Related papers: Orbits in one-dimensional finite linear cellular a…
We show how the trajectories of $d$-dimensional cellular automata (CA) can be used to determine the ground states of $(d+1)$-dimensional classical spin models, and we characterise their quantum phase transition, when in the presence of a…
Computing the configuration of any one-dimensional cellular automaton at generation $n$ can be accelerated by constructing and running a composite rule with a radius proportional to $\log n$. The new automaton is the original one, but with…
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…
We have determined families of two-dimensional deterministic totalistic cellular automaton rules whose stationary density of active sites exhibits a period two in time. Each family of deterministic rules is characterized by an ``average…
The transport and chemical reactions of solutes are modelled as a cellular automaton in which molecules of different species perform a random walk on a regular lattice and react according to a local probabilistic rule. The model describes…
Commonly studied cellular automata are memoryless and have fixed topology of connections between cells. However by allowing updates of links and short-term memory in cells we may potentially discover novel complex regimes of spatio-temporal…
The searching for the stable patterns in the evolution of cellular automata is implemented using stochastic synchronization between the present structures of the system and its precedent configurations. For most of the known evolution rules…
Suppose each site on a one-dimensional chain with periodic boundary condition may take on any one of the states $0,1,..., n-1$, can you find out the most frequently occurring state using cellular automaton? Here, we prove that while the…
This paper shows how to determine all the unidimensional two-state cellular automaton rules of a given number of inputs which conserve the number of active sites. These rules have to satisfy a necessary and sufficient condition. If the…
We conjecture that for a wide class of interacting particle systems evolving in discrete time, namely conservative cellular automata with piecewise linear flow diagram, relaxation to the limit set follows the same power law at critical…
Cyclic cellular automata (CCA) are models of excitable media. Started from random initial conditions, they produce several different kinds of spatial structure, depending on their control parameters. We introduce new tools from information…
Probabilistic cellular automata with deterministic updating are quantum systems. We employ the quantum formalism for an investigation of random probabilistic cellular automata, which start with a probability distribution over initial…
Inspired by the approach of kinetic theory of gases, a three-level description (microscopic, mesoscopic and macroscopic) of cellular automaton is presented. To provide an analytical treatment a simple domino cellular automaton with…
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…
It is shown that for the N-neighbor and K-state cellular automata, the class II, class III and class IV patterns coexist at least in the range $\frac{1}{K} \le \lambda \le 1-\frac{1}{K} $. The mechanism which determines the difference…
The one-dimensional dynamics of identical discrete elements that combine the properties of newtonian mechanical particles and cellular automata are investigated. It is shown that the motion of a cluster of combined discrete elements, which…
We define a cellular automaton where a resting cell excites if number of its excited neighbours belong to some specified interval and boundaries of the interval change depending on ratio of excited and refractory neighbours in the cell's…
We explore the dynamics of a one-dimensional lattice of state machines on two states and two symbols sequentially updated via a process of "reflexive composition." The space of 256 machines exhibits a variety of behavior, including…
For a class of one-dimensional cellular automata, we review and complete the characterization of the invariant measures (in particular, all invariant phase separation measures), the rate of convergence to equilibrium, and the derivation of…
Stochastic processes govern the time evolution of a huge variety of realistic systems throughout the sciences. A minimal description of noisy many-particle systems within a Markovian picture and with a notion of spatial dimension is given…