Synonyms
Definition
Cellular automata (CA) are dynamical systems in which space and time are discrete. A cellular automaton consists of an array of cells, each of which can be in one of a finite number of possible states, updated synchronously in discrete time steps, according to a local, identical interaction rule. The state of a cell at the next time step is determined by its own current state and the current states of a surrounding neighborhood of cells (Wolfram 1994).
Overview
Cellular automata were originally conceived by Ulam and von Neumann in the 1940s to provide a formal framework for investigating the behavior of complex, extended systems (von Neumann 1966). In particular, von Neumann asked whether we could use purely mathematical-logical considerations to discover the specific features of automata that make them formally analogous with self-constructing and self-replicating biological systems.
Thanks to their simplicity and appeal, over the years, CA...
References and Further Reading
Chaudhuri PP, Chowdhury DR, Nandi S, Chattopadhyay S (1997) Additive cellular automata: theory and applications. IEEE Computer Society, Los Alamitos
Chopard B, Droz M (1998) Cellular automata modeling of physical systems. Cambridge University Press, Cambridge
Crutchfield JP, Mitchell M, Das R (2003) Evolutionary design of collective computation in cellular automata. In: Crutchfield JP, Schuster P (eds) Evolutionary dynamics: exploring the interplay of selection, accident, neutrality, and function. Oxford University Press, Oxford, pp 361–411
Fredkin E, Toffoli T (1982) Conservative logic. Int J Theor Phys 21:219–253
Frisch U, Hasslacher B, Pomeau Y (1986) Lattice-gas automata for the Navier-Stokes equation. Phys Rev Lett 56:1505–1508
Margolus N (1984) Physics-like models of computation. Phys D 10:81–95
Pérez-Delgado C, Cheung D (2007) Local unitary quantum cellular automata. Phys Rev A 76:032320
Sipper M (1997) Evolution of parallel cellular machines: the cellular programming approach. Springer-Verlag, Heidelberg
Toffoli T (1980) Reversible computing. In: De Bakker JW, Van Leeuwen J (eds) Automata, languages and programming. Springer-Verlag, Berlin, pp 632–644
Toffoli T (1984) Cellular automata as an alternative to (rather than an approximation of) differential equations in modeling physics. Phys D 10:117–127
Vichniac G (1984) Simulating physics with cellular automata. Phys D 10:96–115
Von Neumann J (1966) Theory of self-reproducing automata. University of Illinois Press, Illinois, Edited and completed by Burks AW
Wolfram S (1994) Cellular automata and complexity. Addison-Wesley, Reading
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Tomassini, M. (2014). Cellular Automata. In: Amils, R., et al. Encyclopedia of Astrobiology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27833-4_254-3
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DOI: https://doi.org/10.1007/978-3-642-27833-4_254-3
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