Cantor topology of cellular automata

Karl Peter Hadeler, Johannes Müller

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

A cellular automaton per seis a discrete structure. Concepts like “continuous” or “arbitrarily close” seem not to be suited for the finite set of states a cell may assume. But if we consider infinite grids, then these concepts suddenly make sense. Imagine an observer placed at the origin of the grid. Although this point is arbitrary, it is tagged and may be used as a reference point. The observer looks at two different states of the cellular automaton. If theses states differ only in sites far away from the tagged location, then the two states look similar as seen from the observer and should be considered “close” to each other (see Fig. 3.1). Fig. 3.1Idea of the Cantor metric: the two checkerboards (a) and (b) as well as (b) and (c) differ in one site only. But (a) and (b) appear less similar than (b) and (c).

Original languageEnglish
Title of host publicationSpringer Monographs in Mathematics
PublisherSpringer Verlag
Pages37-73
Number of pages37
Edition9783319530420
DOIs
StatePublished - 2017
Externally publishedYes

Publication series

NameSpringer Monographs in Mathematics
Number9783319530420
ISSN (Print)1439-7382

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