Related papers: Sequentializing cellular automata
Cellular automata provide a fascinating class of dynamical systems capable of diverse complex behavior. These include simplified models for many phenomena seen in nature. Among other things, they provide insight into self-organized…
Suppose each site on a one-dimensional chain with periodic boundary condition may take on any one of the states $0,1,..., n-1$, can you find out the most frequently occurring state using cellular automaton? Here, we prove that while the…
While the reversibility of multidimensional cellular automata is undecidable and there exists a criterion for determining if a multidimensional linear cellular automaton is reversible, there are only a few results about the reversibility…
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…
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…
In this paper, we study linear cellular automata (CAs) on Cayley tree of order 2 over the field $\mathbb F_p$ (the set of prime numbers modulo $p$). We construct the rule matrix corresponding to finite cellular automata on Cayley tree.…
Let $S$ be a cancellative left-amenable semigroup and let $A$ be a finite set. We prove that every pre-injective cellular automaton $\tau \colon A^S \to A^S$ is surjective.
We study a two-dimensional semi-totalistic binary cell-state cellular automaton, which imitates a reversible precipitation in an abstract chemical medium. The systems exhibits a non-trivial growth and nucleation. We demonstrate how basic…
We show that spacetime diagrams of linear cellular automata $\Phi : {\mathbb F}_p^{\mathbb Z} \to {\mathbb F}_p^{\mathbb Z}$ with $(-p)$-automatic initial conditions are automatic. This extends existing results on initial conditions which…
In a recent paper [arXiv:1506.06649 [nlin.CG]], we presented an example of a 3-state cellular automaton which exhibits behaviour analogous to degenerate hyperbolicity often observed in finite-dimensional dynamical systems. We also…
In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over…
We propose a characteristic representation ofone-dimensional and 2-state, 3-neighbor cellular automaton rules, which describes an effective form of each rule after many time steps. Simulated results of the representation show that complex…
We produce for arbitrary non-amenable group $G$ and field $K$ a non-pre-injective, surjective linear cellular automaton. This answers positively Open Problem (OP-14) in Ceccherini-Silberstein and Coornaert's monograph "Cellular Automata and…
Cellular automata are computers, similar to Turing machines. The main difference is that Turing machines use a one-dimensional tape, whereas cellular automata use a two-dimensional grid. The best-known cellular automaton is the Game of…
We present a preliminary study of a new class of two-input cellular automata called eventually number-conserving cellular automata characterized by the property of evolving after a finite number of time steps to states whose number of…
In this paper, the author aims to establish a mathematical model for a mimic computer. To this end, a novel automaton is proposed. First, a one-dimensional cellular automaton is used for expressing some dynamic changes in the structure of a…
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…
A Cellular Automata (CA) is a computing model of complex System using simple rule. In CA the problem space into number of cell and each cell can be one or several final state. Cells are affected by neighbours' to the simple rule. Cellular…
The cellular automaton is a widely known model of both reversible and irreversible computations. The family of reversible second-order cellular automata considered in this work is appropriate both for construction of logic gates and…
A family of reversible deterministic cellular automata, including the rules 54 and 201 of [Bobenko et al., Commun. Math. Phys. 158, 127 (1993)] as well as their kinetically constrained quantum (unitary) or stochastic deformations, is shown…