Skip to main content
SpringerLink
Log in

Cellular Automata Models of Disorder And Organization

  • Conference paper
Disordered Systems and Biological Organization

Part of the book series: NATO ASI Series ((NATO ASI F,volume 20))

Abstract

Cellular automata are mathematical objects introduced in 1948 by J. von Neumann and S. Ulam to “abstract the logical structure of life” [1], Since then, they have established themselves as unique tools to analyze the emergence of global organization, complexity, and pattern formation from the iteration of local operations between simple elements. They have also been extensively used as models of universal computation, and are being increasingly applied to a variety of concepts from physics and chemistry[2]. They are in fact versatile enough to offer analogies with almost all the themes discussed at this meeting (in particular: self-organization, dissipative systems, spatial vs. thermal fluctuations, neural networks, optimization, ergodicity-breaking, and ultrametricity)

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. W. Burks, Essays on Cellular Automata (University of Illinois Press, 1970).

    MATH  Google Scholar 

  2. D. Farmer, T. Toffoli, and S. Wolfram (eds), Cellular Automata (North-Holland, 1984).

    MATH  Google Scholar 

  3. T. Toffoli, Cellular Automata Mechanics, Tech. Rep. no. 208, Comp. Comm. Sci. Dept., The University of Michigan (1977).

    Google Scholar 

  4. G. Y. Vichniac, Physica 10D (1984) 96–115; reprinted in [2].

    MathSciNet  Google Scholar 

  5. B. Hayes, Scientific American, 250:3 (1984), 12–21.

    Article  Google Scholar 

  6. M. Creutz, to appear in Ann. Phys. (N. Y.).

    Google Scholar 

  7. R. C. Brower, R. Giles, and G. Vichniac, to appear.

    Google Scholar 

  8. G. Enting, J. Phys. C 10 (1977) 1379–1388.

    Article  Google Scholar 

  9. E. Domany and W. Kinzel, Phys. Rev. Lett. 53 (1984) 311–314.

    Article  MathSciNet  Google Scholar 

  10. W. Kinzel, Z. Phys. B 58 (1985) 229–244.

    Article  MATH  MathSciNet  Google Scholar 

  11. A. L. Toom, in Locally Interacting Systems and their Applications in Biology, R. L. Dobrushin, V. I. Kryukov, and A. L. Toom (eds), Lecture Notes in Mathematics, no 653 (Spinger-Verlag, 1978); and in Multicomponent Random Systems, R. L. Dobrushin (ed), in Adv. in Probabilities, Vol. 6 (Dekker, 1980), pp. 549–575.

    Google Scholar 

  12. A. L. Toom, in Multicomponent Random Systems, R. L. Dobrushin (ed), in Adv. in Probabilities, Vol. 6 (Dekker, 1980), pp. 549–575.

    Google Scholar 

  13. A. L. Toom, R. L. Dobrushin (ed), in Adv. in Probabilities, Vol. 6 (Dekker, 1980), pp. 549–575.

    Google Scholar 

  14. P. Gacs and J. Reif, in Proceedings of the Seventeenth ACM Symposium on the Theory of Computing, Providence, R. I., 1985 (ACM, 1985), pp. 388–395.

    Google Scholar 

  15. C. H. Bennett and G. Grinstein, Phys. Rev. Lett. 55 (1985) 657–660.

    Article  Google Scholar 

  16. H. Hartman and G. Y. Vichniac, this volume.

    Google Scholar 

  17. S. A. Kauffman, this volume; Physica 10D (1984) 145–156; reprinted in [2].

    MathSciNet  Google Scholar 

  18. N. H. Margolus, Physica 10D (1984) 85–95; reprinted in [2].

    MathSciNet  Google Scholar 

  19. T. Toffoli, Physica 10D (1984) 195–204; reprinted in [2].

    MathSciNet  Google Scholar 

  20. H. M. Goldstine and J. von Neumann, unpublished (1946), reprinted in J. von Neumann’s Complete Works, Vol. 5 (Pergamon, 1961), pp. 1–32.

    Google Scholar 

  21. J. von Neumann’s Complete Works, Vol. 5 (Pergamon, 1961), pp. 1–32.

    Google Scholar 

  22. Proceedings of the Conference on Physics of Computation, Part II: Computational models of physics, R. Landauer and T. Toffoli (eds), Int. J. Theor. Phys. 21 (1982) no 6–7.

    Google Scholar 

  23. R. P. Feynman, The Character of Physical Law (MIT Press, 1967), pp. 57–58.

    Google Scholar 

  24. M. Gardner, Scientific American 223:4 (1970) 120–123.

    Article  Google Scholar 

  25. E. R. Berlekamp, J. H. Conway, and R. K. Guy, Winning Ways, vol 2. (Academic Press, 1982) Chap. 25; M. Gardner, Wheels, Life and other Mathematical Amusements (Freeman, 1982); W. Poundstone, The Recursive Universe, (W. Morrow, 1985).

    MATH  Google Scholar 

  26. M. Gardner, Wheels, Life and other Mathematical Amusements (Freeman, 1982)

    Google Scholar 

  27. W. Poundstone, The Recursive Universe, (W. Morrow, 1985).

    Google Scholar 

  28. S. Lem, “Non Serviam,” in A Perfect Vacuum: Perfect Reviews of Nonexistent Books (Harcourt Brace Jovanovich, 1978).

    Google Scholar 

  29. R. Penrose, “Lessons From the Game of Life,” Review of W. Poundstone’s book[22], The New York Times, March 17, 1985, VII, 34:2.

    Google Scholar 

  30. W. Poundstone’s, The New York Times, March 17, 1985, VII, 34:2.

    Google Scholar 

  31. F. Dyson, Disturbing the Universe (Harper and Row, 1979).

    Google Scholar 

  32. J. von Neumann, Theory of Self-Reproducing Automata (edited and completed by A. W. Burks), (University of Illinois Press, 1966).

    Google Scholar 

  33. E. F. Codd, Cellular Automata (Academic Press, 1968).

    MATH  Google Scholar 

  34. C. G. Langton, Physica 10D (1984) 135–144; reprinted in [2].

    Google Scholar 

  35. J. S. Langer, in Discover, Jan. 1984, p. 76.

    Google Scholar 

  36. E. Goles, this volume; and in Comportement dynamique de réseaux d’automates, Thèse, Grenoble 1985.

    Google Scholar 

  37. J. Cahn, in Critical Phenomena in Alloys, Magnets, and Superconductors, R. E. Mills, E. Ascher and R. J. Jaffee (eds) (McGraw-Hill, 1971).

    Google Scholar 

  38. B. Halperin and P. C. Hohenberg, Rev. Mod. Phys. 49 (1977) 435–479.

    Article  Google Scholar 

  39. G. Grest and P. Srolovitz, Phys. Rev. B30 (1984) 5150–5155.

    Google Scholar 

  40. P. Grassberger, Physica 10D (1984) 52–58; reprinted in [2].

    MathSciNet  Google Scholar 

  41. S. Kirkpatrick, C. D. Gelatt Jr. and M. P. Vecchi, Science 220 (1983) 671–680; S. Kirkpatrick and G. Toulouse, J. Physique, in press.

    Article  MATH  MathSciNet  Google Scholar 

  42. S. Wolfram, Physica 10D (1984) 1–35; reprinted in [2].

    MathSciNet  Google Scholar 

  43. N. H. Packard and S. Wolfram, J. Stat. Phys. 38 (1985) 901–946.

    Article  MATH  MathSciNet  Google Scholar 

  44. G. Y. Vichniac, SIAM J. Alg. Disc. Meth. 5 (1984) 596–602.

    Article  MATH  MathSciNet  Google Scholar 

  45. N. H. Margolus, private communication.

    Google Scholar 

  46. F. Fogelman-Soulié, this volume; and Contribution à une théorie du calcul sur réseaux, Thèse, Grenoble (1985).

    Google Scholar 

  47. A. E. Gelfand and C.C. Walker, Ensemble Modeling (Marcel Dekker, 1984).

    MATH  Google Scholar 

  48. N. H. Packard, in Dynamical Systems and Cellular Automata, J. Demongeot, E. Goles, and M. Tchuente (eds) (Academic Press, 1985), pp. 123–137.

    Google Scholar 

  49. H. Atlan, F. Fogelman-Soulié, J. Salomon, and G. Weisbuch, Cybernet. Systems, 12 (1981) 103–121.

    Article  MathSciNet  Google Scholar 

  50. T. Toffoli and N. Margolus, in preparation.

    Google Scholar 

  51. I. Oppenheim and R. D. Levine, Physica 99A (1979) 383–402.

    Google Scholar 

  52. J. E. Mayer and M. G. Mayer, Statistical Mechanics (2nd ed.) (Wiley, 1977).

    MATH  Google Scholar 

  53. R. C. Tolman, The Principles of Statistical Mechanics (Oxford University Press, 1938; Dover, 1979).

    Google Scholar 

  54. R. Balian, Y. Alhassid, and H. Reinhardt, to appear in Physics Reports.

    Google Scholar 

  55. R. G. Brewer and E. L. Hahn, Scientific American 251:6 (1984) 50–57.

    Article  Google Scholar 

  56. K. Huang, Statistical Mechanics (Wiley, 1963).

    Google Scholar 

  57. P. C. W. Davies, The Physics of Time Asymmetry (University of California Press, 1977).

    Google Scholar 

  58. J. Hardy, O. de Pazzis, and Y. Pomeau, Phys. Rev. A 13 (1976) 1949–1961.

    Article  Google Scholar 

  59. T. Toffoli, Physica 10D (1984) 117–127; reprinted in [2].

    MathSciNet  Google Scholar 

  60. Y. Pomeau, J. Phys. A 17 (1984) L415–L418.

    Article  MathSciNet  Google Scholar 

  61. See the papers of Mézard, Solla et al. and Virasoro, this volume; and M. Mézard, G. Parisi, N. Sourlas, G. Toulouse, and M. Virasoro, Phys. Rev. Lett. 52 (1984) 1156–1159.

    Article  Google Scholar 

  62. G. Sorkin, private communication.

    Google Scholar 

  63. S. A. Solla, G. B. Sorkin, and S. R. White, this volume.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02189, USA

    Gérard Y. Vichniac

Authors
  1. Gérard Y. Vichniac
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Laboratoire de Neurobiologie du Développement, Université de Paris XI, 91405, Orsay, France

    E. Bienenstock

  2. Laboratoire de Dynamique des Reseaux, L.D.R. CESTA, 1, rue Descartes, 75005, Paris, France

    F. Fogelman Soulié

  3. Groupe de Physique des Solides, École Normale Supérieure, 24, rue Lhomond, 75231, Paris, France

    G. Weisbuch

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Vichniac, G.Y. (1986). Cellular Automata Models of Disorder And Organization. In: Bienenstock, E., Soulié, F.F., Weisbuch, G. (eds) Disordered Systems and Biological Organization. NATO ASI Series, vol 20. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82657-3_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-82657-3_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-82659-7

  • Online ISBN: 978-3-642-82657-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation