Abstract
Natural systems from snowflakes to mollusc shells show a great diversity of complex patterns. The origins of such complexity can be investigated through mathematical models termed ‘cellular automata’. Cellular automata consist of many identical components, each simple., but together capable of complex behaviour. They are analysed both as discrete dynamical systems, and as information-processing systems. Here some of their universal features are discussed, and some general principles are suggested.
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References
Wolfram, S. Rev. Mod. Phys. 55, 601–644 (1983).
Wolfram, S. Physica 10 D, 1–35 (1984).
Wolfram, S. Commun. Math. Phys. (in the press).
Wolfram, S. Cellular Automata (Los Alamos Science, Autumn, 1983).
Mandelbrot, B. The Fractal Geometry of Nature (Freeman, San Francisco, 1982).
Packard, N., Preprint Cellular Automaton Models for Dendritic Growth (Institute for Advanced Study, 1984).
Madore, B. & Freedman, W. Science 222, 615–616 (1983).
Greenberg, J. M., Hassard, B. D. & Hastings, S. P. Bull. Amer. Math. Soc. 84, 1296–1327 (1978).
Vichniac, G. Physica 10 D, 96–116 (1984).
Domany, E. & Kinzel, W. Phys. Rev. Lett. 53, 311–314 (1984).
Waddington, C. H. & Cowe, R. J. J. theor. Biol. 25, 219–225 (1969).
Lindsay, D. T. Veliger 24, 297–299 (1977).
Young, D. A. A Local Activator–Inhibitor Model of Vertebrate Skin Patterns (Lawrence Livermore National Laboratory Rep., 1983).
Guckenheimer, J. & Holmes, P. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer, Berlin, 1983).
Hopcroft, J. E. & Ullman, J. D. Introduction to Automata Theory, Languages, and Computation (Addison-Wesley, New York, 1979).
Packard, N. Preprint, Complexity of Growing Patterns in Cellular Automata (Institute for Advanced Study, 1983).
Martin, O, Odlyzko, A. & Wolfram, S. Commun. Math. Phys. 93, 219–258 (1984).
Grassberger, P. Physica 10 D, 52–58 (1984).
Lind, D. Physica 10 D, 36–44 (1984).
Margolus, N. Physica 10 D, 81–95 (1984).
Smith, A. R. Journal of the Association for Computing Machinery 18, 339–353 (1971).
Berlekamp, E. R., Conway, J. H. & Guy, R. K. Winning Ways for your Mathematical Plays Vol. 2, Ch. 25 (Academic, New York, 1982).
Gardner, M. Wheels, Life and other Mathematical Amusements (Freeman, San Francisco, 1983).
Wolfram, S. SMP Reference Manual (Computer Mathematics Group, Inference Corporation, Los Angeles, 1983).
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Wolfram, S. Cellular automata as models of complexity. Nature 311, 419–424 (1984). https://doi.org/10.1038/311419a0
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DOI: https://doi.org/10.1038/311419a0
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