Progress of Theoretical Physics
Vol. 81 No. 1 (1989) pp. 47-59
URL : http://ptp.ipap.jp/link?PTP/81/47/
DOI : 10.1143/PTP.81.47

Cellular Automata with Particle Conservation

Tamotsu Kohyama

(Received June 21, 1988)

We propose a cellular automaton with particle conservation. We study the model for one-dimensional lattice with two kinds of states on each site. Energetic consideration classifies the rules into four groups. Several characteristic quantities and the phase diagrams obtained numerically show the correspondence between the cellular automata and the binary alloy.

References:

1. J. von Neumann, Theory of Self Reproducing Automata, ed. A. W. Burks (University of Illinois Press, 1966).
2. S. Wolfram, Physica 10D (1984), 1[Elsevier].
3. G. Y. Vichniac, Physica 10D (1984), 96[Elsevier].
   T. Toffoli, Physica 10D (1984), 117[Elsevier].
   T. Toffoli and N. Margolus, Cellular Automata Machines (The MIT Press, 1987).
4. U. Frish, B. Hasslacher and Y. Pomeau, Phys. Rev. Lett. 56 (1986), 1505[APS].
   J. B. Salem and S. Wolfram, Theory and Applications of Cellular Automata, ed. S. Wolfram, (World Scientific, 1986), p. 362.
5. E. F. Codd, Cellular Automata (Academic Press, 1968).
   E. R. Banks, IEEE 11th Annu. Symps. Switching and Automata Theory (1970), p. 194.
6. Y. Pomeau, J. of Phys. A17 (1984), L415[IoP STACKS].
   M. Cruetz, Ann. of Phys. 167 (1986), 62[CrossRef].
   S. Takesue, Phys. Rev. Lett. 59 (1987), 2499[APS].
7. N. Margolus, Physica 10D (1984), 81[Elsevier].

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