Related papers: A weakly universal cellular automaton on the tesse…
In this paper we use the cellular automaton (CA) approach to model one-dimensional binary diffusion in solids. Employing a very simple state change rule we define an asynchronous CA model and take its continuum limit to obtain the governing…
We study monotone cellular automata (also known as $\mathcal{U}$-bootstrap percolation) in $\mathbb{Z}^d$ with random initial configurations. Confirming a conjecture of Balister, Bollob\'as, Przykucki and Smith, who proved the corresponding…
We investigate the modeling of weak boson number densities for leptons and hadrons in practical calculations in the Standard Model. Working in the framework of the Effective $W$ Approximation (EWA) and in $R_\xi$ and axial gauges, we derive…
Cellular automata are one-dimensional arrays of interconnected interacting finite automata. We investigate one of the weakest classes, the real-time one-way cellular automata, and impose an additional restriction on their inter-cell…
We study $2$-neighbor one-dimensional cellular automata with a large number $n$ of states and randomly selected rules. We focus on the rules with weakly robust periodic solutions (WRPS). WRPS are global configurations that exhibit spatial…
If L=Z^D and A is a finite set, then A^L is a compact space. A cellular automaton (CA) is a continuous transformation F:A^L--> A^L that commutes with all shift maps. A quasisturmian (QS) subshift is a shift-invariant subset obtained by…
In this paper we consider cellular automata $(\mathfrak{G},\Phi)$ with algebraic local rules and such that $\mathfrak{G}$ is a topological Markov chain which has a structure compatible to this local rule. We characterize such cellular…
A universal map is derived for all deterministic 1D cellular automata (CA) containing no freely adjustable parameters. The map can be extended to an arbitrary number of dimensions and topologies and its invariances allow to classify all CA…
We construct a cellular automaton (CA) model that describes the movement of a particle in a disordered system. The mathematical properties of the CA model were examined by varying the configuration of grid and determining the number of…
We investigate some general properties of algebraic cellular automata, i.e., cellular automata over groups whose alphabets are affine algebraic sets and which are locally defined by regular maps. When the ground field is assumed to be…
Bijections between sets may be seen as discrete (or crisp) unitary transformations used in quantum computations. So discrete quantum cellular automata are cellular automata with reversible transition functions. This note studies on 1d…
In this paper, we develop a new cellular automata-based linear model for several nonlinear pseudorandom number generators with practical applications in symmetric cryptography. Such a model generates all the solutions of linear binary…
For any group $G$ and set $A$, a cellular automaton over $G$ and $A$ is a transformation $\tau : A^G \to A^G$ defined via a finite neighborhood $S \subseteq G$ (called a memory set of $\tau$) and a local function $\mu : A^S \to A$. In this…
We propose a simple cellular automaton model of a self-healing system and investigate its properties. In the model, the substrate is a two-dimensional checkerboard configuration which can be damaged by changing values of a finite number of…
Cellular automata are topological dynamical systems. We consider the problem of deciding whether two cellular automata are conjugate or not. We also consider deciding strong conjugacy, that is, conjugacy by a map that commutes with the…
Wolfram has provided a qualitative classification of cellular automata(CA) rules according to which, there exits a class of CA rules (called Class 4) which exhibit complex pattern formation and long-lived dynamical activity (long…
The fixed point construction is a method for designing tile sets and cellular automata with highly nontrivial dynamical and computational properties. It produces an infinite hierarchy of systems where each layer simulates the next one. The…
Gauge-invariance is a fundamental concept in physics---known to provide the mathematical justification for all four fundamental forces. In this paper, we provide discrete counterparts to the main gauge theoretical concepts, directly in…
Let A^Z be the Cantor space of bi-infinite sequences in a finite alphabet A, and let sigma be the shift map on A^Z. A `cellular automaton' is a continuous, sigma-commuting self-map Phi of A^Z, and a `Phi-invariant subshift' is a closed,…
We describe a cellular-automaton based, two-dimensional (2D) lattice model which generates global oscillations in the EEG spectrum as well as time series of local field potentials resembling those observed during slow wave sleep. This is…