Continuous automaton

About: Continuous automaton is a research topic. Over the lifetime, 947 publications have been published within this topic receiving 17417 citations.

Attractors in restricted cellular automata

Abstract: The goal of this note is to extend previous results about the dynamics of cellular automata to «restricted cellular automata». Roughly speaking, a cellular automaton is a rule that updates a configuration of «states» that are arranged along the integer lattice in R. In applications one often thinks of one of these states as «bank» or «quiescent», while the other «active» states evolve against a quiescent background. Often the physically relevant configurations are those with only a finite number of active states. If X 0 is the set of all such states, and if a cellular automaton maps X 0 to X 0 , then its restriction to X 0 is a restricted cellular automaton. The main results show that there are rather strong constraints on the collection of attractors for any restricted cellular automaton. These constraints parallel those described in [H1] for the unrestricted case

Stochastic transition model for discrete agent movements

Abstract: We propose a calibrated two-dimensional cellular automaton model to simulate pedestrian motion behavior. It is a vmax= 4 (3) model with exclusion statistics and random shuffled dynamics. The underlying regular grid structure results in a direction-dependent behavior, which has in particular not been considered within previous approaches. We efficiently compensate these grid-caused deficiencies on model level.

Discrete relations on abstract simplicial complexes

Abstract: On the one hand, a system of discrete relations is a generalization of cellular automaton and, on the other hand, it is a set-theoretical analog of a system of polynomial equations. An approach to studying such systems that is based on set-theoretical and topological constructs is considered. The proposed approach is implemented as a C program. Results of application of this approach to some binary cellular automata are given. In the binary case, cellular automata can be represented by systems of polynomial equations, which are normally studied by the Grobner basis method. Our approach is compared with this method on some examples.

Designing discrete-time cellular neural networks for the evaluation of local Boolean functions

Abstract: General methods of designing a discrete-time cellular neural network implementing an arbitrary Boolean function defined on the r-neighborhood are described. This is achieved by operating the network with time-invariant templates as a cellular automaton that processes only binary inputs. These methods are suitable for solving local tasks. As an example, testing minimal distances is discussed. >