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[AL] M. Aizenman, J. Lebowitz, Metastability effects in bootstrap percolation, J. Phys. A: Math. Gen. 21 (1988), 3801-3813.

[Ban] E. R. Banks, Universality in cellular automata, in Proc. 11th IEEE Symposium on Foundations of Computer Science (FOCS) (1970), 194-215.

[BB] C. Bennett, M. Bourzutschky, Life not critical?, Nature 350 (1991), 468.

[BCC] P. Bak, K. Chen, M. Creutz, Self-organized criticality in the Game of Life, Nature 342 (1989), 780.

[BCG] E. Berlekamp, J. Conway, R. Guy, Winning Ways for Your Mathematical Plays, vol. 2, chapter 25, Academic Press, New York, 1982.

[Big] J. Biggins, The asymptotic shape of the branching random walk, Advances in Appl. Probability 10 (1978), no. 1, 62-84.

[Boh] T. Bohman, Discrete Threshold Growth dynamics are omnivorous for box neighborhoods, Trans. Amer. Math. Soc. (1997), to appear.

[BG] T. Bohman, J. Gravner, Random threshold growth models, (1997), submitted.

[BGG] T. Bohman, J. Gravner, D. Griffeath, Asymptotic shapes for random threshold growth models, (1997), in preparation.

[BH] S. Broadbent, J. Hammersley, Percolation processes. I. Crystals and mazes, Proc. Cambridge Philos. Soc. 53 (1957), 629-641.

[BN] M. Bramson, C. Neuhauser, Survival of one-dimensional cellular automata under random perturbations, Ann. Prob. 22 (1994), 244-263.

[BS] A.-L. Barabasi, H. Stanley, Fractal concepts in surface growth, Cambridge University Press, 1995.

[Cal] P. Callahan, Patterns, Programs, and Links for Conway's Game of Life,

[CD] J. T. Cox, R. Durrett, Some limit theorems for percolation processes with necessary and sufficient conditions. Ann. Prob. 9 (1981), 583-603.

[Dura] B. Durand, Inversion of 2D cellular automata: some complexity results, Theoretical Computer Science 134 (1994), 387-401.

[Durr] R. Durrett, Lecture Notes on Particle Systems and Percolation, Wadsworth & Brooks/Cole, 1988.

[DG1] R. Durrett, D. Griffeath, Contact processes in several dimensions, Z. Wahrscheinlichkeitstheorie verw. Gebiete 59 (1982), 535-552.

[DG2] R. Durrett, D. Griffeath, Asymptotic behavior of excitable cellular automata, J. Experimental Math. 2 (1993), 183-208.

[DKS] R. Dobrushin, R. Kotecky, S. Shlosman, Wulff Construction, A Global Shape from Local Interaction, American Mathematical Society, 1992.

[DLi] R. Durrett, T. Liggett, The shape of the limit set in Richardson's growth model, Ann. Prob. 9 (1981), 186-193.

[DS] R. Durrett, J. Steif, Fixation results for the threshold voter models, Ann. Prob. 21 (1993), 232-247.

[EE-K] G. Ermentrout, L. Edelstein-Keshet, Cellular automata approaches to biological modeling. J. Theor. Biol. 160 (1993), 97-133.

[Ede] M. Eden, p.359 in Symp. on Information Theory in Biology, ed. H. Yockey, Pergamon Press, New York, 1958.

[Elk] N. Elkies, The still-Life density problem and its generalizations, preprint, 1997.

[Eva] K. Evans, Larger than Life: it's so nonlinear, Ph.D. dissertation, Univ. of Wisconsin, 1996.

[FG] R. Fisch, D. Griffeath, WinCA: a cellular automaton modeling environment. Windows 3.x/95 software, version 1.0, 1996. Available from [Gri2].

[FGG1] R. Fisch, J. Gravner, D. Griffeath, Threshold-range scaling of excitable cellular automata, Statistics and Computing 1 (1991), 23-39.

[FGG2] R. Fisch, J. Gravner, D. Griffeath, Metastability in the Greenberg-Hastings model, Ann. Appl. Prob. 3 (1993), 935-967.

[FHP] U. Frisch, B. Hasslacher, Y. Pomeau , Lattice-Gas Automata for the Navier-Stokes Equation, Phys. Rev. Lett. 56 (1986), 1505-1508.

[Gar1] M. Gardner, Mathematical Games - The Fantastic Combinations of John Conway's New Solitaire Game, Life, Scientific American, October 1970, 120-123. Subsequent articles about Conway's Life appeared in the Mathematical Games / Computer Recreations column of Scientific American, in the issues of Nov 70, Jan 71, Feb 71, Mar 71, Apr 71, Nov 71, Jan 72, Dec 75, Mar 84, May 85, Feb 87, Aug 88, Aug 89, Sep 89, and Jan 90.

[Gar2] M. Gardner, Wheels, Life and Other Amusements, Freeman, 1983.

[Garz] M. Garzon, Models of Massive Parallelism: Analysis of Cellular Automata and Neural Networks, Springer-Verlag, 1995.

[GHH] J. Greenberg, B. Hassard, S. Hastings, Pattern formation and periodic structures in systems modeled by reaction-diffusion equations, Bull. AMS 84 (1978), 1296-1327.

[Gra1] J. Gravner, The boundary of iterates in Euclidean growth models, T.A.M.S. (1996), 4549-4559.

[Gra2] J. Gravner, Recurrent ring dynamics in two-dimensional cellular automata, (1996), submitted.

[GG1] J. Gravner, D. Griffeath, Threshold Growth dynamics, T.A.M.S. (1993), 837-870.

[GG2] J. Gravner, D. Griffeath, First-passage times for discrete Threshold Growth dynamics, Ann. Prob. (1996), 1752-1778.

[GG3] J. Gravner, D. Griffeath, Multitype Threshold Growth: convergence to Poisson-Voronoi tessellations, Ann. Appl. Prob. 7 (1997), 615-647.

[GG4] J. Gravner, D. Griffeath, Nucleation parameters for discrete threshold growth dynamics, Experimental Math. 6 (1997), 207-220.

[GG5] J. Gravner, D. Griffeath, Scaling limits for critical Threshold Growth (1997), in preparation.

[GHR] R. Greenlaw, H. Hoover, and W. Ruzzo, Limits to Parallel Computation: P-Completeness Theory, Oxford University Press, 1995.

[GN] R. Gaylord, K. Nishidate, Modeling Nature: Cellular Automata Simulations with Mathematics, Springer-Verlag, 1996.

[GQ] J. Gravner, J. Quastel, Internal DLA and the Stefan problem (1998), in preparation.

[Gri1] D. Griffeath, Self-organization of random cellular automata: four snapshots, In Probability and Phase Transitions, ed. G. Grimmett, Kluwer, 1994.

[Gri2] D. Griffeath, Primordial Soup Kitchen,, World Wide Web.

[GM] D. Griffeath, C. Moore, Life without Death is P-complete (1997), submitted.

[Gut] H. Gutowitz, Frequently asked questions about cellular automata,, World Wide Web.

[Har] J. Hartmanis, On the Computing Paradigm and Computational Complexity, MFCS'95, eds. J. Wiederman, P. Hajek, Springer LNCS No.969, 1995, pp. 82-92.

[Hol] J. Holland, Outline for a logical theory of adaptive systems and other articles, In Essays on Cellular Automata, ed. Arthur W. Burks, University of Illinois Press, 1970.

[Jen] E. Jen, Exact solvability and quasiperiodicity of one-dimensional cellular automata, Nonlinearity 4 (1991), 251-276.

[JM] W. Johnson, R. Mehl, Reaction kinetics in processes of nucleation and growth, Trans. A.I.M.M.E. 135 (1939), 416-458.

[Kar] J. Kari, Reversability of 2D cellular automata is undecidable, Physica D 45 (1990), 379-385.

[Kes1] H. Kesten, First passage percolation and a higher-dimensional generalization, in Particle Systems, Random Media and Large Deviations ed. R.Durrett, American Mathematical Society, 1984.

[Kes2] H. Kesten, On the speed of convergence in first-passage percolation, Ann. Appl. Prob. 4 (1994), 76-107.

[KeSc] H. Kesten, R. Schonmann, On some growth models with a small parameter, Probab. Th. Rel. Fields 101 (1995), 435-468.

[KrSp] J. Krug, H. Spohn, Kinetic roughening of growing surfaces, in Solids far from Equilibrium, ed. C. Godreche, Cambridge University Press, 1882, 479-582.

[Lan] C. Langton, Studying Artificial Life with Cellular Automata, Physica D 22 (1986), 120-149.

[LDKB] A. Lawniczak, D. Dab, R. Kapral, and J.-P. Boon, Reactive lattice gas automata. Physica D 47 (1991), 132-158.

[LBG] G. Lawler, M. Bramson, D. Griffeath, Internal diffusion limited aggregation, Ann. Prob. 14 (1992), 2117-2140.

[Lig] T. Liggett, Interacting Particle Systems, Springer-Verlag, 1985.

[Lin] D. Lind, Applications of ergodic theory and sofic systems to cellular automata, Physica 10 D 1984, 36-44.

[LN] K. Lindgren and M. Nordahl, Universal Computation in Simple One-Dimensional Cellular Automata, Complex Systems 4 (1990), 299-318.

[Marg] N. Margolus, CAM-8: a virtual processor cellular automata machine, MIT Laboratory for Computer Science (1995).

[Mart] B. Martin, A universal cellular automaton in quasi-linear time and its S-m-n form, Theoretical Computer Science 123 (1994), 199-237.

[Min] M. Minsky, Computation: Finite and Infinite Machines, Prentice Hall, 1972.

[Mou] T. Mountford, Critical lengths for semi-oriented bootstrap percolation, Stochastic Process. Appl. 95 (1995), 185-205.

[Nie] M. Niemic, Life Page,

[NP] C. Newman, M. Piza, Divergence of shape fluctuations in two dimensions, Ann Prob. 23 (1995), 977-1005.

[NM] M. Nowak and R. May, Evolutionary games and spatial chaos. Nature 359 (1992), 826-829.

[Pac] N. Packard, Institute for Advanced Study 1985.

[Pap] C. Papadimitriou, Computational Complexity, Addison-Wesley, 1994.

[PW] N. Packard, S. Wolfram, Two-dimensional cellular automata, J. Stat. Phys. 38 (1985), 901-946.

[Ric] D. Richardson, Random growth in a tesselation, Proc. Camb. Phil. Soc. 74 (1973), 515-528.

[San] L. Sander, Fractal growth processes, Nature 322 (1986), 789-793.

[Sch] R. Schonmann, On the behavior of some cellular automata related to bootstrap percolation., Ann. Prob. 20 (1992), 174-193.

[TCH] J. Taylor, J. Cahn, C. Handwerker, Geometric models of crystal growth (Overview no. 98-1), Acta Met. 40 (1992), 1443-1474.

[TM] T. Toffoli, N. Margolus, Cellular Automata Machines a new environment for modeling, MIT Press, 1987.

[Toom] A. Toom, Cellular automata with errors: problems for students of probability, in Topics in Contemporary Probability and Its Applications, edited by J. Laurie Snell, CRC Press, 1995.

[Ula] S. Ulam, Random Processes and Transformations, Proc. (1950) Int. Congr. Mathem., 2 (1952), 264-275.

[Vic] G. Vichniac, Simulating physics with cellular automata, Physica 10D (1984) 96-115.

[vK] H. von Koch, 1904.

[vN] J. von Neumann, Theory of Self-Reproducing Automata, (ed. A Burks), Univ. of Illinois Press, 1966.

[WR] N. Weiner, A. Rosenblueth, The mathematical formulation of the problem of conduction of impulses in a network of connected excitable elements, specifically in cardiac muscle, Arch. Inst. Cardiol. Mexico 16 (1946), 205-265.

[WS] T. Witten, L. Sander, Diffusion limited aggregation, Phys. Rev. Lett. 47 (1981), 1400-1403.

[Wil1] S. Willson, On convergence of configurations, Discrete Math. 23 (1978), no. 3, 279-300.

[Wil2] S. Willson, Cellular automata can generate fractals, Discrete Appl. Math. 8 (1984), no. 1, 91-99.

[Wol1] S. Wolfram, Cellular Automata and Complexity, Addison-Wesley, Menlo Park, CA, 1994.

[Wol2] S. Wolfram, Private communication, 1995.


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