Cellular Automata and Discrete Complex Systems (original) (raw)

Cellular automata and dynamical systems

1989

In this thesis we investigate the theoretical nature of the mathematical structures termed cellular automata. Chapter 1: Reviews the origin and history of cellular automata in order to place the current work into context. Chapter 2: Develops a cellular automata framework which contains the main aspects of cellular automata structure which have appeared in the literature. We present a scheme for specifying the cellular automata rules for this general model and present six examples of cellular automata within the model. Chapter 3: Here we develop a statistical mechanical model of cellular automata behaviour. We consider the relationship between variations within the model and their relationship to dynamical systems. We obtain results on the variance of the state changes, scaling of the cellular automata lattice, the equivalence of noise, spatial mixing of the lattice states and entropy, synchronous and asynchronous cellular automata and the equivalence of the rule probability and the ...

CELLULAR AUTOMATA : A SURVEY OF IT'S WIDESPREAD APPLICATION

A cellular automaton is a discrete model studied in computability theory , mathematics, physics and myriad of other areas. It's profound application makes it indispensable in the scientific community. This paper is intended to provide an overview of the concept of cellular automata and it's application in different areas. In this report I have highlighted some general application of cellular automata with the later section of the paper emphasizing more on the application of cellular automata in the field of parallel computing.

Computation in cellular automata: A selected review

1996

Cellular automata (CAs) are decentralized spatially extended systems consisting of large numbers of simple identical components with local connectivity. Such systems have the potential to perform complex computations with a high degree of e ciency and robustness, as well as to model the behavior of complex systems in nature. For these reasons CAs and related architectures have been studied extensively in the natural sciences, mathematics, and in computer science.

Cellular Automata - The Stanford Encyclopedia of Philosophy

Cellular automata (henceforth: CA) are discrete, abstract computational systems that have proved useful both as general models of complexity and as more specific representations of non-linear dynamics in a variety of scientific fields. Firstly, CA are (typically) spatially and temporally discrete: they are composed of a finite or denumerable set of homogenous, simple units, the atoms or cells. At each time unit, the cells instantiate one of a finite set of states. They evolve in parallel at discrete time steps, following state update functions or dynamical transition rules: the update of a cell state obtains by taking into account the states of cells in its local neighborhood (there are, therefore, no actions at a distance). Secondly, CA are abstract: they can be specified in purely mathematical terms and physical structures can implement them. Thirdly, CA are computational systems: they can compute functions and solve algorithmic problems. Despite functioning in a different way from traditional, Turing machine- like devices, CA with suitable rules can emulate a universal Turing machine (see entry), and therefore compute, given Turing’s thesis (see entry on Church-Turing thesis), anything computable...