A Two-Player Game of Life

We present a new extension of Conway's game of life for two players, which we call p2life. P2life allows one of two types of token, black or white, to inhabit a cell, and adds competitive elements into the birth and survival rules of the original game. We solve the mean-field equation for p2life and determine by simulation that the asymptotic density of p2life approaches 0.0362.Comment: 7 pages, 3 figure

A Cellular Automaton Model for Bi-Directionnal Traffic

We investigate a cellular automaton (CA) model of traffic on a bi-directional two-lane road. Our model is an extension of the one-lane CA model of {Nagel and Schreckenberg 1992}, modified to account for interactions mediated by passing, and for a distribution of vehicle speeds. We chose values for the various parameters to approximate the behavior of real traffic. The density-flow diagram for the bi-directional model is compared to that of a one-lane model, showing the interaction of the two lanes. Results were also compared to experimental data, showing close agreement. This model helps bridge the gap between simplified cellular automata models and the complexity of real-world traffic.Comment: 4 pages 6 figures. Accepted Phys Rev

Estimation of the order parameter exponent of critical cellular automata using the enhanced coherent anomaly method.

The stochastic cellular automaton of Rule 18 defined by Wolfram [Rev. Mod. Phys. 55 601 (1983)] has been investigated by the enhanced coherent anomaly method. Reliable estimate was found for the $\beta$ critical exponent, based on moderate sized ($n \le 7$) clusters.Comment: 6 pages, RevTeX file, figure available from [email protected]

Subcritical behavior in the alternating supercritical Domany-Kinzel dynamics

Cellular automata are widely used to model real-world dynamics. We show using the Domany-Kinzel probabilistic cellular automata that alternating two supercritical dynamics can result in subcritical dynamics in which the population dies out. The analysis of the original and reduced models reveals generality of this paradoxical behavior, which suggests that autonomous or man-made periodic or random environmental changes can cause extinction in otherwise safe population dynamics. Our model also realizes another scenario for the Parrondo's paradox to occur, namely, spatial extensions.Comment: 8 figure

Cellular automaton rules conserving the number of active sites

This paper shows how to determine all the unidimensional two-state cellular automaton rules of a given number of inputs which conserve the number of active sites. These rules have to satisfy a necessary and sufficient condition. If the active sites are viewed as cells occupied by identical particles, these cellular automaton rules represent evolution operators of systems of identical interacting particles whose total number is conserved. Some of these rules, which allow motion in both directions, mimic ensembles of one-dimensional pseudo-random walkers. Numerical evidence indicates that the corresponding stochastic processes might be non-Gaussian.Comment: 14 pages, 5 figure

Cluster formation and anomalous fundamental diagram in an ant trail model

A recently proposed stochastic cellular automaton model ({\it J. Phys. A 35, L573 (2002)}), motivated by the motions of ants in a trail, is investigated in detail in this paper. The flux of ants in this model is sensitive to the probability of evaporation of pheromone, and the average speed of the ants varies non-monotonically with their density. This remarkable property is analyzed here using phenomenological and microscopic approximations thereby elucidating the nature of the spatio-temporal organization of the ants. We find that the observations can be understood by the formation of loose clusters, i.e. space regions of enhanced, but not maximal, density.Comment: 11 pages, REVTEX, with 11 embedded EPS file

On Damage Spreading Transitions

We study the damage spreading transition in a generic one-dimensional stochastic cellular automata with two inputs (Domany-Kinzel model) Using an original formalism for the description of the microscopic dynamics of the model, we are able to show analitically that the evolution of the damage between two systems driven by the same noise has the same structure of a directed percolation problem. By means of a mean field approximation, we map the density phase transition into the damage phase transition, obtaining a reliable phase diagram. We extend this analysis to all symmetric cellular automata with two inputs, including the Ising model with heath-bath dynamics.Comment: 12 pages LaTeX, 2 PostScript figures, tar+gzip+u

Generalized mean-field study of a driven lattice gas

Generalized mean-field analysis has been performed to study the ordering process in a half-filled square lattice-gas model with repulsive nearest neighbor interaction under the influence of a uniform electric field. We have determined the configuration probabilities on 2-, 4-, 5-, and 6-point clusters excluding the possibility of sublattice ordering. The agreement between the results of 6-point approximations and Monte Carlo simulations confirms the absence of phase transition for sufficiently strong fields.Comment: 4 pages (REVTEX) with 4 PS figures (uuencoded

Study of the multi-species annihilating random walk transition at zero branching rate - cluster scaling behavior in a spin model

Numerical and theoretical studies of a one-dimensional spin model with locally broken spin symmetry are presented. The multi-species annihilating random walk transition found at zero branching rate previously is investigated now concerning the cluster behaviour of the underlying spins. Generic power law behaviors are found, besides the phase transition point, also in the active phase with fulfillment of the hyperscaling law. On the other hand scaling laws connecting bulk- and cluster exponents are broken - a possibility in no contradiction with basic scaling assumptions because of the missing absorbing phase.Comment: 7 pages, 6 figures, final form to appear in PRE Nov.200

Phase transition of the one-dimensional coagulation-production process

Recently an exact solution has been found (M.Henkel and H.Hinrichsen, cond-mat/0010062) for the 1d coagulation production process: 2A ->A, A0A->3A with equal diffusion and coagulation rates. This model evolves into the inactive phase independently of the production rate with $t^{-1/2}$ density decay law. Here I show that cluster mean-field approximations and Monte Carlo simulations predict a continuous phase transition for higher diffusion/coagulation rates as considered in cond-mat/0010062. Numerical evidence is given that the phase transition universality agrees with that of the annihilation-fission model with low diffusions.Comment: 4 pages, 4 figures include