Related papers: Cellular Automata
Probabilistic cellular automata are prototypes of non equilibrium critical phenomena. This class of models includes among others the directed percolation problem (Domany Kinzel model) and the dynamical Ising model. The critical properties…
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,…
This article presents a new characterization of controllability and regional controllability of Deterministic Cellular Automata (CA for short). It focuses on analyzing these problems within the framework of control theory, which have been…
This talk advocates intrinsic universality as a notion to identify simple cellular automata with complex computational behavior. After an historical introduction and proper definitions of intrinsic universality, which is discussed with…
The model of cellular automata is fascinating because very simple local rules can generate complex global behaviors. The relationship between local and global function is subject of many studies. We tackle this question by using results on…
Cellular Automata (CA), as they are presented in the literature, are abstract mathematical models of computation. In this pa- per we present an alternate approach: using the CA as a model or theory of physical systems and devices. While…
We consider the typical asymptotic behaviour of cellular automata of higher dimension (greater than 2). That is, we take an initial configuration at random according to a Bernoulli (i.i.d) probability measure, iterate some cellular…
The spatial structure, fluctuations as well as all state probabilities of self-organized (steady) states of cellular automata can be found (almost) exactly and {\em explicitly} from their Markovian dynamics. The method is shown on an…
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…
Many natural processes occur over characteristic spatial and temporal scales. This paper presents tools for (i) flexibly and scalably coarse-graining cellular automata and (ii) identifying which coarse-grainings express an automaton's…
We introduce a new class of probabilistic cellular automata that are capable of exhibiting rich dynamics such as synchronization and ergodicity and can be easily inferred from data. The system is a finite-state locally interacting Markov…
In the fields of computation and neuroscience, much is still unknown about the underlying computations that enable key cognitive functions including learning, memory, abstraction and behavior. This paper proposes a mathematical and…
Starting from integrable cellular automata we present a novel form of Painlev\'e equations. These equations are discrete in both the independent variable and the dependent one. We show that they capture the essence of the behavior of the…
This paper reports on patterns exhibiting self-replication with spontaneous, inheritable mutations and exponential genetic drift in Neural Cellular Automata. Despite the models not being explicitly trained for mutation or inheritability,…
The system of cellular automata, which expresses the process of dissemination and publication of the news among separate information resources, has been described. A bell-shaped dependence of news diffusion on internet-sources (web-sites)…
We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…
Number-conserving (or {\em conservative}) cellular automata have been used in several contexts, in particular traffic models, where it is natural to think about them as systems of interacting particles. In this article we consider several…
The theory of cellular automata in operational probabilistic theories is developed. We start introducing the composition of infinitely many elementary systems, and then use this notion to define update rules for such infinite composite…
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…
A probabilistic cellular automaton for cargo transport is presented that generalizes the totally asymmetric exclusion process with a defect from continuous time to parallel dynamics. It appears as an underlying principle in cellular…