References

[1] S. Wolfram, ``Statistical mechanics of cellular automata'', Rev. Mod. Phys. 55 (1983) 601.

[2] O. Martin, A. M. Odlyzko and S. Wolfram, ``Algebraic properties of cellular automata'', Bell Laboratories report (January 1983); Comm. Math. Phys., to be published.

[3] D. Lind, ``Applications of ergodic theory and sofic systems to cellular automata'', University of Washington preprint (April 1983); Physica 10D (1984) 36 (these proceedings).

[4] S. Wolfram, ``CA: an interactive cellular automaton simulator for the Sun Workstation and VAX'', presented and demonstrated at the Interdisciplinary Workshop on Cellular Automata, Los Alamos (March 1983).

[5] T. Toffoli, N. Margolus, G. Vishniac, private demonstrations.

[6] P. Billingsley, Ergodic Theory and Information (Wiley, New York, 1965).

[7] D. Knuth, Seminumerical Algorithms, 2nd. ed. (Addison-Wesley, New York, 1981), section 3.5.

[8] R. G. Gallager, Information Theory and Reliable Communications (Wiley, New York, 1968).

[9] J. D. Farmer, ``Dimension, fractal measures and the probabilistic structure of chaos'', in Evolution of Order and Chaos in Physics, Chemistry and Biology, H. Haken, ed. (Springer, Berlin, 1982).

[10] J. D. Farmer, private communication.

[11] B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1982).

[12] J. D. Farmer, ``Information dimension and the probabilistic structure of chaos'', Z. Naturforsch. 37a (1982) 1304.

[13] P. Grassberger, to be published.

[14] P. Diaconis, private communication; C. Stein, unpublished notes.

[15] F. S. Beckman, Mathematical Foundations of Programming (Addison-Wesley, New York, 1980).

[16] J. E. Hopcroft and J. D. Ullman, Introduction to Automata Theory, Languages, and Computation (Addison-Wesley, New York, 1979).

[17] Z. Manna, Mathematical Theory of Computation (McGraw-Hill, New York, 1974).

[18] M. Minsky, Computation: Finite and Infinite Machines (Prentice-Hall, London, 1967).

[19] B. Weiss, ``Subshifts of finite type and sofic systems'', Monat. Math. 17 (1973) 462; E. M. Coven and M. E. Paul, ``Sofic systems'', Israel J. Math. 20 (1975) 165.

[20] P. Grassberger, ``A new mechanism for deterministic diffusion'', Wuppertal preprint WU B 82-18 (1982).

[21] J. Milnor, unpublished notes.

[22] R. W. Gosper, unpublished; R. Wainwright, ``Life is universal!'', Proc. Winter Simul. Conf., Washington D.C., ACM (1974). E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, for Your Mathematical Plays, vol. 2 (Academic Press, New York, 1982), chap. 25.

[23] R. W. Gosper, ``Exploiting regularities in large cellular spaces'', Physica 10D (1984) 75 (these proceedings).

[24] G. Chaitin, ``Algorithmic information theory'', IBM J. Res. & Dev., 21 (1977) 350; ``Toward a mathematical theory of life'', in The Maximum Entropy Formalism, R. D. Levine and M. Tribus, ed. (MIT press, Cambridge, MA, 1979).

[25] C. Bennett, ``On the logical ``depth'' of sequences and their reducibilities to random sequences'', IBM report (April 1982) (to be published in Info. & Control).

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