Related papers: Self-Organized States in Cellular Automata: Exact …
Markov automata combine non-determinism, probabilistic branching, and exponentially distributed delays. This compositional variant of continuous-time Markov decision processes is used in reliability engineering, performance evaluation and…
We created two dimensional hexagonal cellular automata to obtain complexity. Considering the game of life rules, Wolfram's works about life-like structures and John von Neumann's self-replication, self-maintenance, self-reproduction…
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…
Cellular automata represent physical systems where both space and time are discrete, and the associated physical quantities assume a limited set of values. While previous research has applied cellular automata in modeling chemical,…
We study charge fluctuations of a family of stochastic charged cellular automata away from the deterministic single-file limit and obtain the exact typical charge probability distributions, known to be anomalous, using hydrodynamics. The…
A two-state, three-dimensional, deterministic, reversible cellular automaton is shown to be capable of approximately circular orbits, wavelike undulations, and particle-like configurations that decay in accordance with a half-life law.
Classical Cellular Automata (CCAs) are a powerful computational framework for modeling global spatio-temporal dynamics with local interactions. While CCAs have been applied across numerous scientific fields, identifying the local rule that…
We show techniques of analyzing complex dynamics of cellular automata (CA) with chaotic behaviour. CA are well known computational substrates for studying emergent collective behaviour, complexity, randomness and interaction between order…
We revisit the problem of finding the conditions under which synchronous probabilistic cellular automata indexed by the line $\mathbb{Z}$, or the periodic line $\cyl{n}$, depending on 2 neighbours, admit as invariant distribution the law of…
We study locally interacting processes in discrete time, often called probabilistic cellular automata, indexed by locally finite graphs. For infinite regular trees and certain generalized Galton-Watson trees, we show that the marginal…
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…
Cellular automata (CAs) are fully-discrete dynamical models that have received much attention due to the fact that their relatively simple setup can nonetheless express highly complex phenomena. Despite the model's theoretical maturity and…
A new kind of cellular automaton (CA) for the study of the dynamics of urban systems is proposed. The state of a cell is not described using a finite set, but by means of continuum variables. A population sector is included, taking into…
The synchronization of two stochastically coupled one-dimensional cellular automata (CA) is analyzed. It is shown that the transition to synchronization is characterized by a dramatic increase of the statistical complexity of the patterns…
Cellular automata can show well known features of quantum mechanics, such as a linear rule according to which they evolve and which resembles a discretized version of the Schroedinger equation. This includes corresponding conservation laws.…
The temperature profiles of magnetically confined plasmas can display distinctive longlived pedestals at the edge and internally. Here we show that such structures can arise naturally through avalanching transport in a sandpile model. A…
A ``sandpile'' cellular automaton achieves complex temporal correlations, like a $1/f$ spectrum, if the position where it is perturbed diffuses slowly rather than changing completely at random, showing that the spatial correlations of the…
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…
A small-world cellular automaton network has been formulated to simulate the long-range interactions of complex networks using unconventional computing methods in this paper. Conventional cellular automata use local updating rules. The new…
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…