Related papers: Exponential convergence to equilibrium in cellular…
We propose a probabilistic cellular automata model for the spread of innovations, rumors, news, etc. in a social system. The local rule used in the model is outertotalistic, and the range of interaction can vary. When the range R of the…
Cellular automata are interacting classical bits that display diverse emergent behaviors, from fractals to random-number generators to Turing-complete computation. We discover that quantum cellular automata (QCA) can exhibit complexity in…
The Cellular Automaton (CA) modeling and simulation of solid dynamics is a long-standing difficult problem. In this paper we present a new two-dimensional CA model for solid dynamics. In this model the solid body is represented by a set of…
Almost four decades ago, Gacs, Kurdyumov, and Levin introduced three different cellular automata to investigate whether one-dimensional nonequilibrium interacting particle systems are capable of displaying phase transitions and, as a…
For a d-dimensional cellular automaton with d $\ge$ 1 we introduce a rescaled entropy which estimates the growth rate of the entropy at small scales by generalizing previous approaches [1, 9]. We also define a notion of Lyapunov exponent…
We Propose A Novel Automaton Model which uses Arithmetic Operations as the Evolving Rules, each cell has the states of the Natural Numbers k = (N), a radius of r = 1/2 and operates on an arbitrary input size. The Automaton reads an…
Given an energy-dissipating port-Hamiltonian system, we characterise the exponential decay of the energy via the model ingredients under mild conditions on the Hamiltonian density $\mathcal{H}$. In passing, we obtain generalisations for…
Fuzzy cellular automaton is a dynamical system with a continuous state value embedding a cellular automaton with a discrete state value. We investigate a fuzzy cellular automaton obtained from an elementary cellular automaton of rule number…
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…
This study introduces Skewed Fully Asynchronous Cellular Automata (SACA), a novel update scheme in cellular automata that updates the states of only two consecutive and adjacent cells, such as ci and ci+1, simultaneously at each time step.…
In this work we provide analytic results of infinite one-dimensional cellular automaton(CA). By realizing symbolic products, we investigate a subclass of infinite CA and prove analytically that within this subclass the only allowed…
We propose a novel density based numerical method for uncertainty propagation under certain partial differential equation dynamics. The main idea is to translate them into objects that we call cellular probabilistic automata and to evolve…
We extend recent results on the Asymptotic Equipartition Property for the density of $n$ particles in $\beta$-ensembles, as $n$ tends to infinity. We prove the Large Deviation Principle of the log-density for a general potential and the…
Elementary cellular automata (ECA) are one-dimensional discrete models of computation with a small memory set that have gained significant interest since the pioneer work of Stephen Wolfram, who studied them as time-discrete dynamical…
Following work by Hochman and Meyerovitch on multidimensional SFT, we give computability-theoretic characterizations of the real numbers that can appear as the topological entropies of one-dimensional and two-dimensional cellular automata.
It has been shown that uniform as well as non-uniform cellular automata (CA) can be evolved to perform certain computational tasks. Random Boolean networks are a generalization of two-state cellular automata, where the interconnection…
Spontaneous self-replication in cellular automata has long been considered rare, with most known examples requiring careful design or artificial initialization. In this paper, we present formal, causal evidence that such replication can…
We study the synchronization of totalistic one dimensional cellular automata (CA). The CA with a non zero synchronization threshold exhibit complex non periodic space time patterns and conversely. This synchronization transition is related…
In this paper we introduce the notion of quasi-expansivity for 2D CA and we show that it shares many properties with expansivity (that holds only for 1D CA). Similarly, we introduce the notions of quasi-sensitivity and prove that the…
Probabilistic cellular automata describe the dynamics of classical spin models, which, for sufficiently small temperature $T$, can serve as classical memory capable of storing information even in the presence of nonzero external magnetic…