Related papers: Coxeter Groups and Asynchronous Cellular Automata
We explore some aspects of phase transitions in cellular automata. We start recalling the standard formulation of statistical mechanics of discrete systems (Ising model), illustrating the Monte Carlo approach as Markov chains and stochastic…
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…
A Genetic Algorithm (GA) is proposed in which each member of the population can change schemata only with its neighbors according to a rule. The rule methodology and the neighborhood structure employ elements from the Cellular Automata (CA)…
We study the dynamics of the Rule 150 reversible cellular automaton (RCA). This is a one-dimensional lattice system of binary variables with synchronous (Floquet) dynamics, corresponding to a bulk deterministic and reversible discrete…
We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…
Cellular Automaton (CA) and an Integral Value Transformation (IVT) are two well established mathematical models which evolve in discrete time steps. Theoretically, studies on CA suggest that CA is capable of producing a great variety of…
A small-world cellular automaton network has been formulated to simulate the long-range interactions of complex networks using unconventional computing methods in this paper. Conventional cellular automata use local updating rules. The new…
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,…
Quantum cellular automata consist in arrays of identical finite-dimensional quantum systems, evolving in discrete-time steps by iterating a unitary operator G. Moreover the global evolution G is required to be causal (it propagates…
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…
This study focuses on an extended model of a standard cellular automaton (CA) that includes an extra index consisting of a radius that defines a perception area for each cell in addition to the radius defined by the CA rule. Extended…
In this paper we initiate the study of cellular automata on racks. A rack $R$ is a set with a self-distributive binary operation. The rack $R$ acts on the set $A^R$ of configurations from $R$ to a set $A$. We define the cellular automaton…
We study a quantum cellular automaton (QCA) whose time-evolution is defined from global transition function of classical cellular automata (CA). In order to investigate natural transformations from CA to QCA, the present QCA includes CA…
We describe a class of cellular automata (CAs) that are end-to-end differentiable. DCAs interpolate the behavior of ordinary CAs through rules that act on distributions of states. The gradient of a DCA with respect to its parameters can be…
Cyclic cellular automata (CCA) are models of excitable media. Started from random initial conditions, they produce several different kinds of spatial structure, depending on their control parameters. We introduce new tools from information…
A cellular automaton (CA) is a parallel synchronous computing model, which consists in a juxtaposition of finite automata (cells) whose state evolves according to that of their neighbors. Its trace is the set of infinite words representing…
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…
Discretizing spacetime is often a natural step towards modelling physical systems. For quantum systems, if we also demand a strict bound on the speed of information propagation, we get quantum cellular automata (QCAs). These originally…
We consider the group structure of quantum cellular automata (QCA) modulo circuits and show that it is abelian even without assuming the presence of ancillas, at least for most reasonable choices of control space; this is a corollary of a…
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…