相关论文: About the embedding of one dimensional cellular au…

In this paper, we look at the extention of Hedlund's characterization of cellular automata to the case of cellular automata in the hyperbolic plane. This requires an additionnal condition. The new theorem is proved with full details in the…

This contribution belongs to a combinatorial approach to hyperbolic geometry and it is aimed at possible applications to computer simulations. It is based on the splitting method which was introduced by the author and which is reminded in…

In this paper, we prove that there is a strongly universal cellular automaton in the dodecagrid, the tessellation {5,3,4} of the hyperbolic 3D-space, with five states which is rotation invariant. This improves a previous paper of the author…

In this paper, we prove that there is an outer totalistic weakly universal cellular automaton in the dodecagrid, the tessellation {5,3,4} of the hyperbolic 3D space, with four states. It is the first result in such a context.

We extend the usual definition of cellular automaton on a group in order to deal with a new kind of cellular automata, like cellular automata in the hyperbolic plane and we explore some properties of these cellular automata. This definition…

In this paper, we show a construction of a weakly universal cellular automaton in the 3D hyperbolic space with two states. The cellular automaton is rotation invariant and, moreover, based on a new implementation of a railway circuit in the…

In this paper we study the dynamics of 1- and 2- dimensional cellular automata, using a 2-adic representation of the states, we give a simple graphical technique for finding periodic solutions. We also study the continuity properties of the…

In this paper, we investigate the halting problem for deterministic cellula automata in the pentagrid. We prove that the problem is decidable when the cellular automaton starts its computation from a finite configuration and when it has at…

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 give an application of iterated pushdown automata to contour words of balls and two other domains in infinitely many tilings of the hyperbolic plane. We also give a similar application for the tiling {5,3,4} of the…

In this paper, following the way opened by a previous paper deposited on arXiv, we give an upper bound to the number of states for a hyperbolic cellular automaton in the pentagrid. Indeed, we prove that there is a hyperbolic cellular…

In this paper, we construct a strongly universal cellular automaton on the line with 11 states and the standard neighbourhood. We embed this construction into several tilings of the hyperbolic plane and of the hyperbolic 3D space giving…

In this paper, we construct a new weakly universal cellular automaton on the ternary heptagrid. The previous result, obtained by the same author and Y. Song required six states only. This time, the number of states is four. This is the best…

We introduce and study cellular automata whose cell spaces are left-homogeneous spaces. Examples of left-homogeneous spaces are spheres, Euclidean spaces, as well as hyperbolic spaces acted on by isometries; uniform tilings acted on by…

This paper introduces a communication system for the tiles of the heptagrid, a tiling of the hyperbolic plane. The method can be extended to other tilings of this plane. The paper focuses on an actual implementation at the programming stage…

Cellular automata represent physical systems where both space and time are discrete, and the associated physical quantities assume a limited set of values. While previous research has applied cellular automata in modeling chemical,…

The paper proposes a simple formalism for dealing with deterministic, non-deterministic and stochastic cellular automata in a unifying and composable manner. Armed with this formalism, we extend the notion of intrinsic simulation between…

This paper presents a classification of Cellular Automata rules based on its properties at the nth iteration. Elaborate computer program has been designed to get the nth iteration for arbitrary 1-D or 2-D CA rules. Studies indicate that the…

Exactly ergodicity in boundary-driven semi-infinite cellular automata (CA) are investigated. We establish all the ergodic rules in CA with 3, 4, and 5 states. We analytically prove the ergodicity for 12 rules in 3-state CA and 118320 rules…

This note is a survey of examples and results about cellular automata with the purpose of recalling that there is no 'universal' way of being computationally universal. In particular, we show how some cellular automata can embed efficient…