Difference between revisions of "Cellular automaton"
(New page: A '''cellular automaton''' is a 4-tuple <math> \{ Z, S, N, f\} </math>, where: * <math>Z</math> is a lattice. * <math>S</math> is a finite set of cell ''states'' or ''values''. * <math...) |
DavidB4-bot (talk | contribs) m (→Further reading: clean up) |
||
| (7 intermediate revisions by 2 users not shown) | |||
| Line 1: | Line 1: | ||
| − | A '''cellular automaton''' is a 4-tuple <math> \ | + | [[Image:2dCCA-n16.png|right|thumb|A two-dimensional cyclic cellular automaton with 16 states, on a 300×300 torus, after 400 steps starting from a random initial configuration. At this stage in the automaton's evolution, three different types of pattern can be seen: random fields similar to the starting configuration, large blocks of color, and spirals. Eventually the spirals will take over the entire field.]] |
| + | A '''cellular automaton''' is a 4-tuple <math> \left ( Z, S, N, f\right ) </math>, where: | ||
* <math>Z</math> is a [[lattice]]. | * <math>Z</math> is a [[lattice]]. | ||
* <math>S</math> is a finite set of cell ''states'' or ''values''. | * <math>S</math> is a finite set of cell ''states'' or ''values''. | ||
* <math>I</math> is the finite ''neighborhood''. | * <math>I</math> is the finite ''neighborhood''. | ||
| − | * <math>f</math> is the '' | + | * <math>f</math> is the ''transition function''. |
| − | The lattice is a grid filled with cells, each cell is uniquely identified by its coordinates and value. The cellular automaton evolves via the | + | The lattice is a grid filled with cells, each cell is uniquely identified by its coordinates and value. The cellular automaton evolves via the transition function with respect to the discrete time variable. |
| + | [[Image:Rule 184.png|left|thumb|The Rule 184 cellular automaton, run for 128 steps each from three random initial confgurations with density 25%, 50%, and 75%.]] | ||
| + | Lattice-Gas Cellular Automatons can be used to model physical systems such as fluid and biological systems. ''Mathematica'' uses a cellular automatons as a random number generator. | ||
| − | [[ | + | ==Further reading== |
| − | [[ | + | :[http://www.stephenwolfram.com/publications/articles/ca/86-fluids/index.html Cellular Automaton Fluids: Basic Theory], Stephen Wolfram, 1986. |
| + | :[http://www.stephenwolfram.com/publications/articles/ca/86-random/index.html Random Sequence Generation by Cellular Automata], Stephen Wolfram, 1986. | ||
| + | :[http://www.stephenwolfram.com/publications/articles/ca/85-thermodynamics/index.html Thermodynamics and Hydrodynamics of Cellular Automata], Stephen Wolfram, 1985. | ||
| + | :[http://www.stephenwolfram.com/publications/articles/ca/85-cryptography/index.html Cryptography with Cellular Automata], Stephen Wolfram, 1986. | ||
| + | |||
| + | [[Category:Mathematics]] | ||
| + | [[Category:Computer Science]] | ||
Latest revision as of 15:03, June 23, 2016
A two-dimensional cyclic cellular automaton with 16 states, on a 300×300 torus, after 400 steps starting from a random initial configuration. At this stage in the automaton's evolution, three different types of pattern can be seen: random fields similar to the starting configuration, large blocks of color, and spirals. Eventually the spirals will take over the entire field.
A cellular automaton is a 4-tuple Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \left ( Z, S, N, f\right ) } , where:
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Z} is a lattice.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle S} is a finite set of cell states or values.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle I} is the finite neighborhood.
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f} is the transition function.
The lattice is a grid filled with cells, each cell is uniquely identified by its coordinates and value. The cellular automaton evolves via the transition function with respect to the discrete time variable.
Lattice-Gas Cellular Automatons can be used to model physical systems such as fluid and biological systems. Mathematica uses a cellular automatons as a random number generator.
Further reading
- Cellular Automaton Fluids: Basic Theory, Stephen Wolfram, 1986.
- Random Sequence Generation by Cellular Automata, Stephen Wolfram, 1986.
- Thermodynamics and Hydrodynamics of Cellular Automata, Stephen Wolfram, 1985.
- Cryptography with Cellular Automata, Stephen Wolfram, 1986.