Difference between revisions of "Cellular automaton"
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| − | A '''cellular automaton''' is a 4-tuple <math> \ | + | 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''. | ||
Revision as of 09:43, April 20, 2007
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 dynamics. Mathematica uses a cellular automatons as a random number generator.
Further Readings
- 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.