@inbook{82bf98aecf3f414ebb5a9068d7d39d0a,

title = "Cellular automata: Basic definitions",

abstract = "What is a cellular automaton? This question is not too easy to answer. In the present approach, we define cellular automata in a very narrow sense: the automaton is deterministic and it has a high degree of symmetry. This narrow definition allows us to develop a relatively rich theory. In applications, however, these assumptions are quite often relaxed. Many mathematical systems describe the behavior of single particles, molecules or cells. Such small entities, described on a small spatial scale, do not follow strict deterministic laws but are subject to stochastic variation. Hence it is quite natural to generalize the concept of a cellular automaton in such a way that the local rule depends on random variables.",

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_2",

language = "English",

series = "Springer Monographs in Mathematics",

publisher = "Springer Verlag",

number = "9783319530420",

pages = "19--35",

booktitle = "Springer Monographs in Mathematics",

edition = "9783319530420",

}