Statistical mechanics of cellular automata

Reviews of Modern Physics - Tập 55 Số 3 - Trang 601-644
Stephen Wolfram1
1The Institute for Advanced Study Princeton, New Jersey 08540

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Abelson, H., 1981, Turtle Geometry: The Computer as a Medium for Exploring Mathematics, 10.7551/mitpress/6933.001.0001

Aladyev, V., 1974, Math. Biosci., 22, 121, 10.1016/0025-5564(74)90088-1

Aladyev, V., 1976, Math. Biosci., 29, 99, 10.1016/0025-5564(76)90032-8

Alekseev, V. M., 1981, Phys. Rep., 75, 287, 10.1016/0370-1573(81)90186-1

Amoroso, S., 1971, J. Comput Syst. Sci., 5, 455, 10.1016/S0022-0000(71)80009-0

Apostol, T. M., 1976, Introduction to Analytic Number Theory

ApSimon, H. G., 1970, Philos. Trans. R. Soc. London, Ser. A, 266, 113, 10.1098/rsta.1970.0004

ApSimon, H. G., 1970, Proc. R. Soc. London, Ser. A, 319, 399, 10.1098/rspa.1970.0185

Arbib, M. A., 1969, Theories of Abstract Automata

Atrubin, A. J., 1965, IEEE Trans. Comput., EC-14, 394, 10.1109/PGEC.1965.264145

Baer, R. M., 1974, Ann. Rev. Biophys., 3, 255, 10.1146/annurev.bb.03.060174.001351

Barricelli, N. A., 1972, J. Statist. Comput. Simul., 1, 97, 10.1080/00949657208810008

Berlekamp, E. R., 1968, Algebraic Coding Theory

Berlekamp, E. R., 1982, Winning Ways for Your Mathematical Plays

Buckingham, D. J., 1978, Byte, 3, 54

Burks, A. W., 1970, Essays on Cellular Automata

Burks, A. W., 1973, Cellular Automata and Natural Systems

Butler, J. T., 1977, Math. Biosci., 35, 55, 10.1016/0025-5564(77)90086-4

Codd, E. F., 1968, Cellular Automata

Cole, S. N., 1969, IEEE Trans. Comput., C-18, 349, 10.1109/T-C.1969.222663

Deutsch, E. S., 1972, Commun. ACM, 15, 827, 10.1145/361573.361583

Farmer, J. D., 1982, Z. Naturforsch., 37a, 1304, 10.1515/zna-1982-1117

Fine, N. J., 1947, Am. Math. Mon., 54, 589, 10.2307/2304500

Fischer, P. C., 1965, J. ACM, 12, 388, 10.1145/321281.321290

Fredkin, E., PERQ computer demonstration

Gach, P., 1978, Probl. Peredachi. Info., 14, 92

Gardner, M., 1971, Sci. Amer., 224, 112, 10.1038/scientificamerican0271-112

Gardner, M., Sci. Amer., 224, 106, 10.1038/scientificamerican0371-106

Gardner, M., Sci. Amer., 224, 114, 10.1038/scientificamerican0471-114

Gardner, M., 1972, Sci. Amer., 226, 104, 10.1038/scientificamerican0172-104

Geffen, Y., Phys. Rev. Lett., 47, 1771, 10.1103/PhysRevLett.47.1771

Gerola, H., 1978, Astrophys. J., 223, 129, 10.1086/156243

Glaisher, J. W. L., 1899, Q. J. Math., 30, 150

Golomb, S. W., 1967, Shift Register Sequences

Greenberg, J. M., 1978, Bull. Am. Math. Soc., 84, 1296, 10.1090/S0002-9904-1978-14560-1

Griffeath, D., 1970, Additive and Cancellative Interacting Particle Systems

Haken, H., 1975, Rev. Mod. Phys., 47, 67, 10.1103/RevModPhys.47.67

Haken, H., 1978, Synergetics, 10.1007/978-3-642-96469-5

Haken, H., 1979, Pattern Formation by Dynamic Systems and Pattern Recognition, 10.1007/978-3-642-67480-8

Haken, H., 1981, Chaos and Order in Nature, 10.1007/978-3-642-68304-6

Hardy, G. H., 1979, An Introduction to the Theory of Numbers

Harris, B., 1960, Ann. Math. Stat., 31, 1045, 10.1214/aoms/1177705677

Herman, G. T., 1969, J. Theor. Biol., 25, 421, 10.1016/S0022-5193(69)80030-5

Honsberger, R., 1976, Mathematical Gems II, Dolciani Math. Expositions

Hoogland, A., 1982, A special-purpose processor for the Monte Carlo simulation of Ising spin systems

Hopcroft, J. E., 1979, Introduction to Automata Theory, Languages and Computation

Kauffman, S. A., 1969, J. Theor. Biol., 22, 437, 10.1016/0022-5193(69)90015-0

Kimball, S. H., 1958, Am. Math. Mon., 65, 368, 10.2307/2308812

Kitagawa, T., 1974, Math. Biosci., 19, 27, 10.1016/0025-5564(74)90029-7

Knuth, D. E., 1973, Fundamental Algorithms

Knuth, D. E., 1981, Seminumerical Algorithms

Kosaraju, S. R., 1974, IEEE Trans. Comput., C-23, 561, 10.1109/T-C.1974.223995

Landauer, R., 1979, Ann. N.Y. Acad. Sci., 316, 433, 10.1111/j.1749-6632.1979.tb29487.x

Langer, J. S., 1980, Rev. Mod. Phys., 52, 1, 10.1103/RevModPhys.52.1

Levy, Y. E., 1982, Phys. Lett. A, 88, 1, 10.1016/0375-9601(82)90408-X

Lifshitz, E. M., 1981, Physical Kinetics

Lindenmayer, A., 1968, J. Theoret. Biol., 18, 280, 10.1016/0022-5193(68)90079-9

MacWilliams, F. J., Theory of Error-Correcting Codes

Mandelbrot, B., 1977, Fractals: Form, Chance and Dimension

Mandelbrot, B., 1982, The Fractal Geometry of Nature

Manna, Z., 1974, Mathematical Theory of Computation

Manning, F. B., 1977, IEEE Trans. Comput., C-26, 536, 10.1109/TC.1977.1674879

McIlroy, M. D., 1974, SIAM J. Comput., 3, 255, 10.1137/0203020

Miller, J. C. P., 1970, Philos. Trans. R. Soc. London, Ser. A, 266, 63, 10.1098/rsta.1970.0003

Miller, J. C. P., 1980, Philos. Trans. R. Soc. London Ser. A, 293, 48

Minsky, M. L., 1967, Computation: Finite and Infinite Machines

Moore, E. F., 1970, Essays on Cellular Automata

Nicolis, G., 1977, Self-Organization in Nonequilibrium Systems

Nicolis, G., 1981, Order and Fluctuations in Equilibrium and Nonequilibrium Statistical Mechanics

Ott, E., 1981, Rev. Mod. Phys., 53, 655, 10.1103/RevModPhys.53.655

Peterson, W. W., Error-Correcting Codes

Preston, K., 1979, Proc. IEEE, 67, 826, 10.1109/PROC.1979.11331

Prigogine, I., 1980, From Being to Becoming

Renyi, A., 1970, Probability Theory

Roberts, J. B., 1957, Can. J. Math., 9, 363, 10.4153/CJM-1957-043-6

Rosen, R., 1981, Prog. Theor. Biol., 6, 161, 10.1016/B978-0-12-543106-4.50013-1

Rosenfeld, A., 1979, Picture Languages

Rosenfeld, A., 1981, Amer. Inst. Phys. Pub.

Schulman, L. S., 1978, J. Stat. Phys., 19, 293, 10.1007/BF01011727

Shannon, C. E., 1951, Bell Syst. Tech. J., 30, 50, 10.1002/j.1538-7305.1951.tb01366.x

Sierpinski, W., 1916, Pr. Mat.-Fiz., 27, 77

Sierpinski, W., Oeuvres Choisis

Smith, A. R., 1971, J. ACM, 18, 339, 10.1145/321650.321652

Sternberg, S. R., 1980, Pattern Recognition in Practice

Stevens, P. S., 1974, Patterns in Nature

Stolarsky, K. B., 1977, SIAM J. Appl. Math., 32, 717, 10.1137/0132060

Sutton, C., 1981, New Sci., 90, 209

Thom, R., 1975, Structural Stability and Morphogenesis

Thompson, D'A. W., 1961, On Growth and Form

Toffoli, T., 1977, J. Comput. Sys. Sci., 15, 213, 10.1016/S0022-0000(77)80007-X

Toffoli, T., 1983, Squareland: a hardware cellular automaton simulator

Turing, A. M., 1936, Proc. London Math. Soc. Ser. 2, 42, 230

Turing, A. M., 1965, The Undecidable

Turing, A. M., 1952, Philos. Trans. R. Soc. London, Ser. B, 237, 37, 10.1098/rstb.1952.0012

Ulam, S., 1974, Ann. Rev. Bio., 255

von Neumann, J., 1963, J. von Neumann, Collected Works

von Neumann, J., 1966, Theory of Self-Reproducing Automata

Wainwright, R. T., 1971, Lifeline

Wainwright, R. T., 1974, Life is Universal!, 10.1145/800290.811303

Waksman, A., 1969, J. ACM, 16, 178, 10.1145/321495.321509

Willson, S., 1982, Cellular automata can generate fractals

Witten, T. A., 1981, Phys. Rev. Lett., 47, 1400, 10.1103/PhysRevLett.47.1400

Wolfram, S., 1981, SMP Handbook

Wolfram, S., 1982, Am. Math. Monthly