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We propose and investigate a one-parameter probabilistic mixture of one-dimensional elementary cellular automata under the guise of a model for the dynamics of a single-species unstructured population with nonoverlapping generations in…
Cellular automata are a discrete dynamical system which models massively parallel computation. Much attention is devoted to computations with small time complexity for which the parallelism may provide further possibilities. In this paper,…
Neural Cellular Automata (NCAs) are a promising new approach to model self-organizing processes, with potential applications in life science. However, their deterministic nature limits their ability to capture the stochasticity of…
We discuss the self-deprecating strategy introduced by Peter Blau as one of stages of the process of social integration. Recently we have introduced a two-dimensional space of status, real and surface one ($A$ and $B$), and we have…
We study qualitative properties of two-dimensional freezing cellular automata with a binary state set initialized on a random configuration. If the automaton is also monotone, the setting is equivalent to bootstrap percolation. We explore…
Commonly studied cellular automata are memoryless and have fixed topology of connections between cells. However by allowing updates of links and short-term memory in cells we may potentially discover novel complex regimes of spatio-temporal…
In the present chapter, we focus on the switching of magnetisation, or the metastable lifetime of a ferromagnetic system. In this regard, particularly the Ising model and the Blume-Capel model, have been simulated in the presence of an…
The dynamical behavior of non-uniform cellular automata is compared with the one of classical cellular automata. Several differences and similarities are pointed out by a series of examples. Decidability of basic properties like…
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…
Classical models for competition between two species usually predict exclusion or divergent evolution of resource exploitation. However, recent experimental data show that coexistence is possible for very similar species competing for the…
In this paper, we analyze the behavior of a multi-agent system driven by the interactions of agents within a competitive environment. To achieve this, we describe the transition probabilities that underlie the system's stochastic nature. We…
The cellular automata discrete dynamical system is considered as the two-stage process: the majority rule for the change in the automata state and the rule for the change in topological relations between automata. The influence of changing…
We pose the problem of metastability for a three--state spin system with conservative dynamics. We consider the Blume--Capel model with the Kawasaki dynamics, we prove that, in a particular region of the parameter plane, the metastable…
Probabilistic Cellular Automata are a generalization of Cellular Automata. Despite their simple definition, they exhibit fascinating and complex behaviours. The stationary behaviour of these models changes when model parameters are varied,…
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…
We study the effect of intratumor heterogeneity in the likelihood of cancer cells moving from a primary tumor to other sites in the human body, generating a metastatic process. We model different scenarios of competition between tumor cells…
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…
We study both analytically and numerically metastability and nucleation in a two-dimensional nonequilibrium Ising ferromagnet. Canonical equilibrium is dynamically impeded by a weak random perturbation which models homogeneous disorder of…
We introduce a rejection-free continuous-time kinetic Monte Carlo framework to study stochastic systems governed by multiple concurrent dynamical mechanisms. In this approach, the relative activity of each dynamical channel emerges…
The Prisoner's Dilemma (PD) game is used in several fields due to the emergence of cooperation among selfish players. Here, we have considered a one-dimensional lattice, where each cell represents a player, that can cooperate or defect.…