Related papers: Probabilistic cellular automata with memory two: i…
Dynamic properties of a one-dimensional probabilistic cellular automaton are studied by monte-carlo simulation near a critical point which marks a second-order phase transition from a active state to a effectively unique absorbing state.…
We define quantum cellular automata as infinite quantum lattice systems with discrete time dynamics, such that the time step commutes with lattice translations and has strictly finite propagation speed. In contrast to earlier definitions…
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,…
We construct a parallel stochastic dynamics with invariant measure converging to the Gibbs measure of the low temperature Ising model. The proof of such convergence requires a polymer expansion based on suitably defined Peierls-type…
The expanding cellular automata (XCA) variant of cellular automata is investigated and characterized from a complexity-theoretical standpoint. An XCA is a one-dimensional cellular automaton which can dynamically create new cells between…
The density classification problem is one of the simplest yet non-trivial computing tasks which seem to be ideally suitable for cellular automata (CA). Unfortunately, there exists no one-dimensional two-state CA which classifies binary…
In this exploratory paper we introduce the problem of cognitive agents that learn how to modify their environment according to local sensing to reach a global goal. We concentrate on discrete dynamics (cellular automata) on a…
This paper presents a novel approach to the description and understanding of two-dimensional binary cellular automata with the Moore neighborhood that preserve the number of active cells. Such dynamical systems are known to successfully…
There exists algorithms to detect reversibility of cellular automaton (CA) for both finite and infinite lattices taking quadratic time. But, can we identify a $d$-state CA rule in constant time that is always reversible for every lattice…
Cellular automata (CA) dynamics are ordered in terms of two global parameters, computable {\sl a priori} from the description of rules. While one of them (activity) has been used before, the second one is new; it estimates the average…
We consider transformations between attractor basins of binary cylindrical cellular automata resulting from mutations. A t-point mutation of a state consists in toggling t sites in that state. Results of such mutations are described by a…
Probabilistic Cellular Automata are extended stochastic systems, widely used for modelling phenomena in many disciplines. The possibility of controlling their behaviour is therefore an important topic. We shall present here an approach to…
This paper is devoted to probabilistic cellular automata (PCA) on $\mathbb{N}$, $\mathbb{Z}$ or $\mathbb{Z}/n\mathbb{Z}$, depending of two neighbors, with a general alphabet $E$ (finite or infinite, discrete or not). We study the following…
Topological dynamics of cellular automata (CA), inherited from classical dynamical systems theory, has been essentially studied in dimension 1. This paper focuses on 2D CA and aims at showing that the situation is different and more…
We define and study a few properties of a class of random automata networks. While regular finite one-dimensional cellular automata are defined on periodic lattices, these automata networks, called randomized cellular automata, are defined…
From the perspective of the large deviations theory of occupational measures, the paper considers Probabilistic Cellular Automata (PCA) as Markov chains on infinite dimensional space. It turns out that for a wide range of PCA, the…
Cellular automata with memory (CAM) are widely used in fields such as image processing, pattern recognition, simulation, and cryptography. The invertibility of CAM is generally considered to be chaotic. Paper [Invertible behavior in…
It is well-known that the spacetime diagrams of some cellular automata have a fractal structure: for instance Pascal's triangle modulo 2 generates a Sierpinski triangle. Explaining the fractal structure of the spacetime diagrams of cellular…
We study the dynamics of the Rule 150 reversible cellular automaton (RCA). This is a one-dimensional lattice system of binary variables with synchronous (Floquet) dynamics, corresponding to a bulk deterministic and reversible discrete…
The local structure theory for cellular automata (CA) can be viewed as an finite-dimensional approximation of infinitely-dimensional system. While it is well known that this approximation works surprisingly well for some cellular automata,…