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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 rigorously prove a form of disorder-resistance for a class of one-dimensional cellular automaton rules, including some that arise as boundary dynamics of two-dimensional solidification rules. Specifically, when started from a random…
Cellular automata provide a fascinating class of dynamical systems capable of diverse complex behavior. These include simplified models for many phenomena seen in nature. Among other things, they provide insight into self-organized…
We establish new connections between percolation, bootstrap percolation, probabilistic cellular automata and deterministic ones. Surprisingly, by juggling with these in various directions, we effortlessly obtain a number of new results in…
Cellular automata have been useful artificial models for exploring how relatively simple rules combined with spatial memory can give rise to complex emergent patterns. Moreover, studying the dynamics of how rules emerge under artificial…
Discrete dynamical systems can exhibit complex behaviour from the iterative application of straightforward local rules. A famous example are cellular automata whose global dynamics are notoriously challenging to analyze. To address this, we…
Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and…
We introduce a stochastic cellular automaton with power law spatial decaying long-range interactions. In some limit this model reduces to the Domany-Kinzel cellular automaton. Monte Carlo and mean field calculations of the phase diagram of…
Cellular transformations which involve a significant phenotypical change of the cell's state use bistable biochemical switches as underlying decision systems. In this work, we aim at linking cellular decisions taking place on a time scale…
The proper functioning of multicellular organisms requires the robust establishment of precise proportions between distinct cell-types. This developmental differentiation process typically involves intracellular regulatory and stochastic…
The data generated by long-delayed dynamical systems can be organized in patterns by means of the so-called spatio-temporal representation, uncovering the role of multiple time-scales as independent degrees of freedom. However, their…
We explore some aspects of phase transitions in cellular automata. We start recalling the standard formulation of statistical mechanics of discrete systems (Ising model), illustrating the Monte Carlo approach as Markov chains and stochastic…
We propose that a quantum particle in a potential in one space dimension can be described by a probabilistic cellular automaton. While the simple updating rule of the automaton is deterministic, the probabilistic description is introduced…
Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…
Many diffusion processes in nature and society were found to be anomalous, in the sense of being fundamentally different from conventional Brownian motion. An important example is the migration of biological cells, which exhibits…
An introduction to cellular automata (both deterministic and probabilistic) with examples. Definition of deterministic automata, dynamical properties, damage spreading and Lyapunov exponents; probabilistic automata and Markov processes,…
Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…
Probabilistic Cellular Automata are extended stochastic systems, widely used for modelling phenomena in many disciplines. The possibility of controlling their behaviour is therefore an important topic. We shall present here an approach to…
In the present work we introduce a stochastic cellular automata model in order to simulate the dynamics of the stock market. A direct percolation method is used to create a hierarchy of clusters of active traders on a two dimensional grid.…
We introduce a new class of two-dimensional cellular automata with a bootstrap percolation-like dynamics. Each site can be either empty or occupied by a single particle and the dynamics follows a deterministic updating rule at discrete…