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Publications by Stephen Wolfram * Articles * Cellular Automata * Cellular Automata as Simple Self-Organizing Systems (1982)
Cellular Automata as Simple Self-Organizing Systems (1982)


References

[1] S. Wolfram, ``Statistical Mechanics of Cellular Automata'', Caltech preprint CALT-68-915 (May 1982).

[2] J. von Neumann, ``The General and Logical Theory of Automata'', in J. von Neumann. ``Collected Works'' (ed. A.H. Taub), Vol. 5, p.288; J. von Neumann, ``Theory of Self-Reproducing Automata'', (ed. A.W. Burks), Univ. of Illinois Press (1966); ed. A.W. Burks, ``Essays on Cellular Automata'', Univ. of Illinois Press (1970).

[3] J.S. Langer, ``Instabilities and Pattern Formation in Crystal Growth'', Rev. Mod. Phys. 52 (1980)1.

[4] D'A. W. Thompson, ``On Growth and Form'', (abridged edition ed. J.T. Bonner), Cambridge Univ. Press. 1961; P.S. Stevens, ``Patterns in Nature'', Little, Brown & Co. (Boston) (1974), chaps. 5 and 6; R.M. Baer and H.M. Martinez, ``Automata and Biology'', Ann. Rev. Biophys. (1974) 255.

[5] J.C.P. Miller, ``Periodic Forests of Stunted Trees'', Phil. Tran. Roy. Soc. London A266 (1970) 63; A293 (1980) 48.

[6] M. Gardner, ``Mathematical Games'', Sci. Amer. 224 (1971) 112.

[7] E.R. Berlekamp, J.H. Conway and R.K. Guy, ``Winning Ways, for Your Mathematical Plays'', vol. 2, Academic Press (1982), chap. 25; ed. R. T. Wainwright, ``Lifeline'', nos. 1 (March 1971) through 11 (Sept. 1973); D.J. Buckingham, ``Some Facts of Life'', Byte 3 (1978) 54; R.T. Wainwright, ``Life is Universal!'', Proc. Winter Simul. Conf., Washington D.C., ACM (1974).

[8] M.L. Minsky, ``Computation: Finite and Infinite Machines'', Prentice-Hall (1967); M.A. Arbib, ``Theories of Abstract Automata'', Prentice-Hall (1969); Z. Manna, ``Mathematical Theory of Computation'', McGraw-Hill (1974).

[9] B. Mandelbrot, ``Fractals: Form, Chance and Dimension'', Freeman (1977).

[10] J.W.L. Glaisher, ``On the Residue of a Binomial-Theorem Coefficient with Respect to a Prime Modulus'', Quart. J. Math. 30 (1899) 150; S.H. Kimball et al., ``Odd Binomial Coefficients'', Amer. Math. Mon. 65 (1958) 368; J.B. Roberts, ``On Binomial Coefficient Residues'', Canad. J. Math. 9 (1957) 363; R. Honsberger, ``Mathematical Gems II'', Dolciani Math. Expositions, Math Assoc. Amer. (1976), p.1.

[11] E. Ott, ``Strange Attractors and Chaotic Motions of Dynamical Systems'', Rev. Mod. Phys. 53 (1981) 655.

[12] G. Nicolis and I. Prigogine, ``Self-Organization in Nonequilibrium Systems'', Wiley (1977); I. Prigogine, ``From Being to Becoming'', Freeman (1980).

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