Related papers: Designing Complex Dynamics in Cellular Automata wi…
We show techniques of analyzing complex dynamics of cellular automata (CA) with chaotic behaviour. CA are well known computational substrates for studying emergent collective behaviour, complexity, randomness and interaction between order…
Using Rule 126 elementary cellular automaton (ECA) we demonstrate that a chaotic discrete system --- when enriched with memory -- hence exhibits complex dynamics where such space exploits on an ample universe of periodic patterns induced…
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…
Complexity has been a recurrent research topic in cellular automata because they represent systems where complex behaviors emerge from simple local interactions. A significant amount of previous research has been conducted proposing…
Elementary cellular automata (ECA) present iconic examples of complex systems. Though described only by one-dimensional strings of binary cells evolving according to nearest-neighbour update rules, certain ECA rules manifest complex…
Cellular automata (CAs) are fully-discrete dynamical models that have received much attention due to the fact that their relatively simple setup can nonetheless express highly complex phenomena. Despite the model's theoretical maturity and…
Cellular automata (CAs) are dynamical systems which exhibit complex global behavior from simple local interaction and computation. Since the inception of cellular automaton (CA) by von Neumann in 1950s, it has attracted the attention of…
A simple mechanism for the emergence of complexity in cellular automata out of predictable dynamics is described. This leads to unfold the concept of conditional predictability for systems whose trajectory can only be piecewise known. The…
Cellular automata are a discrete dynamical system which models massively parallel computation. Much attention is devoted to computations with small time complexity for which the parallelism may provide further possibilities. In this paper,…
Elementary cellular automata (ECA) are one-dimensional discrete models of computation with a small memory set that have gained significant interest since the pioneer work of Stephen Wolfram, who studied them as time-discrete dynamical…
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 cellular automata with respect to a new communication complexity problem: each of two players know half of some finite word, and must be able to tell whether the state of the central cell will follow a given evolution, by…
Deep learning techniques have recently demonstrated broad success in predicting complex dynamical systems ranging from turbulence to human speech, motivating broader questions about how neural networks encode and represent dynamical rules.…
The model of cellular automata is fascinating because very simple local rules can generate complex global behaviors. The relationship between local and global function is subject of many studies. We tackle this question by using results on…
In cellular automata with memory, the unchanged maps of the conventional cellular automata are applied to cells endowed with memory of their past states in some specified interval. We implement Rule 30 automata with a majority memory and…
Biological systems are notorious for complex behavior within short timescales (e.g. metabolic activity) and longer time scales (e.g. evolutionary selection), along with their complex spatial organization. Because of their complexity and…
The notions of universality and completeness are central in the theories of computation and computational complexity. However, proving lower bounds and necessary conditions remains hard in most of the cases. In this article, we introduce…
The goal of this paper is to show why the framework of communication complexity seems suitable for the study of cellular automata. Researchers have tackled different algorithmic problems ranging from the complexity of predicting to the…
We show that a large number of elementary cellular automata are computationally simple. This work is the first systematic classification of elementary cellular automata based on a formal notion of computational complexity. Thanks to the…
Cellular Automata (CA), as they are presented in the literature, are abstract mathematical models of computation. In this pa- per we present an alternate approach: using the CA as a model or theory of physical systems and devices. While…