Related papers: Classification of Cellular Automata based on Stati…
Wolfram has provided a qualitative classification of cellular automata(CA) rules according to which, there exits a class of CA rules (called Class 4) which exhibit complex pattern formation and long-lived dynamical activity (long…
Based on computer simulations Wolfram presented in several papers conjectured classifications of cellular automata into 4 types. He distinguishes the 4 classes of cellular automata by the evolution of the pattern generated by applying a…
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,…
Cellular Automata(CA) is a discrete computing model which provides simple, flexible and efficient platform for simulating complicated systems and performing complex computation based on the neighborhoods information. CA consists of two…
The notions of universality and completeness are central in the theories of computation and computational complexity. However, proving lower bounds and necessary conditions remains hard in most of the cases. In this article, we introduce…
Here I describe a view of the evolution of cellular automata that allows to operate on larger structures. Instead of calculating the next state of all cells in one step, the method here developed uses a time slice that can proceed at…
There exists an index theory to classify strictly local quantum cellular automata in one dimension. We consider two classification questions. First, we study to what extent this index theory can be applied in higher dimensions via…
Cellular automata (CA) models are widely used to simulate complex systems with emergent behaviors, but identifying hidden parameters that govern their dynamics remains a significant challenge. This study explores the use of Convolutional…
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…
A simple mathematical expression for the universal map for cellular automata is found in closed form with the help of a digit function, whose most basic properties are established. This result is found after proving a theorem on the…
The dynamical behavior of non-uniform cellular automata is compared with the one of classical cellular automata. Several differences and similarities are pointed out by a series of examples. Decidability of basic properties like…
To identify potential universal cellular automata, a method is developed to measure information processing capacity of elementary cellular automata. We consider two features of cellular automata: Ability to store information, and ability to…
This note is a survey of examples and results about cellular automata with the purpose of recalling that there is no 'universal' way of being computationally universal. In particular, we show how some cellular automata can embed efficient…
Partitioned cellular automata are known to be an useful tool to simulate linear and nonlinear problems in physics, specially because they allow for a straightforward way to define conserved quantities and reversible dynamics. Here we show…
In this article, we have proposed an epidemic model by using probability cellular automata theory. The essential mathematical features are analyzed with the help of stability theory. We have given an alternative modelling approach for the…
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…
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 extend the usual definition of cellular automaton on a group in order to deal with a new kind of cellular automata, like cellular automata in the hyperbolic plane and we explore some properties of these cellular automata. This definition…
We propose a novel density based numerical method for uncertainty propagation under certain partial differential equation dynamics. The main idea is to translate them into objects that we call cellular probabilistic automata and to evolve…
Elementary cellular automata (ECA) present iconic examples of complex systems. Though described only by one-dimensional strings of binary cells evolving according to nearest-neighbour update rules, certain ECA rules manifest complex…