Related papers: Cellular automata can classify data by inducing tr…
The subject of this paper is the evolution of the concept of information processing in regular structures based on multi-level processing in nested cellular automata. The essence of the proposed model is a discrete space-time containing…
Probabilistic cellular automata describe the dynamics of classical spin models, which, for sufficiently small temperature $T$, can serve as classical memory capable of storing information even in the presence of nonzero external magnetic…
This study aims at finding a method for constructing molecular dynamics like models using the formalism of cellular automata for fast simulation of fluid dynamic systems (including compressible phenomena). In as much as the results…
A simple relation of the order of $n$ abstract objects generates an $n-2$ dimensional basis of three dimensional vectors. A cellular automaton-like model of evolution of this system is postulated. During this evolution, some quantities…
Complexity has been a recurrent research topic in cellular automata because they represent systems where complex behaviors emerge from simple local interactions. A significant amount of previous research has been conducted proposing…
A discrete model for computer simulations of the clustering dynamics of Social Amoebae is presented. This model incorporates the wavelike propagation of extracellular signaling cAMP, the sporadic firing of cells at early stage of…
The issue of data-driven neural network model construction is one of the core problems in the domain of Artificial Intelligence. A standard approach assumes a fixed architecture with trainable weights. A conceptually more advanced…
Distinguishing active from passive dynamics is a fundamental challenge in understanding the motion of living cells and other active matter systems. Here, we introduce a framework that combines physical modeling, analytical theory, and…
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…
In this paper, we propose a novel approach to generate images (or other artworks) by using neural cellular automatas (NCAs). Rather than training NCAs based on single images one by one, we combined the idea with variational autoencoders…
We present applications of a cellular automaton approach to pedestrian dynamics introduced in [1,2]. It is shown that the model is able to reproduce collective effects and self-organization phenomena encountered in pedestrian traffic, e.g.…
Neural Cellular Automata (NCA) models are trainable variations of traditional Cellular Automata (CA). Emergent motion in the patterns created by NCA has been successfully applied to synthesize dynamic textures. However, the conditions…
A universal map is derived for all deterministic 1D cellular automata (CA) containing no freely adjustable parameters. The map can be extended to an arbitrary number of dimensions and topologies and its invariances allow to classify all CA…
Neural cellular automata (Neural CA) are a recent framework used to model biological phenomena emerging from multicellular organisms. In these systems, artificial neural networks are used as update rules for cellular automata. Neural CA are…
We propose a four-way classification of two-dimensional semi-totalistic cellular automata that is different than Wolfram's, based on two questions with yes-or-no answers: do there exist patterns that eventually escape any finite bounding…
We introduce a new class of cellular automata to model reaction-diffusion systems in a quantitatively correct way. The construction of the CA from the reaction-diffusion equation relies on a moving average procedure to implement diffusion,…
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…
The dynamics group of an asynchronous cellular automaton (ACA) relates properties of its long term dynamics to the structure of Coxeter groups. The key mathematical feature connecting these diverse fields is involutions. Group-theoretic…
We propose a model-based clustering algorithm for a general class of functional data for which the components could be curves or images. The random functional data realizations could be measured with error at discrete, and possibly random,…
We extend the theory of Cellular Automata to arbitrary, time-varying graphs. In other words we formalize, and prove theorems about, the intuitive idea of a labelled graph which evolves in time - but under the natural constraint that…