Related papers: Cellular automata can classify data by inducing tr…
Elementary cellular automata are the simplest form of cellular automata, studied extensively by Wolfram in the 1980s. He discovered complex behavior in some of these automata and developed a classification for all cellular automata based on…
We study the classification of cellular-automaton update rules into Wolfram's four classes. We start with the notion of the input entropy of a spatiotemporal block in the evolution of a cellular automaton, and build on it by introducing two…
Layered Cellular Automata (LCA) extends the concept of traditional cellular automata (CA) to model complex systems and phenomena. In LCA, each cell's next state is determined by the interaction of two layers of computation, allowing for…
We discuss here the mean-field theory for a cellular automata model of meta-learning. The meta-learning is the process of combining outcomes of individual learning procedures in order to determine the final decision with higher accuracy…
Cellular Automata (CA) have long been foundational in simulating dynamical systems computationally. With recent innovations, this model class has been brought into the realm of deep learning by parameterizing the CA's update rule using an…
Cellular automata are a class of computational models based on simple rules and algorithms that can simulate a wide range of complex phenomena. However, when using conventional computers, these 'simple' rules are only encapsulated at the…
Suppose each site on a one-dimensional chain with periodic boundary condition may take on any one of the states $0,1,..., n-1$, can you find out the most frequently occurring state using cellular automaton? Here, we prove that while the…
This article introduces new tools to study self-organisation in a family of simple cellular automata which contain some particle-like objects with good collision properties (coalescence) in their time evolution. We draw an initial…
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…
Cellular automata (CAs) are fully-discrete dynamical models that have received much attention due to the fact that their relatively simple setup can nonetheless express highly complex phenomena. Despite the model's theoretical maturity and…
Rapid advancements in deep learning over the past decade have fueled an insatiable demand for efficient and scalable hardware. Photonics offers a promising solution by leveraging the unique properties of light. However, conventional neural…
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…
Cellular automata represent physical systems where both space and time are discrete, and the associated physical quantities assume a limited set of values. While previous research has applied cellular automata in modeling chemical,…
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 (CA) theory is a discrete model that represents the state of each of its cells from a finite set of possible values which evolve in time according to a pre-defined set of transition rules. CA have been applied to a number…
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…
Nonlinear cellular automata are extensively used in simulations, image processing, cryptography, and so on. The determination of their fundamental properties, injectivity and surjectivity, related to information loss during the evolution,…
Cellular automata are synchronous discrete dynamical systems used to describe complex dynamic behaviors. The dynamic is based on local interactions between the components, these are defined by a finite graph with an initial node coloring…
In this paper, we propose a new approach for building cellular automata to solve real-world segmentation problems. We design and train a cellular automaton that can successfully segment high-resolution images. We consider a colony that…
Texture recognition is one of the most important tasks in computer vision and, despite the recent success of learning-based approaches, there is still need for model-based solutions. This is especially the case when the amount of data…