Related papers: Protecting information via probabilistic cellular …
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…
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…
We present a family of one-dimensional cellular automata modeling the diffusion of an innovation in a population. Starting from simple deterministic rules, we construct models parameterized by the interaction range and exhibiting a…
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…
We discuss various properties of Probabilistic Cellular Automata, such as the structure of the set of stationary measures and multiplicity of stationary measures (or phase transition) for reversible models.
The emergent dynamics in spacetime diagrams of cellular automata (CAs) is often organised by means of a number of behavioural classes. Whilst classification of elementary CAs is feasible and well-studied, non-elementary CAs are generally…
Binary spatio-temporal data are common in many application areas. Such data can be considered from many perspectives, including via deterministic or stochastic cellular automata, where local rules govern the transition probabilities that…
We introduce a novel framework of reservoir computing, that is capable of both connectionist machine intelligence and symbolic computation. Cellular automaton is used as the reservoir of dynamical systems. Input is randomly projected onto…
We propose a four-way classification of two-dimensional semi-totalistic cellular automata that is different than Wolfram's, based on two questions with yes-or-no answers: do there exist patterns that eventually escape any finite bounding…
How do cellular automata behave in the limit of a very large number of cells? Is there a continuum limit with simple properties? We attack this problem by mapping certain classes of automata to quantum field theories for which powerful…
Partitioned cellular automata are known to be an useful tool to simulate linear and nonlinear problems in physics, specially because they allow for a straightforward way to define conserved quantities and reversible dynamics. Here we show…
We study the phase diagram and the critical behavior of a one-dimensional radius-1 two-state totalistic probabilistic cellular automaton having two absorbing states. This system exhibits a first-order phase transition between the fully…
Invertible cellular automata are useful as models of physical systems with microscopically revesible dyanmics. There are several well-understood ways to construct them: partitioning rules, second-order rules, and alternating-grid rules. We…
Recently, Land and Belew [Phys. Rev. Lett. 74, 5148 (1995)] have shown that no one-dimensional two-state cellular automaton which classifies binary strings according to their densities of 1's and 0's can be constructed. We show that a pair…
We consider two relatively natural topologizations of the set of all cellular automata on a fixed alphabet. The first turns out to be rather pathological, in that the countable space becomes neither first-countable nor sequential. Also,…
We study the classification of cellular-automaton update rules into Wolfram's four classes. We start with the notion of the input entropy of a spatiotemporal block in the evolution of a cellular automaton, and build on it by introducing two…
What substrate features allow life? We exhaustively classify all 262,144 outer-totalistic binary cellular automata rules with Moore neighbourhood for self-replication and produce phase diagrams in the $(\lambda, F)$ plane, where $\lambda$…
Bijections between sets may be seen as discrete (or crisp) unitary transformations used in quantum computations. So discrete quantum cellular automata are cellular automata with reversible transition functions. This note studies on 1d…
Dynamic properties of a one-dimensional probabilistic cellular automaton are studied by monte-carlo simulation near a critical point which marks a second-order phase transition from a active state to a effectively unique absorbing state.…
A cellular automaton is a deterministic and exactly computable dynamical system which mimics certain fundamental aspects of physical dynamics such as spatial locality and finite entropy. CA systems can be constructed which have additional…