Algebraic properties of cellular automata

@article{Martin1984AlgebraicPO,
  title={Algebraic properties of cellular automata},
  author={O. Martin and Andrew M. Odlyzko and S. Wolfram},
  journal={Communications in Mathematical Physics},
  year={1984},
  volume={93},
  pages={219-258}
}
Cellular automata are discrete dynamical systems, of simple construction but complex and varied behaviour. Algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata. The complete structure of state transition diagrams is derived in terms of algebraic and number theoretical quantities. The systems are usually irreversible, and are found to evolve through transients to attractors consisting of cycles sometimes containing a large… Expand
404 Citations

Figures and Tables from this paper

Global Dynamics of Finite Cellular Automata
  • 3
Global properties of cellular automata
  • 56
Universality and complexity in cellular automata
  • 1,902
  • PDF
Algebraic Theory of Bounded One-dimensional Cellular Automata
  • 9
  • PDF
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 32 REFERENCES
Statistical mechanics of cellular automata
  • 2,548
  • PDF
On Some Dynamical Properties of Finite Cellular Automaton
  • 6
String Overlaps, Pattern Matching, and Nontransitive Games
  • 385
  • PDF
Principles of Algebraic Geometry
  • 6,935
Periodic forest whose largest clearings are of size 3
  • H. ApSimon
  • Mathematics
  • Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
  • 1970
  • 4
Periodic forests whose largest clearings are of size n ≥ 4
  • H. ApSimon
  • Mathematics
  • Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1970
  • 3
Periodic forests of stunted trees
  • J. P. Miller
  • Mathematics
  • Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
  • 1970
  • 13
...
1
2
3
4
...