Difference between revisions of "Cellular automaton"
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| + | [[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: | 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]]. | ||
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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. | 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== | |
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| − | ==Further | ||
:[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-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/86-random/index.html Random Sequence Generation by Cellular Automata], Stephen Wolfram, 1986. | ||
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:[http://www.stephenwolfram.com/publications/articles/ca/85-cryptography/index.html Cryptography with Cellular Automata], Stephen Wolfram, 1986. | :[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 300Ã300 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 , where:
- is a lattice.
- is a finite set of cell states or values.
- is the finite neighborhood.
- 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.