Related papers: A Comprehensive Taxonomy of Cellular Automata
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…
Cellular automata (CAs) and convolutional neural networks (CNNs) are closely related due to the local nature of information processing. The connection between these topics is beneficial to both related fields, for conceptual as well as…
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…
We extend a previously introduced semi-analytical representation of a decomposition of CA dynamics in arbitrary dimensions and neighborhood schemes via the use of certain universal maps in which CA rule vectors are derivable from the…
The emergence of complex behaviors in cellular automata is an area that has been widely developed in recent years with the intention to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic…
Emergent processes in complex systems such as cellular automata can perform computations of increasing complexity, and could possibly lead to artificial evolution. Such a feat would require scaling up current simulation sizes to allow for…
A stochastic cellular automata (CA) model for pedestrian dynamics is presented. Our goal is to simulate different types of pedestrian movement, from regular to panic. But here we emphasize regular situations which imply that pedestrians…
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…
The goal of this paper is to show why the framework of communication complexity seems suitable for the study of cellular automata. Researchers have tackled different algorithmic problems ranging from the complexity of predicting to the…
Cellular automata (CA) consist of an array of identical cells, each of which may take one of a finite number of possible states. The entire array evolves in discrete time steps by iterating a global evolution G. Further, this global…
A cellular automaton is a parallel synchronous computing model, which consists in a juxtaposition of finite automata whose state evolves according to that of their neighbors. It induces a dynamical system on the set of configurations, i.e.…
Cellular automata (CA) are quintessential ALife and ubiquitous in many studies of collective behaviour and emergence, from morphogenesis to social dynamics and even brain modelling. Recently, there has been an increased interest in…
Research on asynchronous cellular automata has received a great amount of attention these last years and has turned to a thriving field. We survey the recent research that has been carried out on this topic and present a wide state of the…
A Cellular Automata (CA) rule is presented that can generate "loop patterns" in a 2D grid under fixed boundary conditions. A loop is a cyclically closed path represented by one-cells enclosed by zero-cells. A loop pattern can contain…
We construct a two dimensional Cellular Automata based model for the description of pedestrian dynamics. Wide range of complicated pattern formation phenomena in pedestrian dynamics are described in the model, e.g. lane formation, jams in a…
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…
We investigate one-dimensional elementary probabilistic cellular automata (PCA) whose dynamics in first-order mean-field approximation yields discrete logisticlike growth models for a single-species unstructured population with…
Cellular automata are often used to model systems in physics, social sciences, biology that are inherently asynchronous. Over the past 20 years, studies have demonstrated that the behavior of cellular automata drastically changed under…
Neural Cellular Automata (NCA) are a powerful combination of machine learning and mechanistic modelling. We train NCA to learn complex dynamics from time series of images and PDE trajectories. Our method is designed to identify underlying…
A general mathematical method is presented for the systematic construction of coupled map lattices (CMLs) out of deterministic cellular automata (CAs). The entire CA rule space is addressed by means of a universal map for CAs that we have…