相关论文: Non-uniform cellular automata and distributions of…

This paper studies the number conservation property of 1-dimensional non-uniform cellular automata (CAs). In a non-uniform cellular automaton (CA), different cells may follow different rules. The present work considers that the cells follow…

Non-uniform cellular automata (NUCA) are an extension of cellular automata (CA), which transform cells according to multiple different local rules. A NUCA is defined by a configuration of local rules called a local rule distribution. We…

Cellular automata (CA) are a class of computational models that exhibit rich dynamics emerging from the local interaction of cells arranged in a regular lattice. In this work we focus on a generalised version of typical CA, called graph…

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…

This paper explores the algebraic conditions under which a cellular automaton with a non-linear local rule exhibits surjectivity and reversibility. We also analyze the role of permutivity as a key factor influencing these properties and…

This work studies Temporally Non-Uniform Cellular Automata (t-NUCAs), a variant of non-uniform cellular automata, which temporally use two rules in a sequence during their evolution. The one-dimensional t-NUCAs, under finite as well as…

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…

Non-uniform cellular automata (NUCA) are an extension of cellular automata with multiple local rules in different cells. We show that if the distribution of local rules is uniformly recurrent, or recurrent in the one-dimensional case, the…

Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and…

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…

Every transitive cellular automaton (CA) is sensitive to initial conditions. We study this implication in the more general context of non-uniform cellular automata (NUCA) with finitely many different local update rules assigned to cells. We…

The properties of two-state nearest-neighbour cellular automata (CA) that are capable of density classification are discussed. It is shown that these CA actually conserve the total density, rather than merely classifying it. This is also…

We discovered that certain patterns called injective patterns remain stable during the revolution process, allowing us to create many reversible CA simply by using them to design the revolution rules. By examining injective patterns, we…

Cellular Automata (CA) are commonly investigated as a particular type of dynamical systems, defined by shift-invariant local rules. In this paper, we consider instead CA as algebraic systems, focusing on the combinatorial designs induced by…

In this paper, linear Cellular Automta (CA) rules are recursively generated using a binary tree rooted at "0". Some mathematical results on linear as well as non-linear CA rules are derived. Integers associated with linear CA rules are…

Layered Cellular Automata (LCA) extends the concept of traditional cellular automata (CA) to model complex systems and phenomena. In LCA, each cell's next state is determined by the interaction of two layers of computation, allowing for…

Cellular automata (CA) have been utilized for decades as discrete models of many physical, mathematical, chemical, biological, and computing systems. The most widely known form of CA, the elementary cellular automaton (ECA), has been…

We study a two-dimensional cellular automaton (CA), called Diffusion Rule (DR), which exhibits diffusion-like dynamics of propagating patterns. In computational experiments we discover a wide range of mobile and stationary localizations…

A synopsis is offered of the properties of discrete and integer-valued, hence "natural", cellular automata (CA). A particular class comprises the "Hamiltonian CA" with discrete updating rules that resemble Hamilton's equations. The…

Number-conserving cellular automata (NCCA) are particularly interesting, both because of their natural appearance as models of real systems, and because of the strong restrictions that number-conservation implies. Here we extend the…