Skip to main content
Log in

Fractal growth processes

  • Review Article
  • Published:

From Nature

View current issue Submit your manuscript

Abstract

The methods of fractal geometry allow the classification of non-equilibrium growth processes according to their scaling properties. This classification and computer simulations give insight into a great variety of complex structures.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Mandelbrot, B. The Fractal Geometry of Nature (Freeman, San Francisco, 1982).

    MATH  Google Scholar 

  2. Family, F. & Landau, D. (eds) Kinetics of Aggregation and Gelation (North-Holland, New York, 1984).

    Book  Google Scholar 

  3. Pynn, R. & Skjeltorp, A. (eds) Scaling Phenomena in Disordered Systems (Plenum, NewYork, 1985).

  4. Stanley, H. & Ostrowsky, N. (eds) On Growth and Form (Nijhoff, The Hague, 1985).

    Google Scholar 

  5. Witten, T. & Sander, L. Phys. Rev. Lett. 47, 1400–1403 (1981).

    Article  ADS  CAS  Google Scholar 

  6. Witten, T. & Sander, L. Phys. Rev. B. 27 5686–5697 (1983).

    Article  ADS  MathSciNet  Google Scholar 

  7. Brady, R. & Ball, R. Nature 309, 225–229 (1984).

    Article  ADS  CAS  Google Scholar 

  8. Matsushita, M., Sano, M., Hayakawa, Y., Honjo, H. & Sawada, Y. Phys. Rev. Lett. 53, 286–289 (1984).

    Article  ADS  CAS  Google Scholar 

  9. Meakin, P. Phys. Rev. A 27, 2616–2623 (1983).

    Article  ADS  Google Scholar 

  10. Niemeyer, L., Pietronero, L. & Wiesmann, H. Phys. Rev. Lett. 52, 1033–1036 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  11. Paterson, L. Phys. Rev. Lett. 52, 1621–1624 (1984).

    Article  ADS  CAS  Google Scholar 

  12. Saffman, P. & Taylor, G. Proc. R. Soc. A245, 312–329 (1958).

    ADS  CAS  Google Scholar 

  13. Chen, J. & Wilkinson, D. Phys. Rev. Lett. 55, 1892–1895 (1985).

    Article  ADS  CAS  Google Scholar 

  14. Nittman, J., Daccord, G. & Stanley, H. Nature 314, 141–144 (1985).

    Article  ADS  Google Scholar 

  15. Ben-Jacob, E. et al. Phys. Rev. Lett. 55, 1315–1318 (1985).

    Article  ADS  CAS  Google Scholar 

  16. Leamy, H., Gilmer, G. & Dirks, A. in Current Topics in Materials Science Vol. 6 (ed. Kaldis, E.) (North-Holland, New York, 1980).

    Google Scholar 

  17. Bensimon, D., Shraiman, B. & Liang, S. Phys. Lett. 102A, 238–240 (1984).

    Article  ADS  Google Scholar 

  18. Meakin, P. Phys. Rev. B 28, 5221–5224 (1983).

    Article  ADS  Google Scholar 

  19. Family, F. & Viscek, T. J. Phys. A 18, L75–L81 (1985).

    Article  ADS  Google Scholar 

  20. Voss, R., in Scaling Phenomena in Disordered Systems (eds Pynn, R. & Skjeltorp, A.) 1–11 (Plenum, New York, 1985).

    Google Scholar 

  21. Ramanlal, P. & Sander, L. Phys. Rev. Lett. 54, 1828–1831 (1985).

    Article  ADS  CAS  Google Scholar 

  22. Peters, H. P., Stauffer, D., Holters, H. P. & Loewenich, K. Z. Phys. B34, 399–408 (1979).

    Google Scholar 

  23. Racz, Z. & Plischke, M. Phys. Rev. A31, 985–993 (1985).

    Article  ADS  CAS  Google Scholar 

  24. Richter, R., Sander, L. & Cheng, Z. J. Coll. Interf. Sci. 100, 203–209 (1984).

    Article  ADS  CAS  Google Scholar 

  25. Weitz, D. & Oliveria, M. Phys. Rev. Lett. 52, 1433–1436 (1984).

    Article  ADS  CAS  Google Scholar 

  26. Meakin, P. Phys. Rev. Lett. 51, 1119–1122 (1983).

    Article  ADS  Google Scholar 

  27. Kolb, M., Botet, R. & Jullien, R. Phys. Rev. Lett. 51, 1123–1126 (1983).

    Article  ADS  Google Scholar 

  28. Jullien, R. & Kolb, M. J. Phys. A 17, L639–L643 (1984).

    Article  ADS  CAS  Google Scholar 

  29. Schaefer, D., Martin, J. Wiltzius, P. & Cannell, D. Phys. Rev. Lett. 52, 2371–2374 (1984).

    Article  ADS  CAS  Google Scholar 

  30. Weitz, D., Huang, J., Lin, M. & Sung, J. Phys. Rev. Lett. 54, 1416–1419 (1985).

    Article  ADS  CAS  Google Scholar 

  31. Botet, R. Jullien, R. & Kolb, M. J. Phys. A 17, L75–L79 (1984).

    Article  ADS  Google Scholar 

  32. Botet, R. & Jullien, R. J. Phys. A 17, 2517–2530 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  33. Ball, R. & Witten, T. J. statist. Phys. 36, 863–866 (1984).

    Article  ADS  Google Scholar 

  34. Langer, J. Rev. mod. Phys. 52, 1–28 (1980).

    Article  ADS  CAS  Google Scholar 

  35. Mullins, W. & Sekerka, R. J. appl. Phys. 34, 323–329 (1963).

    Article  ADS  CAS  Google Scholar 

  36. Turkevich, L. & Scher, H. Phys. Rev. Lett. 55, 1026–1031 (1985).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  37. Halsey, T., Meakin, P. & Procaccia, I. Phys. Rev. Lett. 56, 854–857 (1986).

    Article  ADS  CAS  Google Scholar 

  38. Kadanoff, L. J. statist. Phys. 39, 267–283 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  39. Viscek, T. Phys. Rev. Lett. 53, 2281–2284 (1984).

    Article  ADS  Google Scholar 

  40. Brower, R., Kessler, D., Koplik, J. & Levine, H. Phys. Rev. A29, 1335–1342 (1984).

    Article  ADS  CAS  Google Scholar 

  41. Ben-Jacob, E., Goldenfeld, N., Langer, J. & Schon, G. Phys. Rev. A29, 330–340 (1984).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  42. Ball, R. & Brady, R. J. Phys. A 18, L809–L813 (1985).

    Article  ADS  Google Scholar 

  43. Ball, R., Brady, R., Rossi, G. & Thompson, B. Phys. Rev. Lett. 55, 1406–1409 (1985).

    Article  ADS  CAS  Google Scholar 

  44. Sander, L., Ramanlal, P. & Ben-Jacob, E. Phys. Rev. A32, 3160–3163 (1985).

    Article  ADS  CAS  Google Scholar 

  45. Grier, D., Ben-Jacob, E., Clarke, R. & Sander, L. Phys. Rev. Lett. 56, 1264–1267 (1986).

    Article  ADS  CAS  Google Scholar 

  46. Sawada, Y., Doughtery, A. & Gollub, J. Phys. Rev. Lett. 56, 1260–1263 (1986).

    Article  ADS  CAS  Google Scholar 

  47. Kertesz, J. & Vicsek, T. J. Phys. A 19, L257–L262 (1986).

    ADS  Google Scholar 

  48. Nittmann, J. & Stanley, H. E. Nature 321, 663–668 (1986).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sander, L. Fractal growth processes. Nature 322, 789–793 (1986). https://doi.org/10.1038/322789a0

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1038/322789a0

  • Springer Nature Limited

This article is cited by

Navigation