相关论文: Cellular Automata and Ultra-Discrete Painlev\'e Eq…

The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In particular, there is strong evidence that all integrable…

The `ultra-discrete limit' has provided a link between integrable difference equations and cellular automata displaying soliton like solutions. In particular, this procedure generally turns strictly positive solutions of algebraic…

We establish new connections between percolation, bootstrap percolation, probabilistic cellular automata and deterministic ones. Surprisingly, by juggling with these in various directions, we effortlessly obtain a number of new results in…

Let us consider the simplest model of one-dimensional probabilistic cellular automata (PCA). The cells are indexed by the integers, the alphabet is {0, 1}, and all the cells evolve synchronously. The new content of a cell is randomly…

We have developed a simple cellular automata model for nonlinearly coupled phase oscillators which can exhibit many important collective dynamical states found in other synchronizing systems. The state of our system is specified by a set of…

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…

This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes…

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 can show well known features of quantum mechanics, such as a linear updating rule that resembles a discretized form of the Schr\"odinger equation together with its conservation laws. Surprisingly, a whole class of…

We carried out a Cellular Automata simulation of a model polyelectrolyte solution at infinite dilution, in order to reproduce qualitatively its conformational properties. Our results predict the so called \emph{pearl necklace} structures,…

We present the discrete, q-, form of the Painlev\'e VI equation written as a three-point mapping and analyse the structure of its singularities. This discrete equation goes over to P_{VI} at the continuous limit and degenerates towards the…

We derive integrable discrete systems which are contiguity relations of two equations in the Painlev\'e-Gambier classification depending on some parameter. These studies extend earlier work where the contiguity relations for the six…

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…

It is known that discrete Painlev\'e equations have symmetries of the affine Weyl groups. In this paper we propose a new representation of discrete Painlev\'e equations in which the symmetries become clearly visible. We know how to obtain…

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…

We present a preliminary study of a new class of two-input cellular automata called eventually number-conserving cellular automata characterized by the property of evolving after a finite number of time steps to states whose number of…

We demonstrate that the concept of a conservation law can be naturally extended from deterministic to probabilistic cellular automata (PCA) rules. The local function for conservative PCA must satisfy conditions analogous to conservation…

The problem of competitive nucleation in the framework of Probabilistic Cellular Automata is studied from the dynamical point of view. The dependence of the metastability scenario on the self--interaction is discussed. An intermediate…

This study presents a unitary quantum cellular automaton (QCA) that, in the continuum limit, converges to the (1+1)-dimensional Generalized Dirac Equation (GDE). We outline the construction of the unitary, discrete-time evolution and derive…

In this paper, we study special solutions of five autonomous integrable partial difference equations (P$\Delta$Es). More precisely, we show that these P$\Delta$Es admit special solutions that are described by non-autonomous ordinary…