相关论文: Response Curves and Preimage Sequences of Two-Dime…

We consider the problem of computing a response curve for binary cellular automata -- that is, the curve describing the dependence of the density of ones after many iterations of the rule on the initial density of ones. We demonstrate how…

We consider the problem of computing a response curve for binary cellular automata -- that is, the curve describing the dependence of the density of ones after many iterations of the rule on the initial density of ones. We demonstrate how…

We search for regularities in the sequences of numbers of preimages for elementary cellular automata. For 46 out of 88 "minimal" rules, we find recognizable patterns, usually in the form of second order recurrence equations with constant…

Recently, Land and Belew [Phys. Rev. Lett. 74, 5148 (1995)] have shown that no one-dimensional two-state cellular automaton which classifies binary strings according to their densities of 1's and 0's can be constructed. We show that a pair…

The density classification problem is one of the simplest yet non-trivial computing tasks which seem to be ideally suitable for cellular automata (CA). Unfortunately, there exists no one-dimensional two-state CA which classifies binary…

Given a (finite) string of zeros and ones, we report a way to determine if the number of ones is less than, greater than, or equal to a prescribed number by applying two sets of cellular automaton rules in succession. Thus, we solve the…

We consider the problem of finding the density of 1's in a configuration obtained by $n$ iterations of a given cellular automaton (CA) rule, starting from disordered initial condition. While this problems is intractable in full generality…

Microscopic modeling of multi-lane traffic is usually done by applying heuristic lane changing rules, and often with unsatisfying results. Recently, a cellular automaton model for two-lane traffic was able to overcome some of these problems…

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…

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 surjectivity of the global map in two-dimensional cellular automata (2D CA) is undecidable in general, in specific cases one can often decide if the rule is surjective or not. We attempt to classify as many 2D CA as possible by…

Consider an infinite graph with nodes initially labeled by independent Bernoulli random variables of parameter p. We address the density classification problem, that is, we want to design a (probabilistic or deterministic) cellular…

We systematically study the boundaries of one-dimensional, 2-color cellular automata depending on 4 cells, begun from simple initial conditions. We determine the exact growth rates of the boundaries that appear to be reducible. Morphic…

Two-dimensional nine neighbor hood rectangular Cellular Automata rules can be modeled using many different techniques like Rule matrices, State Transition Diagrams, Boolean functions, Algebraic Normal Form etc. In this paper, a new model is…

The density classification problem is the computational problem of finding the majority in a given array of votes in a distributed fashion. It is known that no cellular automaton rule with binary alphabet can solve the density…

In this article we investigate the computational complexity of predicting two dimensional freezing majority cellular automata with states $\{-1,+1\}$, where the local interactions are based on an L-shaped neighborhood structure. In these…

We present a general setting in which the formula describing the linear response of the physical measure of a perturbed system can be obtained. In this general setting we obtain an algorithm to rigorously compute the linear response. We…

This work introduces a new problem, named as, affinity classification problem which is a generalization of the density classification problem. To solve this problem, we introduce temporally stochastic cellular automata where two rules are…

We introduce density dependence of the cell size in cellular-automaton models for traffic flow, which allows a more precise correspondence between real-world phenomena and what observed in simulation. Also, we give an explicit calibration…

The density classification task is to determine which of the symbols appearing in an array has the majority. A cellular automaton solving this task is required to converge to a uniform configuration with the majority symbol at each site. It…