Related papers: A new weakly universal cellular automaton in the 3…
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…
Young's cellular automaton, recently applied to study the spatiotemporal evolution of binary patterns for favorable/hostile environments, has now been modified from a different point of view. In this model, each differentiated cell (DC)…
This paper describes a new concept of cellular automaton (CA). XCA consists of a set of arcs (edges) that correspond to cells in CA. At a particular time, the arcs are connected to a directed graph. With each time step, the arcs exchange…
We classify quantum cellular automata whose cells are qubits, on hypercubic lattices $\mathbb Z^s$, with the von Neumann neighborhood scheme, in terms of realizability as finite-depth quantum circuits. We show the most general structure of…
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…
A probabilistic cellular automaton for cargo transport is presented that generalizes the totally asymmetric exclusion process with a defect from continuous time to parallel dynamics. It appears as an underlying principle in cellular…
In this paper we propose a rule-independent description of applications of cellular automata rules for one-dimensional additive cellular automata on cylinders of finite sizes. This description is shown to be a useful tool for for answering…
The emergence of complex behaviors in cellular automata is an area that has been widely developed in recent years with the intention to generate and analyze automata that produce space-moving patterns or gliders that interact in a periodic…
The spectrum and properties of quantum bound states is strongly dependent on the dimensionality of space. How this comes about and how one may theoretically and experimentally study the interpolation between different dimensions is a topic…
In this paper we study the statistical properties of a reversible cellular automaton in two out-of-equilibrium settings. In the first part we consider two instances of the initial value problem, corresponding to the inhomogeneous quench and…
We introduce an efficient cellular automaton for the coagulation-fission process with diffusion 2A->3A, 2A->A in arbitrary dimensions. As the well-known Domany-Kinzel model, it is defined on a tilted hypercubic lattice and evolves by…
The Besicovitch pseudo-metric is a shift-invariant pseudo-metric on the set of infinite sequences, that enjoys interesting properties and is suitable for studying the dynamics of cellular automata. They correspond to the asymptotic behavior…
The memristor is a device whose resistance changes depending on the polarity and magnitude of a voltage applied to the device's terminals. We design a minimalistic model of a regular network of memristors using structurally-dynamic cellular…
Linear quantum cellular automata were introduced recently as one of the models of quantum computing. A basic postulate of quantum mechanics imposes a strong constraint on any quantum machine: it has to be unitary, that is its time evolution…
We study two common types of time-noncontinuous updates for one dimensional stochastic cellular automata with arbitrary nearest neighbor interactions and arbitrary open boundary conditions. We first construct the stationary states using the…
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…
As quantum devices scale to larger and larger sizes, a significant challenge emerges in scaling their coherent controls accordingly. Quantum cellular automata (QCAs) constitute a promising framework that bypasses this control problem:…
Number-conserving cellular automata are discrete dynamical systems that simulate interacting particles like e.g. grains of sand. In an earlier paper, I had already derived a uniform construction for all transition rules of one-dimensional…
We investigate subshifts with a general algebraic structure and cellular automata on them, with an emphasis on (order-theoretic) lattices. Our main results concern the characterization of Boolean algebraic subshifts, conditions for…
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…