Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Growth Phenomena in Cellular Automata

  • Janko GravnerEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_266-5

Definition of the Subject

In essence, analysis of growth models is an attempt to study properties of physical systems far from equilibrium (e.g., (Meakin 1998) and its more than 1,300 references). Cellular automata (CA) growth models, by virtue of their simplicity and amenability to computer experimentation (Toffoli and Margolus 1997; Wójtowicz 2001), have become particularly popular in the last 30 years in many fields, such as physics (Chopard and Droz 1998; Toffoli and Margolus 1997; Vichniac 1984), biology (Deutsch and Dormann 2005), chemistry (Chopard and Droz 1998; Kier et al. 2005), social sciences (Bäck et al. 1996), and artificial life (Lindgren and Nordahl 1994). In contrast to voluminous empirical literature on CA in general and their growth properties in particular, precise mathematical results are rather scarce. A general CA theory is out of the question, since a Turing machine can be embedded in a CA, so that examples as “simple” as elementary one-dimensional CA (Cook 2005...


Cellular Automaton Cellular Automaton Cellular Automaton Modeling Asymptotic Density Moore Neighborhood 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of CaliforniaDavisUSA