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...is a mathematical [[Characterization (mathematics)|characterization]] of [[cellular automata]] in terms of their [[symbolic dynamics]]. It is named after [[Mor | title = Cellular automata and groups, by Tullio Ceccherini-Silberstein and Michel Coornaert ...

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

...nal on Applied Mathematics|volume=54|year=1978|pages=515–523|title=Spatial Patterns for Discrete Models of Diffusion in Excitable Media|author=J. M. Greenberg As in a typical two dimensional [[cellular automaton]],<ref name="siam" /> consider a rectangular grid, or checkerboard pattern, ...

...[Stanislaw_Ulam|S. M. Ulam]], On some mathematical problems connected with patterns of growth of figures, Mathematical Problems in BiologicalSciences, 14 (1962 ...(2002), 11 </ref><ref>[[David_Singmaster|D. Singmaster]], On the cellular automaton of Ulam and Warburton, [http://m500.org.uk/magazine/ M500 Magazine of The O ...

...e, thereby interacting with nearby particles. Contrary to classic cellular automaton models, particles in BIO-LGCA are defined by their position and velocity. T ...tern Formation|url=http://dx.doi.org/10.1007/0-8176-4415-6_3|work=Cellular Automaton Modeling of Biological Pattern Formation|series=Modeling and Simulation in ...

== Example: rule 110 variant of the elementary cellular automaton == ...ssociated with complex systems and which imply the capability of groups of automaton cells to remember that a glider is passing through them. It is therefore to ...

{{short description|Cellular automaton}} | title = Self-organized Critical State of Sandpile Automaton Models ...

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

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

...hesizes the scope of synergetics as "the study of how nature works, of the patterns inherent in nature, the geometry of environmental forces that impact on hum ...erse. He modeled a threshold between associative and disassociative energy patterns with his T-to-E module transformation ("E" for "Einstein").(Fig 986.411A) ...

...e overall level of information, cartographic generalization helps discover patterns and trends in data that underlie many techniques and technologies employed ...n's I example.png|thumb|Moran's I statistic computed for different spatial patterns. Using '[[Rook (chess)|rook]]' neighbors for each grid cell, setting <math> ...

...delbrot set]], and sometimes explores other mathematical objects such as [[cellular automata]]. Controversially, the artist [[David Hockney]] has argued that a {{further|Planar symmetry|Wallpaper group|Islamic geometric patterns|Kilim}} ...