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...p (mathematics)|group]] such that every [[injective function|injective]] [[cellular automaton]] with the group elements as its cells is also [[surjective funct A [[cellular automaton]] consists of a regular system of cells, each containing a symbol ...

{{Short description|Cellular automaton with probabilistic rules}} ...or '''probabilistic cellular automata''' ('''PCA''') or '''random cellular automata''' or '''locally interacting [[Markov chain]]s'''<ref>{{citation ...

...ematical [[Characterization (mathematics)|characterization]] of [[cellular automata]] in terms of their [[symbolic dynamics]]. It is named after [[Morton L. Cu | title = Cellular automata and groups, by Tullio Ceccherini-Silberstein and Michel Coornaert (book rev ...

...llular automata]] or [[Stochastic cellular automata|probabilistic cellular automata]] over <math>\mathbb{Z}^k</math> or [[interacting particle systems]] when s == Generalized cellular automata (GCA) == ...

{{Short description|Continuous generalization of cellular automata}} ...in Lenia are described as differing from those appearing in other cellular automata, being "geometric, [[Metamerism (biology)|metameric]], fuzzy, resilient, ad ...

...ernd Gartner |first=Ahad N. Zehmakan |year=2017 |title=Color War: Cellular Automata with Majority Rule |journal=Lata2017 |pages=393–404}}</ref> The model also [[File:CA-Tooms_neighborhood.svg|thumbnail|Neighborhood of Toom's cellular automaton. ]] ...

|title = Movable cellular automaton method |caption = Animation of a movable cellular automaton being used to simulate [[friction]] at the interface between two ...

The '''Ulam–Warburton [[cellular automaton]]''' (UWCA) is a 2-dimensional [[fractal]] pattern that grows on ...f 188]''' (2002), 11 </ref><ref>[[David_Singmaster|D. Singmaster]], On the cellular automaton of Ulam and Warburton, [http://m500.org.uk/magazine/ M500 Magazin ...

...It was a precursor to the [[lattice Boltzmann methods]]. From lattice gas automata, it is possible to derive the macroscopic [[Navier-Stokes equation]]s.<ref> ...luid-mechanics/A1CF87F3328666715F18278ADEE51786 |work=Lattice-Gas Cellular Automata: Simple Models of Complex Hydrodynamics |pages=1–11 |editor-last=Rothman |e ...

...etermined in Rule 30, one of the 256 possible rules of elementary cellular automata.]] ...mulae.org/?script=examples/Elementary_cellular_automaton |title=Elementary cellular automaton in the Fōrmulæ programming language |first=Laurence |last = R.Uga ...

...r Automaton''' (abbrev. '''GH model''') is a three state two dimensional [[cellular automaton]] (abbrev '''CA''') named after James M. Greenberg and Stuart Has As in a typical two dimensional [[cellular automaton]],<ref name="siam" /> consider a rectangular grid, or checkerboar ...

...ystems]] which generalize many aspects of for example classical [[cellular automata]], and they provide a framework for studying asynchronous processes over [[ ...

''The Nonlinear Workbook: Chaos, Fractals, Cellular Automata, Neural Networks, Genetic Algorithm, Gene Expression Programming, Wavelets, ...

...ear science series 6}}</ref> However, the value of each site in a cellular automata network is strictly dependent on its neighbor(s) from the previous time ste *[[Cellular automata]] ...

== Example: rule 110 variant of the elementary cellular automaton == The [[rule 110]] variant of the [[elementary cellular automaton]] has been [[Rule 110#The proof of universality|proven]] to be ca ...

...components. IPS are the continuous-time analogue of [[stochastic cellular automata]]. ...

* [[stochastic cellular automata|Probabilistic Cellular Automata]] ...

...is, dating back to the 1960s, states that the entire universe is a huge [[cellular automaton]] which continuously updates its rules.<ref name="Fredkin90">Fred ...established "classical" nature-inspired models of computation are cellular automata, neural computation, and evolutionary computation. More recent computationa ...

...inary operations, used to characterize one-dimensional reversible cellular automata ...

...tt (1996) "Periodic travelling waves in a family of deterministic cellular automata", ''Physica D'' 95: 319–335. ...urbage (1997) "On the abundance of traveling waves in 1D infinite cellular automata", ''Physica D'' 103: 133–144. ...