Related papers: Pattern Formation without Favored Local Interactio…

One elucidates specific findings of our recent computational study, arxiv.org/cond-mat/0307215 with the purpose to reveal a prospect of relevant feasibility research on regulating the process of assembling nano-sized elements into…

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…

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…

A new class of automata networks is defined. Their evolution rules are determined by a probability measure p on the set of all integers Z and an indicator function I_A on the interval [0,1]. It is shown that any cellular automaton rule can…

We study the the asymptotic dynamics of elementary cellular automaton 18 through its limit set, generic limit set and $\mu$-limit set. The dynamics of rule 18 are characterized by persistent local patterns known as kinks. We characterize…

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…

This paper studies directional dynamics in cellular automata, a formalism previously introduced by the third author. The central idea is to study the dynamical behaviour of a cellular automaton through the conjoint action of its global rule…

The mechanism which discriminates the pattern classes at the same $\lambda$, is found. It is closely related to the structure of the rule table and expressed by the numbers of the rules which break the strings of the quiescent states. It is…

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 designs an efficient two-class pattern classifier utilizing asynchronous cellular automata (ACAs). The two-state three-neighborhood one-dimensional ACAs that converge to fixed points from arbitrary seeds are used here for pattern…

Locally interacting dynamical systems, such as epidemic spread, rumor propagation through crowd, and forest fire, exhibit complex global dynamics originated from local, relatively simple, and often stochastic interactions between dynamic…

Evolution produces complex and structured networks of interacting components in chemical, biological, and social systems. We describe a simple mathematical model for the evolution of an idealized chemical system to study how a network of…

Cortical circuits are characterized by exquisitely complex connectivity patterns that emerge during development from undifferentiated networks. The development of these circuits is governed by a combination of precise molecular cues that…

This study aims at finding a method for constructing molecular dynamics like models using the formalism of cellular automata for fast simulation of fluid dynamic systems (including compressible phenomena). In as much as the results…

Diffusion plays an important role in a wide variety of phenomena, from bacterial quorum sensing to the dynamics of traffic flow. While it generally tends to level out gradients and inhomogeneities, diffusion has nonetheless been shown to…

Many biological systems collectively construct complex, adaptive, and functional architectures, where function emerges from bottom-up building processes rather than top-down planning or centralized control. However, general strategies for…

In this article, I propose a systematic method for the inverse ultra-discretization of cell automata using a functionally complete operation. We derive difference equations for the 256 kinds of elementary cellular automata(ECA) introduced…

We show that macro-molecular self-assembly can recognize and classify high-dimensional patterns in the concentrations of $N$ distinct molecular species. Similar to associative neural networks, the recognition here leverages dynamical…

This paper deals with the theory and application of 2-Dimensional, nine-neighborhood, null- boundary, uniform as well as hybrid Cellular Automata (2D CA) linear rules in image processing. These rules are classified into nine groups…

Cellular automata are interacting classical bits that display diverse emergent behaviors, from fractals to random-number generators to Turing-complete computation. We discover that quantum cellular automata (QCA) can exhibit complexity in…