Abstract
We present evidence that one of the “elementary” one-dimensional cellular automata in the sense of Wolfram (rule 22 in Wolfram's notation) involves very complex long-range effects, similar to a critical phenomenon. This is in contrast to superficial evidence that would suggest that this rule leads to fairly simple behavior.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S. Wolfram,Commun. Math. Phys. 96:15 (1984).
P. Grassberger, Towards a quantitative theory of self-generated complexity, Wuppertal preprint (1986).
L. Schulmann and P. E. Seiden,J. Slat. Phys. 19:293 (1978).
P. Grassberger, F. Krause, and T. von der Twer,J. Phys. A 17:L105 (1984).
W. Kinzel,Z. Phys. B 58:229 (1985).
J. von Neumann,Theory of Self-Reproducing Automata (A. W. Burks, ed.) (University of Illinois Press, 1966).
D. Farmer and S. Wolfram, eds., Proceedings of workshop on cellular automata, Los Alamos 1983Physica D 10 (1984).
S. Wolfram,Rev. Mod. Phys. 55:601 (1983).
S. Wolfram,Physica D 10:1 (1984).
P. Grassberger,Physica D 10:52 (1984).
R. Shaw,Z. Naturforsch. 36a:80 (1981).
P. Grassberger, inChaos — An Introduction, A. V. Holden, ed. (1986).
F. Ledrappier and L.-S. Young, Berkeley preprints (1984).
E. R. Berlekamp, J. H. Conway, and R. K. Guy,Winning Ways, for Your Mathematical Plays (Academic Press, 1982).
P. Grassberger, unpublished.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Grassberger, P. Long-range effects in an elementary cellular automaton. J Stat Phys 45, 27–39 (1986). https://doi.org/10.1007/BF01033074
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01033074