine neighbor hood rectangular Cellular Automata rules can be modeled using many different techniques like Rule matrices, State Transition Diagrams, Boolean functions, Algebraic Normal Form etc. In this paper, a new model is…
A number-conserving cellular automaton is a cellular automaton whose states are integers and whose transition function keeps the sum of all cells constant throughout its evolution. It can be seen as a kind of modelization of the physical…