Systems Engineering: Cellular Automata (Definitions)

"Cellular automata are mathematical models for complex natural systems containing large numbers of simple identical components with local interactions. They consist of a lattice of sites, each with a finite set of possible values. The value of the sites evolve synchronously in discrete time steps according to identical rules. The value of a particular site is determined by the previous values of a neighbourhood of sites around it." (Stephen Wolfram, "Nonlinear Phenomena, Universality and complexity in cellular automata", Physica 10D, 1984)

"A mathematical construct and technique that models a system in discrete time and discrete space in which the state of a cell depends on transition rules and the states of neighboring cells." (Charles M Macal, "Agent Based Modeling and Artificial Life", 2009) 

[Cellular automaton:] A spatially-extended dynamical system in which spatially-discrete cells take on discrete values, and evolve according to a spatially-localized discrete-time update rule." (James E Hanson, "Emergent Phenomena in Cellular Automata", 2009)

"A spatiotemporal modeling technique in which a set of rules is applied to determine the state transitions of individual cells based on each cell’s current state and the states of its neighbors." (May Yuan, "Challenges and Critical Issues for Temporal GIS Research and Technologies", 2009) 

"Cellular Automata (CA) are discrete, spatially explicit extended dynamic systems composed of adjacent cells characterized by an internal state whose value belongs to a finite set. The updating of these states is made simultaneously according to a common local transition rule involving only a neighborhood of each cell." (Ramon Alonso-Sanz, "Cellular Automata with Memory", 2009) 

"Cellular automata are dynamical systems that are discrete in space, time, and value. A state of a cellular automaton is a spatial array of discrete cells, each containing a value chosen from a finite alphabet. The state space for a cellular automaton is the set of all such configurations." (Burton Voorhees, "Additive Cellular Automata", 2009) 

"They are dynamical systems that are continuous, local, parallel, synchronous and space and time uniform. Cellular automata are used to model phenomena where the space can be regularly partitioned and where the same rules are used everywhere [...]" (Jerome Durand-Lose, "Universality of Cellular Automata", 2009)

"A discrete model consisting of a grip of cells each of which have a finite number of defined states where the state of a cells is a function of the states of neighboring cells and the transition among states is according to some predefined updating rule. (Brian L Heath & Raymond R Hill, "Agent-Based Modeling: A Historical Perspective and a Review of Validation and Verification Efforts, 2010)

"A cellular automaton is composed of a set of discrete elements - the cells - connected with other cells of the automaton, and in each time unit each cell receives information about the current state of the cells to which it is connected. The cellular automaton evolve according a transition rule that specifies the current possible states of each cell as a function of the preceding state of the cell and the states of the connected cells." (Francesc S Beltran et al, "A Language Shift Simulation Based on Cellular Automata", 2011)

"Cellular automata (CA) are idealizations of physical systems in which both space and time are assumed to be discrete and each of the interacting units can have only a finite number of discrete states." (Andreas Schadschneider et al, "Vehicular Traffic II: The Nagel–Schreckenberg Model" , 2011)

"Cellular automata (henceforth: CA) are discrete, abstract computational systems that have proved useful both as general models of complexity and as more specific representations of non-linear dynamics in a variety of scientific fields." (Francesco Berto & Jacopo Tagliabue, "Cellular Automata", Stanford Encyclopedia of Philosophy, 2012)