@inbook{676a1c13f3a945e0b1f2d2532171a2ec,

title = "Cantor topology of cellular automata",

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).",

author = "Hadeler, {Karl Peter} and Johannes M{\"u}ller",

note = "Publisher Copyright: {\textcopyright} 2017, Springer International Publishing AG.",

year = "2017",

doi = "10.1007/978-3-319-53043-7_3",

language = "English",

series = "Springer Monographs in Mathematics",

publisher = "Springer Verlag",

number = "9783319530420",

pages = "37--73",

booktitle = "Springer Monographs in Mathematics",

edition = "9783319530420",

}