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Publications by Stephen Wolfram * Articles * Mathematics * Twenty Problems in the Theory of Cellular Automata (1985)
Twenty Problems in the Theory of Cellular Automata (1985)


References

[1] Wolfram, S., Nature 311, 419 (1984).

[2] Wolfram, S., Rev. Mod. Phys. 55, 601 (1983).

[3] Farmer, D., Toffoli, T. and Wolfram, S. (editors), ``Cellular automata: proceedings of an interdisciplinary workshop'', Physica 10D numbers 1 and 2 (1984), North-Holland Publishing Co. (1984).

[4] Wolfram, S., ``Cellular automata'', Los Alamos Science (fall 1983).

[5] Wolfram, S., Physica 10D, 1 (1984).

[6] Guckenheimer, J. and Holmes, P., Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag (1983).

[7] Wolfram, S., Comm. Math. Phys. 96, 15 (1984).

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

[9] Wolfram, S., ``Computer software in science and mathematics'', Scientific American (September 1984).

[10] Packard, N., ``Complexity of growing patterns in cellular automata'', Institute for Advanced Study preprint (October 1983).

[11] Milnor, J., ``Entropy of cellular automaton-maps'', Institute for Advanced Study preprint (May 1984).

[12] Packard, N. and Wolfram, S., ``Two-dimensional cellular automata'', J. Stat. Phys. 38, 901 (1985).

[13] Packard, N., Private communication.

[14] Ahmed, N. and Rao, K. R., Orthogonal Transforms for Digital Signal Processing, Springer-Verlag (1975).

[15] Franks, J. and Fried, D., Private communications.

[16] Margolus, N., Physica 10D, 81 (1984).

[17] Vichniac, G., Physica 10D, 96 (1984).

[18] Pomeau, Y., J. Phys. A17, L415 (1984).

[19] Hedlund, G., Private communication.

[20] Milnor, J. and Wolfram, S., In preparation.

[21] Milnor, J., ``Notes on surjective cellular automaton-maps'', Institute for Advanced Study preprint (June 1984).

[22] Chaitin, G., ``Towards a mathematical definition of life'', in The Maximum Entropy Formalism'', R. D. Levine and M. Tribus (eds.), MIT press (1979).

[23] Crutchfield, J. and Packard, N., Private communication.

[24] Collet, P. and Eckmann, J.-P., Iterated Maps on the Interval as Dynamical Systems, Birkhauser (1980).

[25] Amit, D., Field Theory, the Renormalization Group, and Critical Phenomena, McGraw-Hill (1978).

[26] Milnor, J., Unpublished.

[27] Mandelbrot, B., The Fractal Geometry of Nature, Freeman (1982).

[28] Grassberger, P., Physica 10D, 52 (1984).

[29] Greenberg, J. M., Hassard, B. D., and Hastings, S. P., Bull. Amer. Math. Soc. 84, 1296 (1975); Madore, B. and Freedman, W., Science 222, 615 (1983).

[30] Winfree, A. and Winfree, E., ``Organizing centers in a cellular excitable medium'', to be published.

[31] Packard, N., ``Cellular automaton models for dendritic growth'', Institute for Advanced Study preprint, in preparation.

[32] Bennett, C., Neuberger, H., Pomeau, Y. and Vichniac, G., Private communications.

[33] Martin, O., Odlyzko, A. and Wolfram, S., Comm. Math. Phys. 93, 219 (1984).

[34] Grassberger, P., Krause, F. and von der Twer, T., ``A new type of kinetic critical phenomena'', University of Wuppertal preprint WU B 83-22 (October 1983).

[35] Domany, E. and Kinzel, W., Phys. Rev. Lett. 53, 311 (1984).

[36] Ingerson, T. E. and Buvel, R. L., Physica 10D, 59 (1984).

[37] Kauffman, S., Physica 10D, 145 (1984).

[38] Hopcroft, J., ``An algorithm for minimizing states in a finite automaton'', in Proc. Int. Symp. on the Theory of Machines and Computations, Academic Press (1971).

[39] Harary, F., Graph Theory, Chapter 15, Addison-Wesley (1972).

[40] Hurd, L., ``Formal language characterizations of cellular automaton limit sets'', to be published.

[41] Hasslacher, B., Private communication.

[42] Yaku, T., J. Comput. System Sci. 7, 481 (1973); Golze, U., ``Differences between 1- and 2-dimensional cell spaces'', in A. Lindenmayer and G. Rozenberg (eds.), Automata, Languages, Development, North-Holland (1976).

[43] Berger, R., Mem. Amer. Math. Soc., no. 66 (1966); Robinson, R., Inventiones Math. 12, 177 (1971).

[44] Walters, P., An Introduction to Ergodic Theory, Springer (1982).

[45] Knuth, D., Seminumerical Algorithms, 2nd. ed., Addison-Wesley (1981).

[46] Furstenberg, H. and Lind, D., Private communication.

[47] Berlekamp, E. R., Conway, J. H. and Guy, R. K., Winning Ways for Your Mathematical Plays, vol. 2, chap. 25, Academic Press (1982); Gardner, M., Wheels, Life and Other Mathematical Amusements, Freeman (1983).

[48] Smith, A. R., J. ACM 18, 339 (1971).

[49] Banks, E. R., ``Information processing and transmission in cellular automata'', MIT project MAC report no. TR-81 (1971).

[50] Smith, A. R., J. Comput. Sys. Sci. 6, 233 (1972); Sommerhalder, R. and van Westrhenen, S. C., Acta Inform. 19, 397 (1983).

[51] Steiglitz, K., Private communication.

[52] Bennett, C. H., ``On the logical ``depth'' of sequences and their reducibilities to random sequences'', Info. & Control, to be published.

[53] Garey, M. R. and Johnson, D. S., Computers and Intractability: a Guide to the Theory of NP-completeness, Freeman (1979).

[54] Sewelson, V., Private communication.

[55] Cole, S. N., IEEE Trans. Comput. C-18, 349 (1969).

[56] Preston, K. et al., Proc. IEEE 67, 826 (1979).

[57] Hillis, D. and Wolfram, S., Work in progress.

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