Abstract
The neologism 'multifractal phenomena' describes the concept that different regions of an object have different fractal properties. Multifractal scaling provides a quantitative description of a broad range of heterogeneous phenomena.
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References
Mandelbrot, B. B. The Fractal Geometry of Nature (Freeman, San Francisco, 1982).
Family, F. & Landau, D. P. (eds) Kinetics of Aggregation and Gelation (Elsevier, Amsterdam, 1984).
Stanley, H. E. & Ostrowsky, N. (eds) On Growth and Form: Fractal and Non-Fractal Patterns in Physics (Nijhoff, Dordrecht, 1985).
Boccara, N. & Daoud, M. (eds) Physics of Finely Divided Matter (Springer, Heidelberg, 1985).
Pynn, R. & Skjeltorp, A. (eds) Scaling Phenomena in Disordered Systems (Plenum, New York, 1986).
Pietronero, L. & Tosatti, E. (eds) Fractals in Physics (North-Holland, Amsterdam, 1986).
Stanley, H. E. Introduction to Fractal Phenomena (Oxford University Press, in the press).
Meakin, P. CRC Critical Rev. in Solid State and Materials Sciences 13, 143–189 (1987).
Witten, T. A. & Sander, L. M. Phys. Rev. Lett. 47, 1400–1403 (1981); Phys. Rev. B 27, 5686–5697 (1983).
Sander, L. M. Nature 332, 789–793 (1986); Scient. Am. 256, 94–100 (1986).
Brady, R. M. & Ball, R. C. Nature 309, 225–229 (1984).
Matsushita, M., Sano, M., Hakayawa, Y., Honjo, H. & Sawada, Y. Phys. Rev. Lett. 53, 286–289 (1984).
Elam, W. T. et al. Phys. Rev. Lett. 54, 701 (1985).
Ben-Jacob, E. et al. Phys. Rev. Lett. 55, 1315–1318 (1985).
Buka, A., Kertèsz, J. & Vicsek, T. Nature 323, 424–425 (1986).
Couder, Y., Cardoso, O., Dupuy, D., Tavernier, P. & Thom, W. Europhys. Lett. 2, 437–443 (1986).
Nittmann, J. N. & Stanley, H. E. Nature 321, 663–668 (1986).
Niemeyer, L., Pietronero, L. & Wiesmann, H. J. Phys. Rev. Lett. 52, 1033–1036 (1984).
Pietronero, L. & Wiesmann, H. J. J. statist. Phys. 36, 909–916 (1984).
Nittemann, J., Daccord, G. & Stanley, H. E. Nature 314, 141–144 (1985).
Daccord, G., Nittmann, J. & Stanley, H. E. Phys. Rev. Lett. 56, 336–339 (1986).
Chen, J. D. & Wilkinson, D. Phys. Rev. Lett. 55, 1892–1895 (1985).
Måløy, K. J., Feder, J. & Jøssang, T. Phys. Rev. Lett. 55, 2688–2691 (1985).
Van Damme, H., Obrecht, F., Levitz, P., Gatineau, L. & Laroche, C. Nature 320, 731–733 (1986).
Daccord, G. Phys. Rev. Lett. 58, 479–482 (1987).
Daccord, G. & Lenormand, R. Nature 325, 41–43 (1987).
Meakin, P., Coniglio, A., Stanley, H. E. & Witten, T. A. Phys. Rev. A 34, 3325–3340 (1986).
Stanley, H. E. Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, 1971).
Meakin, P., Stanley, H. E., Coniglio A. & Witten, T. A. Phys. Rev. A 32, 2364–2369 (1985).
Halsey, T. C., Meakin, P. & Procaccia, I. Phys. Rev. Lett. 56, 854–857 (1986).
Amitrano, C., Coniglio, A. & di Liberto, F. Phys. Rev. Lett. 57, 1016–1019 (1987).
Nittmann, J., Stanley, H. E., Touboul, E. & Daccord, G. Phys. Rev. Lett. 58, 619 (1987).
Jensen, M. H., Kadanoff, L. P., Libchaber, A., Procaccia, I. & Stavans, J. Phys. Rev. Lett. 55, 2798–2801 (1985).
Coniglio, A. in On Growth and Form: Fractal and Non-Fractal Patterns in Physics (eds Stanley, H. E. & Ostrowsky, N.) 101 (Nijhoff, Doredrecht, 1985).
Halsey, T. C., Jensen, M. H., Kadanoff, L. P., Procaccia, I. & Shraiman, B. Phys. Rev. A 33, 1141–1151 (1986).
Coniglio, A. in Fractals in Physics (eds Pietronero, L. & Tosatti, E.) (North-Holland, Amsterdam, 1986).
Coniglio, A. Physica A 140, 51–61 (1986).
Meakin, P. Phys. Rev. A 34, 710–713 (1986).
Grassberger, P. & Procaccia, I. Physica 13D, 34–54 (1984).
Grassberger, P. Phys. Lett. 107A, 101–105 (1985).
Benzi, R., Paladin, G., Parisi, G. & Vulpiani, A. J. Phys. A 17, 3521–3531 (1984); Ibid. 18, 2157–2165 (1985).
Badii, R. & Politi, A. J. statist. Phys. 40, 725–750 (1985).
Stauffer, D. Introduction to Percolation Theory (Taylor and Francis, Philadelphia, 1985).
Rammal, R., Tannous, C., Breton, P. & Tremblay, A. M. S. Phys. Rev. Lett. 54, 1718–1721 (1985).
de Arcangelis, L., Redner, S. & Coniglio, A. Phys. Rev. B 31, 4725–4727 (1985); Phys. Rev. B 34, 4656–4673 (1986).
Rammal, R., Tannous, C. & Tremblay, A. M. S. Phys. Rev. A 31, 2662–2671 (1985).
Rammal, R. J. Phys., Paris 46, L129 (1985); Phys. Rev. Lett. 55, 1428 (1985).
Meir, Y., Blumenfeld, R., Aharony, A. & Harris, A. B. Phys. Rev. B 34, 3424–3428 (1986).
Blumenfeld, R., Meir, Y., Harris, A. B. & Aharony, A. J. Phys. A 19, L791–L796 (1986).
Blumenfeld, R., Meir, Y., Aharony, A. & Harris, A. B. Phys. Rev. B 35, 3524–3535 (1987).
Meir, Y. & Aharony, A. Phys. Rev. A 37, 596–600 (1988).
Rammal, R. & Tremblay, A.-M. S. Phys. Rev. Lett. 58, 415–418 (1987).
Fourcade, B., Breton, P. & Tremblay, A.-M. S. Phys. Rev. Lett. (in the press).
Stanley, H. E. J. Phys. A 10, L211–L220 (1977).
Coniglio, A. Phys. Rev. Lett. 46, 250–253 (1981).
Coniglio, A. J. Phys. A 15, 3829–2844 (1981).
Pike, R. & Stanley, H. E. J. Phys. A 14, L169–L177 (1981).
Herrmann, H. J. & Stanley, H. E. Phys. Rev. Lett. 53, 1121–1124 (1984).
Alstrøm, P. in Time-Dependent Effects in Disordered Materials (eds Pynn, R. & Riste, T.) 185–193 (Plenum, New York, 1987); Phys. Rev. A 37, 1378–1380 (1988); Phys. Rev. A 36, 827–833 (1987).
Frisch, U., Sulem, P. & Nelkin, M. J. Fluid Mech. 87, 719–736 (1978).
Meakin, P. Phys. Rev. A 36, 2833–2837; J. Phys. A 20, L779–L784 (1987).
Lovejoy, S. & Schertzer, D. Bull. Am. met. Soc. 67, 221 (1986).
Lovejoy, S., Schertzer, D. & Tsonis, A. A. Science 231, 1036–1038 (1987).
Schertzer, D. & Lovejoy, S. in IUTAM Symposium on Turbulence and Chaotic Phenomena in Fluids, Kyoto, Japan 141–144 (1983).
Mandelbrot, B. B. J. Fluid Mech. 62, 331–358 (1974).
Mandelbrot, B. B. in Proc. 13th IUPAP Conference on Statistical Physics (eds Cabib, E., Kuper, C. G. & Reiss, L.) (Hilger, Bristol, 1978).
Grassberger, P. Phys. Lett. A 97, 277–230 (1983).
Hentschel, H. G. E. & Procaccia, I. Physica 8D, 435–444 (1983).
Frisch, U. & Parisi, G. in Turbulence and Predictability in Geophysical Fluid Dynamics and Climate Dynamics Proc. Int. School of Physics Enrico Fermi, Course LXXXVIII (eds Ghil, M., Benzi, R. & Parisi G.) (North-Holland, Amsterdam, 1985).
Katzen, D. & Procaccia, I. Phys. Rev. Lett. 58, 1169–1172 (1987).
Cates, M. E. & Witten, T. A. Phys. Rev. Lett. 56, 2497–2500 (1986); Phys. Rev. A 35, 1809–1824 (1987).
Evertsz, C. & Lyklema, J. W. Phys. Rev. Lett. 58, 397–400 (1987).
Lyklema, J. W., Evertsz, C. & Pietronero, L. Europhys. Lett. 2, 77–82 (1986).
Lyklema, J. W. & Evertsz, C. J. Phys. A 19, L895–L900 (1986).
Pietronero, L. & Siebesma, A. Phys. Rev. Lett. 57, 1098–1101 (1986).
Waissmann, H. & Havlin, S. Phys. Rev. B 37, 5994–5997 (1988).
Trus, B., Havlin, S. & Stauffer, D. J. Phys. A 20, 6627–6630 (1987).
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Stanley, H., Meakin, P. Multifractal phenomena in physics and chemistry. Nature 335, 405–409 (1988). https://doi.org/10.1038/335405a0
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DOI: https://doi.org/10.1038/335405a0
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