Continuous automaton

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

Globally Synchronized Oscillations in AN One-Dimensional Cellular Automaton

Abstract: Using a genetic algorithm a population of one-dimensional binary cellular automata is evolved to perform a computational task for which the best evolved rules cause the concentration to display a period-three oscillation. One run is studied in which the final state reached by the best evolved rule consists of a regular pattern or domain Λ, plus some propagating particles. It is shown that globally synchronized period-three oscillations can be obtained if the lattice size L is a multiple of the spatial periodicity S(Λ) of the domain. When L=m.S(Λ)-1 there is a cyclic particle reaction that keeps the system in two different phases and the concentration has a temporal periodicity that depends on the lattice size. The effects of random noise on the evolved cellular automata has also been investigated.

Research on the classifier with the tree frame based on multiple attractor cellular automaton

Abstract: The partition of a pattern space as the view of a cell space is a uniform partition, it is difficult to adapt to the needs of spatial non-uniform partition. In this paper, a cellular automaton classifier with a tree structure is constructed by combing with the CART algorithm. The construction method of the characteristic matrix of the multiple attractor cellular automata is studied based on the particle swarm optimization method, and this method can build the nodes of the multiple attractor cellular automata. This kind of classifier can solve the non-uniform partition problem and obtain a good classification performance while using a pseudo-exhaustive field with less bits. The experiment results show that our algorithm is more accurate than those obtained through the multiple attractor cellular automata.

Post-surjectivity and balancedness of cellular automata over groups

Abstract: We discuss cellular automata over arbitrary finitely generated groups. We call a cellular automaton post-surjective if for any pair of asymptotic configurations, every pre-image of one is asymptotic to a pre-image of the other. The well known dual concept is pre-injectivity: a cellular automaton is pre-injective if distinct asymptotic configurations have distinct images. We prove that pre-injective, post-surjective cellular automata are reversible. Moreover, on sofic groups, post-surjectivity alone implies reversibility. We also prove that reversible cellular automata over arbitrary groups are balanced, that is, they preserve the uniform measure on the configuration space.

Modeling linear dynamical systems by continuous-valued cellular automata

Abstract: This paper exposes a procedure for modeling and solving linear systems using continuous-valued cellular automata. The original part of this work consists on showing how the cells in the automaton may contain both real values and operators for carrying out numerical calculations and solve a desired problem. In this sense the automaton acts as a program, where data and operators are mixed in the evolution space for obtaining the correct calculations. As an example, Euler's integration method is implemented in the configuration space in order to achieve an approximated solution for a dynamical system. Three examples showing linear behaviors are presented.

Explicit Solution of the Cauchy Problem for Cellular Automaton Rule.

Abstract: Cellular automata (CA) are fully discrete alternatives to partial differential equations (PDE). For PDEs, one often considers the Cauchy problem, or initial value problem: find the solution of the PDE satisfying a given initial condition. For many PDEs of the first order in time, it is possible to find explicit formulae for the solution at the time $t>0$ if the solution is known at $t=0$. Can something similar be achieved for CA? We demonstrate that this is indeed possible in some cases, using elementary CA rule 172 as an example. We derive an explicit expression for the state of a given cell after $n$ iteration of the rule 172, assuming that states of all cells are known at $n=0$. We then show that this expression ("solution of the CA") can be used to obtain an expected value of a given cell after $n$ iterations, provided that the initial condition is drawn from a Bernoulli distribution. This can be done for both finite and infinite lattices, thus providing an interesting test case for investigating finite size effects in CA.