相关论文: The B36/S125 "2x2" Life-Like Cellular Automaton

We study life over the course of video game history as represented by their mechanics. While there have been some variations depending on genre or "character type", we find that most games converge to a similar representation. We also…

We rigorously prove a form of disorder-resistance for a class of one-dimensional cellular automaton rules, including some that arise as boundary dynamics of two-dimensional solidification rules. Specifically, when started from a random…

A transition from asymmetric to symmetric patterns in time-dependent extended systems is described. It is found that one dimensional cellular automata, started from fully random initial conditions, can be forced to evolve into complex…

It is well-known that the spacetime diagrams of some cellular automata have a fractal structure: for instance Pascal's triangle modulo 2 generates a Sierpinski triangle. It has been shown that such patterns can occur when the alphabet is…

Previous publications by the authors put forward the argument that Lifelike Cellular Automata can be treated as a bona fide example of livingness in and of themselves, not simply a toy analogue to biological life. Traits known to be…

We demonstrate a discrete implementation of a wave-based majority gate in a chaotic Life-like cellular automaton. The gate functions via controlling of patterns' propagation into stationary channels. The gate presented is realisable in many…

Signal machines form an abstract and idealised model of collision computing. Based on dimensionless signals moving on the real line, they model particle/signal dynamics in Cellular Automata. Each particle, or signal, moves at constant speed…

A polyomino is said to be L-convex if any two of its cells are connected by a 4-connected inner path that changes direction at most once. The 2-dimensional language representing such polyominoes has been recently proved to be recognizable…

In a probabilistic cellular automaton in which all local transitions have positive probability, the problem of keeping a bit of information indefinitely is nontrivial, even in an infinite automaton. Still, there is a solution in 2…

We investigate the dynamics of a conservative version of Conway's Game of Life, in which a pair consisting of a dead and a living cell can switch their states following Conway's rules but only by swapping their positions, irrespective of…

A cellular automaton that is a generalization of the box-ball system with either many kinds of balls or finite carrier capacity is proposed and studied through two discrete integrable systems: nonautonomous discrete KP lattice and…

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…

Consider a graph $G=(V,E)$ and a random initial vertex-coloring, where each vertex is blue independently with probability $p_{b}$, and red with probability $p_r=1-p_b$. In each step, all vertices change their current color synchronously to…

One-dimensional cellular automata are discrete dynamical systems that operate on an infinite lattice of sites and are characterized by the locality and uniformity of their update rule. Permutations of the state set and isometric…

Periodicity and relaxation are investigated for the trajectories of the states in one-dimensional finite cellular automata with rule-90 and 150. The time evolutions are described with matrices. Eigenvalue analysis is applied to clarify the…

We study one-dimensional cellular automata evolutions with both temporal and spatial periodicity. The main objective is to investigate the longest temporal periods among all two-neighbor rules, with a fixed spatial period $\sigma$ and…

We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…

Cellular automata are dynamical systems defined on lattices and commuting with the Bernoulli shift. In this work, we focus on the spectral properties of D-dimensional cellular automata. We give a characterization of their spectrum from both…

We study the effect of mixing two rules on the dynamics of one-dimensional cellular automata by large scale numerical simulations. We calculate the decay of the magnetization for the Domany-Kinzel automaton (XOR/AND mixing) to its…

A cellular automaton is presented whose governing rule is that the Kolmogorov complexity of a cell's neighborhood may not increase when the cell's present value is substituted for its future value. Using an approximation of this…