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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…
We carried out a Cellular Automata simulation of a model polyelectrolyte solution at infinite dilution, in order to reproduce qualitatively its conformational properties. Our results predict the so called \emph{pearl necklace} structures,…
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…
We study the asymptotic behaviour of symbolic computing systems, notably one-dimensional cellular automata (CA), in order to ascertain whether and at what rate the number of complex versus simple rules dominate the rule space for increasing…
We show that cellular automata can classify data by inducing a form of dynamical phase coexistence. We use Monte Carlo methods to search for general two-dimensional deterministic automata that classify images on the basis of activity, the…
Neural cellular automata represent an evolution of the traditional cellular automata model, enhanced by the integration of a deep learning-based transition function. This shift from a manual to a data-driven approach significantly increases…
We propose a 2-dimensional cellular automaton model to simulate pedestrian traffic. It is a vmax=1 model with exclusion statistics and parallel dynamics. Long-range interactions between the pedestrians are mediated by a so called floor…
The original local, discrete example of Linear Unitary Cellular Automata (LUCA) is analyzed in terms of a new representation previously introduced in [1] for classical CA. Several important underlying symmetries are reviewed and their tight…
Starting from integrable cellular automata we present a novel form of Painlev\'e equations. These equations are discrete in both the independent variable and the dependent one. We show that they capture the essence of the behavior of the…
In this paper we present a quantization of Cellular Automata. Our formalism is based on a lattice of qudits, and an update rule consisting of local unitary operators that commute with their own lattice translations. One purpose of this…
We present a diagrammatic method to build up sophisticated cellular automata (CAs) as models of complex physical systems. The diagrams complement the mathematical approach to CA modeling, whose details are also presented here, and allow CAs…
In cellular automata with memory, the unchanged maps of the conventional cellular automata are applied to cells endowed with memory of their past states in some specified interval. We implement Rule 30 automata with a majority memory and…
A multispecies artificial ecosystem is formulated using cellular automata with species interactions and food chain hierarchy. The constructed finite state automaton can simulate the complexity and self-organized characteristics of the…
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…
In this paper we introduce a new quantum computation model, the linear quantum cellular automaton. Well-formedness is an essential property for any quantum computing device since it enables us to define the probability of a configuration in…
Cellular automata on the triangular grid are here referred to as Triangular Automata (TA). This paper focuses on the simplest class of TA, called Elementary Triangular Automata (ETA). They are argued to be the two-dimensional counterpart of…
The emerging field of Nominal Computation Theory is concerned with the theory of Nominal Sets and its applications to Computer Science. We investigate here the impact of nominal sets on the definition of Cellular Automata and on their…
This paper aims at providing a survey on the problems that can be easily addressed by cellular automata in bioinformatics. Some of the authors have proposed algorithms for addressing some problems in bioinformatics but the application of…
We present simulations of evacuation processes using a recently introduced cellular automaton model for pedestrian dynamics. This model applies a bionics approach to describe the interaction between the pedestrians using ideas from…
We describe a class of cellular automata (CAs) that are end-to-end differentiable. DCAs interpolate the behavior of ordinary CAs through rules that act on distributions of states. The gradient of a DCA with respect to its parameters can be…