Related papers: Limit dynamics of elementary cellular automaton 18
A simple one-dimensional cellular automaton model with threshold dynamics is introduced. The cumulative distribution of the size of the relaxations is analytically computed and behaves as a power law with an exponent equal to -1. This…
In this paper I present a first attempt for a possible description of fluids dynamics by mean of a cellular automata technique. With the use of simple and elementary rules, based on random behaviour either, the model permits to obtain the…
Operation parameters of magnetic quantum cellular automata are evaluated for the purposes of reliable logic operation. The dynamics of the nanomagnets is simulated via the Landau-Lifshitz-Gilbert equations with a stochastic magnetic field…
We investigate the long-term dynamics of a five-dimensional nonlinear system describing the non-ideal excitation of a spherical pendulum coupled to a limited-power electric motor. By analyzing the phase trajectories y(t) = (y1, y2, y3, y4,…
We study the effect of topology variation on the dynamic behavior of a system with local update rules. We implement one-dimensional binary cellular automata on graphs with various topologies by formulating two sets of degree-dependent…
We propose and discuss two variants of kinetic particle models - cellular automata in 1+1 dimensions, which have some appeal due to their simplicity and intriguing properties which could warrant further research and applications. The first…
We present numerical and analytical results for a special kind of one-dimensional probabilistic cellular automaton, the so called Domany-Kinzel automaton. It is shown that the phase boundary separating the active and the recently found…
We study limit sets of stable cellular automata standing from a symbolic dynamics point of view where they are a special case of sofic shifts admitting a steady epimorphism. We prove that there exists a right-closing almost-everywhere…
Genetic regulatory networks control ontogeny. For fifty years Boolean networks have served as models of such systems, ranging from ensembles of random Boolean networks as models for generic properties of gene regulation to working dynamical…
A family of multi-value cellular automaton (CA) associated with traffic flow is presented in this paper. The family is obtained by extending the rule-184 CA, which is an ultradiscrete analogue to the Burgers equation. CA models in the…
We study the statistical properties of the long-time dynamics of the rule 54 reversible cellular automaton (CA), driven stochastically at its boundaries. This CA can be considered as a discrete-time and deterministic version of the…
The cellular automaton (CA) pulsing model (arXiv:1806.06416) described the surprising phenomenon of spontaneous, sustained and robust rhythmic oscillations, pulsing dynamics, when random wiring is applied to a 2D `glider' rule running in a…
We present a model of the evolution of control systems in a genome under environmental constraints. The model conceptually follows the Jacob and Monod model of gene control. Genes contain control elements which respond to the internal state…
We establish central and non-central limit theorems for sequences of functionals of the Gaussian output of an infinitely-wide random neural network on the d-dimensional sphere . We show that the asymptotic behaviour of these functionals as…
In addition to the $\lambda$ parameter, we have found another parameter which characterize the class III, class II and class IV patterns more quantitatively. It explains why the different classes of patterns coexist at the same $\lambda$.…
Effects of a bottleneck in a linear trafficway is investigated using a simple cellular automaton model. Introducing a blockage site which transmit cars at some transmission probability into the rule-184 cellular automaton, we observe three…
In this paper, we perform a theoretical analysis of the sequential convergence of elementary cellular automata that have at least one fixed point. Our aim is to establish which elementary rules always reach fixed points under sequential…
We consider random rooted maps without regard to their genus, with fixed large number of edges, and address the problem of limiting distributions for six different parameters: vertices, leaves, loops, root edges, root isthmus, and root…
In this paper we study $\nu$-CA on one-dimensional lattice defined over a finite set of local rules. The main goal is to determine how the local rules can be mixed to ensure the produced $\nu$-CA has some properties. In a first part, we…
We have developed a simple cellular automata model for nonlinearly coupled phase oscillators which can exhibit many important collective dynamical states found in other synchronizing systems. The state of our system is specified by a set of…