Related papers: Cellular Automata as a Model of Physical Systems
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…
This article introduces the notion of clouds in asynchronous cellular automata (ACAs). We show that the cloud behaviour of ACAs has similarity with natural clouds across the sky, election model of parliamentary democratic system, and…
We present a preliminary study of a new class of two-input cellular automata called eventually number-conserving cellular automata characterized by the property of evolving after a finite number of time steps to states whose number of…
A small-world cellular automaton network has been formulated to simulate the long-range interactions of complex networks using unconventional computing methods in this paper. Conventional cellular automata use local updating rules. The new…
Cellular automata (CA) exemplify systems where simple local interaction rules can lead to intricate and complex emergent phenomena at large scales. The various types of dynamical behavior of CA are usually categorized empirically into…
Inspired by cellular growth and self-organization, Neural Cellular Automata (NCAs) have been capable of "growing" artificial cells into images, 3D structures, and even functional machines. NCAs are flexible and robust computational systems…
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…
We define a new transfinite time model of computation, infinite time cellular automata. The model is shown to be as powerful than infinite time Turing machines, both on finite and infinite inputs; thus inheriting many of its properties. We…
In mathematics and engineering, control theory is concerned with the analysis of dynamical systems through the application of suitable control inputs. One of the prominent problems in control theory is controllability which concerns the…
Cellular Automata are discrete--time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata, are discrete…
Cellular automata are one-dimensional arrays of interconnected interacting finite automata. We investigate one of the weakest classes, the real-time one-way cellular automata, and impose an additional restriction on their inter-cell…
We study intrinsic simulations between cellular automata and introduce a new necessary condition for a CA to simulate another one. Although expressed for general CA, this condition is targeted towards surjective CA and especially linear…
Let $G$ be a group and let $A$ be a finite set with at least two elements. A cellular automaton (CA) over $A^G$ is a function $\tau : A^G \to A^G$ defined via a finite memory set $S \subseteq G$ and a local function $\mu :A^S \to A$. The…
Probabilistic Cellular Automata (PCA) are simple models used to study dynamical phase transitions. There exist mean field approximations to PCA that can be shown to exhibit a phase transition. We introduce a model interpolating between a…
The prediction of the behavior of the disease, the level of affectation in a population and the ways to control it are the most important aspects studied by epidemiology using tools such as historical data and mathematical models. So, our…
In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over…
One-dimensional quantum cellular automata (QCA) consist in a line of identical, finite dimensional quantum systems. These evolve in discrete time steps according to a local, shift-invariant unitary evolution. By local we mean that no…
Nowadays, in societies threatened by atomization, selfishness, short-term thinking, and alienation from political life, there is a renewed debate about classical questions concerning the quality of democratic decision-making. In this work a…
Biological systems are notorious for complex behavior within short timescales (e.g. metabolic activity) and longer time scales (e.g. evolutionary selection), along with their complex spatial organization. Because of their complexity and…
Classical Cellular Automata (CCAs) are a powerful computational framework for modeling global spatio-temporal dynamics with local interactions. While CCAs have been applied across numerous scientific fields, identifying the local rule that…