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Two-Dimensional Cellular Automata (1985) |
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[1] S. Wolfram, Cellular automata as models for complexity, Nature 311:419 (1984).
[2] T. Toffoli, Cellular automata mechanics, Ph.D. thesis and Technical Report 208, The Logic of Computers Group, University of Michigan (1977).
[3] G. Vichniac, Simulating physics with cellular automata, Physica 10D:96 (1984).
[4] S. Wolfram, Statistical mechanics of cellular automata, Rev. Mod. Phys. 55:601 (1983).
[5] O. Martin, A. Odlyzko, and S. Wolfram, Algebraic properties of cellular automata, Comm. Math. Phys. 93:219 (1984).
[6] N. Packard, Cellular automaton models for dendritic crystal growth, Institute for Advanced Study, preprint (1985).
[7] S. Wolfram, Universality and complexity in cellular automata, Physica 10D:1 (1984).
[8] E. R. Berlekamp, J. O. Conway, and R. K. Guy, Winning Ways for Your Mathematical Plays, Vol. 2 (Academic Press, New York, 1982), Chap. 25; M. Gardner, Wheels, Life and Other Mathematical Amusements (Freeman, San Francisco, 1983).
[9] T. Toffoli, CAM: A high-performance cellular-automaton machine, Physica 10D:195 (1984).
[10] J. Guckenheimer and P. Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer, New York, 1983).
[11] J. E. Hopcroft and J. D. Ullman, Introduction to Automata Theory, Languages, and Computation (Addison-Wesley, Reading, Massachusetts, 1979).
[12] S. Wolfram, Computation theory of cellular automata, Commun. Math. Phys. 96:15 (1984).
[13] L. Hurd, Formal language characterizations of cellular automaton limit sets, to be published.
[14] S. Willson, On convergence of configurations, Discrete Math. 23:279 (1978).
[15] T. Yaku, The constructability of a configuration in a cellular automaton, J. Comput. Syst. Sci. 7:481 (1973); U. Golze, Differences between 1- and 2-dimensional cell spaces, in Automata, Languages, Development, A. Lindenmayer and G. Rozenberg, eds. (North-Holland, Amsterdam, 1976).
[16] J. Hardy, O. de Pazzis, and Y. Pomeau, Molecular dynamics of a classical lattice gas: transport properties and time correlation functions, Phys. Rev. A13:1949 (1976).
[17] S. Wolfram, Cellular automata, Los Alamos Science (Fall 1983); Some recent results and questions about cellular automata, Institute for Advanced Study preprint (September 1983).
[18] S. Wolfram, Twenty problems in the theory of cellular automata, Physica Scripta T9:170 (1985).
[19] S. Wolfram, Computer software in science and mathematics, Sci. Am. 251(3):188 (1984).
[20] S. Willson, Comparing limit sets for certain increasing cellular automata, Mathematics Department, Iowa State University preprint (June 1984).
[21] S. Willson, Growth rates and fractional dimensions in cellular automata, Physica 10D:69 (1984).
[22] N. Packard, Notes on a Go-playing program, unpublished (1984).
[23] Y. Sawada, M. Matsushita, M. Yamazaki, and H. Kondo, Morphological phase transition measured by ``surface kinetic dimension'' of growing random patterns, Phys. Scripta (to be published).
[24] J. M. Greenberg, B. D. Hassard, and S. P. Hastings, Pattern formation and periodic structures in systems modelled by reaction-diffusion equations, Bull. Amer. Math. Soc. 84:1296 (1975); B. Madore and W. Freedman, Computer simulations of the Belousov-Zhabotinsky reaction, Science 222:615 (1983).
[25] K. Preston et al., Basics of cellular logic with some applications in medical image processing, Proc. IEEE 67:826 (1979).
[26] J. W. Essam, Percolation theory, Rep. Prog. Phys. 43:833 (1980).
[27] P. Grassberger, Chaos and diffusion in deterministic cellular automata, Physica 10D:52 (1984).
[28] G. Vichniac, Cellular automaton dynamics for interface motion and ordering, M.I.T. report, to appear.
[29] R. Rosensweig, Fluid dynamics and science of magnetic liquids, Adv. Electronics Electron Phys. 48:103 (1979); Magnetic fluids, Sci. Am. 247(4):136 (1982).
[30] G. A. Hedlund, Endomorphisms and automorphisms of the shift dynamical system, Math. Syst. Theory 3:320 (1969); G. A. Hedlund, Transformations commuting with the shift, in Topological dynamics, J. Auslander and W. H. Gottschalk, eds. (Benjamin, New York, 1968); S. Amoroso and Y. N. Patt, Decision procedures for surjectivity and injectivity of parallel maps for tessellation structures, J. Comp. Sys. Sci. 6:448 (1972); M. Nasu, Local maps inducing surjective global maps of one-dimensional tessellation automata, Math. Syst. Theory 11:327 (1978).
[31] H. Wang, Proving theorems by pattern recognition---II, Bell Sys. Tech. J. 40:1 (1961).
[32] R. Berger, Undecidability of the domino problem, Mem. Am. Math. Soc., No. 66 (1966).
[33] R. Robinson, Undecidability and nonperiodicity for tilings of the plane, Inventiones Math. 12:177 (1971).
[34] D. Ruelle, Thermodynamic Formalism (Addison-Wesley, Reading, Massachusetts, 1978), p. 68.
[35] R. Penrose, Pentaplexity: a class of nonperiodic tilings of the plane, Math. Intelligencer 2:32 (1979); M. Gardner, Extraordinary nonperiodic tiling that enriches the theory of tiles, Sci. Am. 236(1):110 (1977); N. de Bruijn, Algebraic theory of Penrose's nonperiodic tilings of the plane, Nederl. Akad. Wetensch. Indag. Math. 43:39 (1981).
[36] P. Kramer, Non-periodic central space filling with icosahedral symmetry using copies of seven elementary cells, Acta Crystallogr. A38:257 (1982).
[37] M. Garey and D. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness, (Freeman, San Francisco, 1979), p. 257.
[38] J. Milnor, Entropy of cellular automaton-maps, Institute for Advanced Study preprint (May 1984).
[39] J. Milnor, Directional entropies in higher dimensions, rough notes (September 1984).
[40] N. Packard, Complexity of growing patterns in cellular automata, Institute for Advanced Study preprint (October 1983).
[41] J. Milnor, Notes on surjective cellular automaton-maps, Institute for Advanced Study preprint (June 1984).
[42] N. D. Mermin, The topological theory of defects in ordered media, Rev. Mod. Phys. 51:591 (1979).
[43] A. Winfree and E. Winfree, Organizing centers in a cellular excitable medium, Purdue University preprint (July 1984) and Physica D (to be published).
