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

We show that a behaviour analogous to degenerate hyperbolicity can occur in nearest-neighbour cellular automata (CA) with three states. We construct a 3-state rule by "lifting" elementary CA rule 140. Such "lifted" rule is equivalent to…

We present an intuitive formalism for implementing cellular automata on arbitrary topologies. By that means, we identify a symmetry operation in the class of elementary cellular automata. Moreover, we determine the subset of topologically…

This paper introduces a simple formalism for dealing with deterministic, non- deterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is…

In this paper we study the word problem of groups corresponding to tessellations of the hyperbolic plane. In particular using the Fibonacci technology developed by the second author we show that groups corresponding to the pentagrid or the…

We define and study a few properties of a class of random automata networks. While regular finite one-dimensional cellular automata are defined on periodic lattices, these automata networks, called randomized cellular automata, are defined…

There exists an index theory to classify strictly local quantum cellular automata in one dimension. We consider two classification questions. First, we study to what extent this index theory can be applied in higher dimensions via…

In this paper, we analyze the algebraic structure of some null boundary as well as some periodic boundary 2-D Cellular Automata (CA) rules by introducing a new matrix multiplication operation using only AND, OR instead of most commonly used…

Classical cellular automata represent a class of explicit discrete spacetime lattice models in which complex large-scale phenomena emerge from simple deterministic rules. With the goal to uncover different physically distinct classes of…

While for synchronous deterministic cellular automata there is an accepted definition of reversibility, the situation is less clear for asynchronous cellular automata. We first discuss a few possibilities and then investigate what we call…

Cellular Automata are discrete--time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata, are discrete…

In this work, the one-dimensional Cellular Automaton is extended to one that involves two sets of symbols and two global rules. As a main result, the Extended Curtis-Hedlund-Lyndon Theorem is demonstrated. Such constructions can be useful…

This paper studies complexity of recognition of classes of bounded configurations by a generalization of conventional cellular automata (CA) -- finite dynamic cellular automata (FDCA). Inspired by the CA-based models of biological and…

We present an exact renormalisation scheme for fermionic cellular automata on hypercubic lattices. By grouping neighbouring cells into tiles and selecting subspaces within them, multiple evolution steps on the original system correspond to…

Multi-cellular robot design aims to create robots comprised of numerous cells that can be efficiently controlled to perform diverse tasks. Previous research has demonstrated the ability to generate robots for various tasks, but these…

Cellular automata are both computational and dynamical systems. We give a complete classification of the dynamic behaviour of elementary cellular automata (ECA) in terms of fundamental dynamic system notions such as sensitivity and…

We consider quantum cellular automata for one-dimensional chains of Fermionic modes and study their implementability as finite depth quantum circuits. Fermionic automata have been classified in terms of an index modulo circuits and the…

We created two dimensional hexagonal cellular automata to obtain complexity. Considering the game of life rules, Wolfram's works about life-like structures and John von Neumann's self-replication, self-maintenance, self-reproduction…

Cellular automata on the triangular grid are here referred to as Triangular Automata (TA). This paper focuses on the simplest class of TA, called Elementary Triangular Automata (ETA). They are argued to be the two-dimensional counterpart of…

In this paper, we construct a weakly universal cellular automaton in the heptagrid, the tessellation $\{7,3\}$ which is not rotation invariant but which is truly planar. This result, under these conditions, cannot be improved for the…

We prove the existence of a semilinear representation of Cellular Automata (CA) with the introduction of multiple convolution kernels. Examples of the technique are presented for rules akin to the "edge-of-chaos" including the Turing…