Cellular Automata and Lattice Gases
Continuum descriptions of epithelial tissue mechanics can replace expensive individual-based simulations with tractable macroscopic models, yet the link between cell-scale forces and tissue-scale transport remains poorly understood. We show…
We investigate modular Laplacian automata on triangular lattices with evolution governed by binary and ternary moduli. Extending previous studies on square lattices, we examine how lattice geometry influences long-term growth, density,…
We investigate the asymptotic behaviour of diploid Elementary Cellular Automata (ECA), that is, the stochastic mixtures between two ECAs. In this model, each cell independently applies one rule with probability $\lambda$ and the other rule…
The coordination of prices in economics is one of the most complex phenomena. In particular, the classical and neoclassical approaches related to the economic theory provide some insights into such a complex coordination based on different…
We study one dimensional binary Probabilistic Cellular Automaton (PCA) that interpolate between Wolfram's classical rules 23, 77, 178 and 232. These rules are the only ones that satisfy two criteria: (i) in the case of a majority in the…
Stochastic models of diffusion are routinely used to study dispersal of populations, including populations of animals, plants, seeds and cells. Advances in imaging and field measurement technologies mean that data are often collected across…
A one-dimensional cellular automaton $\tau : A^\mathbb{Z} \to A^\mathbb{Z}$ is a transformation of the full shift defined via a finite neighborhood $S \subset \mathbb{Z}$ and a local function $\mu : A^S \to A$. We study the family of…
Previous publications by the authors put forward the argument that Lifelike Cellular Automata can be treated as a bona fide example of livingness in and of themselves, not simply a toy analogue to biological life. Traits known to be…
Computational power can be measured by assigning an algebraic structure to a computational device. Here, we convert a small patch of Conway's Game of Life into a transformation semigroup. The conversion captures not only time evolution but…
We investigate Boolean, totalistic cellular automata with a majority or frustrated majority vote rule, and an interaction range of variable span. These two models show a behavior which differs from the mean-field one. The majority vote…
In mathematics and engineering, control theory is concerned with the analysis of dynamical systems through the application of suitable control inputs. One of the prominent problems in control theory is controllability which concerns the…
In this exploratory paper we introduce the problem of cognitive agents that learn how to modify their environment according to local sensing to reach a global goal. We concentrate on discrete dynamics (cellular automata) on a…
Exactly ergodicity in boundary-driven semi-infinite cellular automata (CA) are investigated. We establish all the ergodic rules in CA with 3, 4, and 5 states. We analytically prove the ergodicity for 12 rules in 3-state CA and 118320 rules…
Cellular automata generate spatially extended, temporally persistent emergent structures from local update rules. No general method derives the mechanisms of that generation from the rule itself; existing tools reconstruct structure from…
We investigate the conditions under which the mean-field formulation of a probabilistic, totalistic cellular automaton approximates the logistic equation. We show that this goal can be only fulfilled for an infinite-range neighborhood. We…
We study a probabilistic cellular automaton obtained as a mixture of the additive elementary rules 60 and 102. We prove that, for any finite periodic lattice and for mixing parameter $\lambda=1/2$, the system almost surely reaches the…
Large Language Models (LLMs), trained solely on massive text data, have achieved high performance on the Winograd Schema Challenge (WSC), a benchmark proposed to measure commonsense knowledge and reasoning abilities about the real world.…
We analyze the structure and dynamics in the low-density phase of the deterministic two-dimensional cellular automaton model of traffic flow introduced in [O. Biham, A.A. Middleton and D. Levine, Phys. Rev. A 46, R6124 (1992)]. The model…
Cellular automata (CA), originally developed as computational models of natural processes, have become a central subject in the study of complex systems and generative visual forms. Among them, the Ulam-Warburton Cellular Automaton (UWCA)…
We propose a general method for constructing a fuzzy cellular automaton from a given cellular automaton. Unlike previous approaches that use fuzzy distinctive normal form, whose update function is restricted to third-order polynomials, our…