Fractal structures

Mandelbrot, 1975 Mandelbrot, 1977 Mandelbrot, 1982 Mandelbrot, 1987, Vol. 5, 579 Feder, 1988 Mandelbrot, 1986, 3 Vicsek, 1983, J. Phys. A, 16, L647, 10.1088/0305-4470/16/17/003 Fournier D'Albe, 1907 Broadbent, 1957, 53, 629 Hammersley, 1957, 53, 642 Essam, 1972, Vol. 2, 192 Kirkpatrick, 1973, Rev. Mod. Phys., 45, 574, 10.1103/RevModPhys.45.574 Stauffer, 1979, Phys. Rep., 54, 1, 10.1016/0370-1573(79)90060-7 Stauffer, 1985 Leath, 1976, Phys. Rev. B, 14, 5046, 10.1103/PhysRevB.14.5046 Alexandrowicz, 1980, Phys. Lett., 80A, 284, 10.1016/0375-9601(80)90023-7 den Nijs, 1979, J. Phys. A, 12, 1857, 10.1088/0305-4470/12/10/030 Pearson, 1980, Phys. Rev. B, 22, 2579, 10.1103/PhysRevB.22.2579 Nienhuis, 1980, J. Phys A, 13, L189, 10.1088/0305-4470/13/6/005 R.M. Ziff and G. Stell, unpublished. Witten, 1981, Phys. Rev. Lett., 47, 1400, 10.1103/PhysRevLett.47.1400 Kremer, 1985, Phys. Rev. Lett., 54, 267, 10.1103/PhysRevLett.54.267 Djordjevic, 1983, J. Phys. A, 16, L519, 10.1088/0305-4470/16/14/006 Lyklema, 1985, Phys. Rev. B, 31, 3182, 10.1103/PhysRevB.31.3182 Kantor, 1984, J. Phys. (Paris), 45, L675, 10.1051/jphyslet:019840045013067500 Witten, 1983, Phys. Rev. B, 27, 5686, 10.1103/PhysRevB.27.5686 Elam, 1985, Phys. Rev. Lett., 54, 701, 10.1103/PhysRevLett.54.701 Jullien, 1987 Meakin, 1988, Vol. 12, 335 Meakin, 1983, Phys. Rev. Lett., 51, 1119, 10.1103/PhysRevLett.51.1119 Kolb, 1983, Phys. Rev. Lett., 51, 1123, 10.1103/PhysRevLett.51.1123 Martin, 1987, J. Appl. Crystallogr., 20, 61, 10.1107/S0021889887087107 J. Teixeira in On Growth and Form: Fractal and Non-Fractal Patterns in Physics, H. E. Stanley and N. Ostrowsky, eds., NATO ASI series E100, Martinus Nijhoff, p. 145. Schmidt, 1989, 67 R. Klein, D.A. Weitz, M.Y. Lin, H.M. Lindsay, R.C. Ball and P. Meakin, preprint. Weitz, 1984, Phys. Rev. Lett., 52, 1433, 10.1103/PhysRevLett.52.1433 Kjems, 1985, 133 Schaefer, 1984, Phys. Rev. Lett., 52, 2371, 10.1103/PhysRevLett.52.2371 Sinha, 1984, 87 Vacher, 1988, Phys,. Rev. B, 37, 6500, 10.1103/PhysRevB.37.6500 Allain, 1986, Phys. Rev. B, 33, 3566, 10.1103/PhysRevB.33.3566 Lin, 1989, Nature, 339, 360, 10.1038/339360a0 Dimon, 1986, Phys. Rev. Lett., 57, 595, 10.1103/PhysRevLett.57.595 Ramsay, 1986, Chem. Soc. Rev., 15, 335, 10.1039/cs9861500335 Martin, 1985, Phys. Rev. A, 31, 1180, 10.1103/PhysRevA.31.1180 Schmidt, 1982, J. Appl. Crystallogr., 15, 567, 10.1107/S002188988201259X Martin, 1986, J. Appl. Crystallogr., 19, 25, 10.1107/S0021889886090052 Guinier, 1955 Aubert, 1986, Phys. Rev. Lett., 56, 738, 10.1103/PhysRevLett.56.738 Kolb, 1984, J. Physique Lett., 45, L977, 10.1051/jphyslet:019840045020097700 Jullien, 1984, J. Phys. A, 17, L639, 10.1088/0305-4470/17/12/003 Brown, 1985, J. Phys. A, 18, L517, 10.1088/0305-4470/18/9/006 Meakin, 1987, Phys. Rev. A, 36, 5498, 10.1103/PhysRevA.36.5498 Meakin, 1988, Phys. Rev. A, 38, 2110, 10.1103/PhysRevA.38.2110 Bale, 1984, 79 Bale, 1984, Phys. Rev. Lett., 53, 596, 10.1103/PhysRevLett.53.596 Hentschel, 1983, Physica, 8D, 435 Meakin, 1984, Chem. Phys., 91, 391, 10.1016/0301-0104(84)80071-3 Argoul, 1989, Phys. Rev. Lett., 61, 2558, 10.1103/PhysRevLett.61.2558 Li, 1989, Phys. Rev. Lett., 63, 1322, 10.1103/PhysRevLett.63.1322 Tel, 1987, J, Phys. A, 20, L835, 10.1088/0305-4470/20/13/005 Tel, 1989, Physica A, 159, 155, 10.1016/0378-4371(89)90563-3 Tel, 1988, Z. Naturforsch, 43a, 1154, 10.1515/zna-1988-1221 Hansen, 1988, 310 J. Feder, private communication. Mandelbrot, 1985, Physca Scripta, 32, 257, 10.1088/0031-8949/32/4/001 Hurst, 1951, Trans Am. Soc.Civil Eng., 116, 770, 10.1061/TACEAT.0006518 Hurst, 1965 Voss, 1986 Wong, 1985, Phys. Rev B, 32, 7417, 10.1103/PhysRevB.32.7417 S. Alexander, preprint. Mandelbrot, 1968, Water Resour. Res., 4, 909, 10.1029/WR004i005p00909 Mandelbrot, 1969, Water Resour. Res., 5, 321, 10.1029/WR005i002p00321 Mandelbrot, 1969, Water Resour. Res., 5, 228, 10.1029/WR005i001p00228 Mandelbrot, 1969, Water Resour. Res., 5, 242, 10.1029/WR005i001p00242 Mandelbrot, 1969, Water Resour. Res., 5, 260, 10.1029/WR005i001p00260 Mandelbrot, 1969, Water Resour. Res., 5, 967, 10.1029/WR005i005p00967 J. Froyland, J. Feder and T. Jossang, to be published. Dubuc, 1989, Phys. Rev. A, 39, 1500, 10.1103/PhysRevA.39.1500 Berry, 1980, 370, 459 Tricot, 1986, Gaz Sci. Math, Quebec, 10, 3 Mandelbrot, 1968, SIAM Rev., 10, 422, 10.1137/1010093 Farmer, 1985, Phys. Rev. Lett., 55, 351, 10.1103/PhysRevLett.55.351 Eykholt, 1986, Phys. Rev. Lett., 57, 2333, 10.1103/PhysRevLett.57.2333 Grebogi, 1985, Physics Lett. A, 110, 1, 10.1016/0375-9601(85)90220-8 Pfeifer, 1989, 11 Stanley, 1988, Nature, 335, 6189, 10.1038/335405a0 Mandelbrot, 1974, J. Fluid Mech., 62, 331, 10.1017/S0022112074000711 Mandelbrot, 1989, 3 Halsey, 1986, Phys. Rev. A, 33, 1141, 10.1103/PhysRevA.33.1141 Meakin, 1986, Phys. Rev. A, 34, 710, 10.1103/PhysRevA.34.710 Meakin, 1987, Phys. Rev. A, 35, 2234, 10.1103/PhysRevA.35.2234 Mandelbrot, 1988, 279 Chhabra, 1989, Phys Rev. Lett., 62, 1327, 10.1103/PhysRevLett.62.1327 A. Atmanspacker, H. Scheingraber and G. Wiedenmann, preprint. Amritkar, 1988, Phys. Rev. Lett., 60, 245, 10.1103/PhysRevLett.60.245 Chhabra, 1989, Phys. Rev. A, 40, 4593, 10.1103/PhysRevA.40.4593 M.E. Cates and J.M. Deutch, 35, 4907 (1987). S.J. Lee and T.C. Halsey, preprint (1990). Mandelbrot, 1990, 17 Bak, 1987, Phys. Rev. Lett., 59, 381, 10.1103/PhysRevLett.59.381 Bak, 1988, Phys. Rev. A, 38, 364, 10.1103/PhysRevA.38.364 Tang, 1988, J. Stat. Phys., 60, 2347 Tang, 1988, J. Stat. Phys., 51, 797, 10.1007/BF01014884 Hwa, 1989, Phys. Rev. Lett., 62, 1813, 10.1103/PhysRevLett.62.1813 Dhar, 1989, Phys. Rev. Lett., 63, 1659, 10.1103/PhysRevLett.63.1659 Zhang, 1989, Phys. Rev. Lett., 63, 470, 10.1103/PhysRevLett.63.470 Kadanoff, 1989, Phys. Rev. A, 39, 6524, 10.1103/PhysRevA.39.6524 Bak, 1989, Physica D, 38, 5, 10.1016/0167-2789(89)90166-8 Eckmann, 1989, Phys. Rev., 39, 3185, 10.1103/PhysRevA.39.3185 Eckmann, 1990, Phys. Rev. Lett., 65, 52, 10.1103/PhysRevLett.65.52 Meakin, 1985, Phys. Rev. A, 31, 1195, 10.1103/PhysRevA.31.1195 Turkevich, 1985, Phys. Rev. Lett., 55, 1026, 10.1103/PhysRevLett.55.1026 Halsey, 1986, Phys. Lett., 56, 854, 10.1103/PhysRevLett.56.854 Ball, 1986, Physica, 104A, 62, 10.1016/0378-4371(86)90205-0 Ball, 1989, 423, 1 Muthukumar, 1983, Phys. Rev. Lett., 50, 839, 10.1103/PhysRevLett.50.839 Ball, 1984, Phys. Rev. A, 29, 2966, 10.1103/PhysRevA.29.2966 Gould, 1983, Phys. Rev. Lett., 50, 686, 10.1103/PhysRevLett.50.686 Pietronero, 1988, Phys. Rev. Lett., 61, 861, 10.1103/PhysRevLett.61.861 Eden, 1961 Jullien, 1985, Phys Rev. Lett., 54, 2055, 10.1103/PhysRevLett.54.2055 Jullien, 1985, J. Phys. A, 18, 2279, 10.1088/0305-4470/18/12/026 Freche, 1985, J. Phys. A, 15, L1163, 10.1088/0305-4470/18/18/009 Hirsch, 1986, J. Phys. A, 19, L251, 10.1088/0305-4470/19/5/007 Zabolitzky, 1986, Phys. Rev. A, 34, 1523, 10.1103/PhysRevA.34.1523 Meakin, 1986, Europhys. Lett., 1, 609, 10.1209/0295-5075/1/12/001 Richardson, 1973, 74, 515 Meakin, 1988, Phys. Rev. A, 38, 418, 10.1103/PhysRevA.38.418 Tang, 1985, Phys. Rev. A, 31, 1977, 10.1103/PhysRevA.31.1977 Kertsz, 1986, J. Phys. A, 19, 2257 Forrest, 1979, J. Phys. A, 12, L109, 10.1088/0305-4470/12/5/008 Jullien, 1986, Ann. Telecommun., 41, 343, 10.1007/BF02997881 Sander, 1986, Nature, 322, 789, 10.1038/322789a0 Meakin, 1988, Advances in Colloid and Interface Sci., 28, 249, 10.1016/0001-8686(87)80016-7 Meakin, 1988, Ann. Rev. Phys. Chem., 39, 237, 10.1146/annurev.pc.39.100188.001321 Vicsek, 1988 Witten, 1986, Science, 232, 1607, 10.1126/science.232.4758.1607 Jullien, 1987 Meakin, 1985, J. Phys. A, 18, L661, 10.1088/0305-4470/18/11/006 Ball, 1985, J. Phys. A, 18, L809, 10.1088/0305-4470/18/13/014 Tolman, 1989, Phys. Rev. A, 40, 428, 10.1103/PhysRevA.40.428 Meakin, 1983, Phys Rev. A, 27, 2616, 10.1103/PhysRevA.27.2616 Meakin, 1984, Phys. Rev. B, 30, 4207, 10.1103/PhysRevB.30.4207 Jullien, 1984, J. Phys. (Paris), 45, 395, 10.1051/jphys:01984004503039500 Meakin, 1986, Phys. Rev. A, 34, 2558, 10.1103/PhysRevA.34.2558 K. J. Maloy, private communication. Matsushita, 1985, Phys. Rev. A, 32, 3814, 10.1103/PhysRevA.32.3814 Helgesen, 1987, 89 van Damme, 1989, 199 Racz, 1983, Phys. Rev. Lett., 51, 2382, 10.1103/PhysRevLett.51.2382 Meakin, 1985, Phys. Rev. A, 32, 1026 Halsey, 1985, Phys. Rev. A, 32, 2547, 10.1103/PhysRevA.32.2546 Kolb, 1985, J. Phys. (Paris) Lett., 46, L632, 10.1051/jphyslet:019850046014063100 Meakin, 1983, Phys. Rev. A, 27, 604, 10.1103/PhysRevA.27.604 Meakin, 1983, Phys. Rev. A, 27, 2495 Tokayama, 1984, Phys. Lett., 100A, 337, 10.1016/0375-9601(84)91083-1 Matsushita, 1986, J. Phys. Soc, Japan, 55, 2618, 10.1143/JPSJ.55.2618 Matsushita, 1987, Phys. Rev. Lett., 59, 86, 10.1103/PhysRevLett.59.86 Honda, 1986, J. Phys. Soc. Japan, 55, 2479, 10.1143/JPSJ.55.2479 Leyvraz, 1985, J. Phys. A, 18, L941, 10.1088/0305-4470/18/15/007 Turkevich, 1986, Phys. Rev. A, 33, 786, 10.1103/PhysRevA.33.786 Morse, 1963 Meakin, 1986, Phys. Rev. A, 33, 3371, 10.1103/PhysRevA.33.3371 Ball, 1985, Phys. Rev. Lett., 55, 1406, 10.1103/PhysRevLett.55.1406 Meakin, 1985, Phys. Rev. A, 32, 2364, 10.1103/PhysRevA.32.2364 Meakin, 1986, Phys. Rev A, 34, 3325, 10.1103/PhysRevA.34.3325 Amitrano, 1986, Phys. Rev. Lett., 57, 1016, 10.1103/PhysRevLett.57.1016 Lee, 1988, Phys. Rev. Lett., 61, 2945, 10.1103/PhysRevLett.61.2945 Lee, 1989, Phys. Rev. A, 39, 6545, 10.1103/PhysRevA.39.6545 Blumenfeld, 1989, Phys. Rev. Lett., 62, 2977, 10.1103/PhysRevLett.62.2977 Harris, 1990, Phys. Rev. A, 41, 971, 10.1103/PhysRevA.41.971 Nagatini, 1987, J. Phys. A, 20, L381, 10.1088/0305-4470/20/6/008 Nagatini, 1987, Phys. Rev. A, 35, 2765, 10.1103/PhysRevA.35.2765 Procaccia, 1988, Phys. Rev. Lett., 60, 2511, 10.1103/PhysRevLett.60.2511 Alstrom, 1988, 340 Gould, 1983, Phys. Rev. Lett., 50, 686, 10.1103/PhysRevLett.50.686 Niemeyer, 1984, Phys. Rev. Lett., 52, 1033, 10.1103/PhysRevLett.52.1033 Meakin, 1986, J. Theor. Biol., 118, 101, 10.1016/S0022-5193(86)80011-X Matsushita, 1986, J. Phys. Soc. Japan, 55, 2618, 10.1143/JPSJ.55.2618 Hayakawa, 1986, J. Phys. Soc. Japan, 55, 2479, 10.1143/JPSJ.55.2479 Tolman, 1989, Physica A, 158, 801, 10.1016/0378-4371(89)90492-5 Evertsz, 1989, Laplacian Fractals Wiesmann, 1986, 151 Nittmann, 1986, Nature, 321, 663, 10.1038/321663a0 Meakin, 1986, 423, 133 Vold, 1963, J. Colloid Sci., 18, 684, 10.1016/0095-8522(63)90061-8 Sutherland, 1966, J. Colloid Interface Sci., 22, 300, 10.1016/0021-9797(66)90037-3 Meakin, 1985, J. Colloid Interface Sci., 105, 240, 10.1016/0021-9797(85)90364-9 Bensimon, 1984, Phys. Lett., 102A, 238, 10.1016/0375-9601(84)90701-1 Vold, 1959, J. Colloid Sci., 14, 168, 10.1016/0095-8522(59)90041-8 Vold, 1959, J. Phys. Chem., 63, 1608, 10.1021/j150580a011 Jullien, 1987, Europhys. Lett., 4, 1385, 10.1209/0295-5075/4/12/008 Voss, 1984, J. Phys. A, 17, L373, 10.1088/0305-4470/17/7/001 Saleur, 1987, Phys. Rev. Lett., 58, 2325, 10.1103/PhysRevLett.58.2325 Coniglio, 1987, Phys. Rev. B, 35, 3617, 10.1103/PhysRevB.35.3617 Ziff, 1986, Phys. Rev. Lett., 56, 545, 10.1103/PhysRevLett.56.545 Sapoval, 1985, J. Phys. (Paris), 46, 2149 Grossman, 1986, J. Phys. A, 19, L745, 10.1088/0305-4470/19/12/009 Havlin, 1984, J. Phys. A, 17, L957, 10.1088/0305-4470/17/18/004 Kirkpatrick, 1978, AIP Conf. Proc., 40, 99, 10.1063/1.31180 Stanley, 1977, J. Phys. A, 10, L211, 10.1088/0305-4470/10/11/008 Meakin, 1990, Europhys. Lett., 11, 7, 10.1209/0295-5075/11/1/002 Family, 1985, J. Phys. A, 18, L75, 10.1088/0305-4470/18/2/005 Henderson, 1974, J. Appl. Phys. Lett., 25, 641, 10.1063/1.1655341 Kim, 1977, Thin Solid Films, 47, 155, 10.1016/0040-6090(77)90355-8 Dirks, 1977, Thin Solid Films, 47, 219, 10.1016/0040-6090(77)90037-2 Leamy, 1978, J. Appl. Phys., 49, 33430, 10.1063/1.325249 Leamy, 1980 Meakin, Critical Reviews in Solid State and Materials Science, 13, 143, 10.1080/01611598608241265 Personne, 1987, J. Phys. (Paris), 48, C1, 10.1051/jphys:019870048010100 Amar, 1990, Phys. Rev. Lett., 64, 543, 10.1103/PhysRevLett.64.543 Kardar, 1986, Phys. Rev. Lett., 56, 889, 10.1103/PhysRevLett.56.889 Meakin, 1986, Phys. Rev. A, 34, 5091, 10.1103/PhysRevA.34.5091 Kim, 1989, Phys. Rev. Lett., 62, 2289, 10.1103/PhysRevLett.62.2289 Krug, 1987, Phys. Rev. A, 36, 5465, 10.1103/PhysRevA.36.5465 J. Krug and H. Spohn, preprint. Halpin-Healy, 1989, Phys. Rev. Lett., 62, 442, 10.1103/PhysRevLett.62.442 Wolf, 1988, J. Phys. A, 20, 747 Kertesz, 1988, J. Phys. A, 32, 747, 10.1088/0305-4470/21/3/030 Krug, 1989, J. Phys. A, 22, L769, 10.1088/0305-4470/22/16/002 Meakin, 1987, Europhys. Lett., 4, 1385, 10.1209/0295-5075/4/12/008 Meakin, 1988, Phys. Rev. A, 38, 994, 10.1103/PhysRevA.38.994 Krug, 1989, Phys. Rev. A, 40, 2064, 10.1103/PhysRevA.40.2064 Burgers, 1974 Jullien, 1987, J. Phys. (Paris), 48, 1651, 10.1051/jphys:0198700480100165100 Family, 1986, J. Phys. A, 19, L441, 10.1088/0305-4470/19/8/006 Edwards, 1982, 381, 17 P. Meakin and R. Jullien, unpublished. G.Y. Onoda and J. Toner, Phys. Rev. Lett.57, 1340. Pellegrini, 1990, Phys. Rev. Lett., 64, 1745, 10.1103/PhysRevLett.64.1745 J.P. Pellegrini and R. Jullien, preprint. Yan, 1990, Phys. Rev. Lett., 64, 926, 10.1103/PhysRevLett.64.926 Amar, 1990, Phys. Rev. A, 41, 3399, 10.1103/PhysRevA.41.3399 Krug, 1990, Phys. Rev. Lett., 64, 2332, 10.1103/PhysRevLett.64.2332 Kim, 1990, Phys. Rev. Lett., 64, 2333, 10.1103/PhysRevLett.64.2333 Huse, 1990, Phys. Rev. A, 41, 7075, 10.1103/PhysRevA.41.7075 J. Krug and P. Meakin, preprint. van Beijeren, 1985, Phys. Rev. Lett., 54, 2026, 10.1103/PhysRevLett.54.2026 Sivashinski, 1979, Acta Astronautica, 6, 569, 10.1016/0094-5765(79)90019-5 S. Zalesky, Physica D, to be published. Kardar, 1985, Phys. Rev. Lett., 55, 2923, 10.1103/PhysRevLett.55.2923 Weeks, 1973, Phys. Rev. Lett., 31, 549, 10.1103/PhysRevLett.31.549 Saito, 1984, 223 Jasnow, 1984, Rep. Prog. Phys., 47, 1059, 10.1088/0034-4885/47/9/001 Gilmer, 1976, J. Crystal Growth, 35, 15, 10.1016/0022-0248(76)90209-8 Jiang, 1988, Phys. Rev. B, 38, 6766, 10.1103/PhysRevB.38.6766 Bedeaux, 1985, Physica, 130A, 88, 10.1016/0378-4371(85)90099-8 Buff, 1983, Phys. Rev. Lett., 15, 621, 10.1103/PhysRevLett.15.621 Bedeaux, 1985, J. Chem. Phys., 82, 972, 10.1063/1.448474 Metropolis, 1953, J. Chem. Phys., 21, 1087, 10.1063/1.1699114 1984 Bales, 1990, Science, 249, 264, 10.1126/science.249.4966.264 P. Meakin, unpublished. Meakin, 1986, J. Chem. Phys., 85, 2320, 10.1063/1.451129 Patterson, 1984, Phys. Rev. Lett., 18, 1621, 10.1103/PhysRevLett.52.1621 J. Krug and P. Meakin, preprint. Kantor, 1987, Phys. Rev. Lett., 58, 2774, 10.1103/PhysRevLett.58.2774 Kantor, 1987, Phys. Rev. A, 36, 4020, 10.1103/PhysRevA.36.4020 Kantor, 1986, Phys. Rev. Lett., 57, 791, 10.1103/PhysRevLett.57.791 Kantor, 1987, Phys. Rev. A, 35, 3056, 10.1103/PhysRevA.35.3056 Plischke, 1988, Phys. Rev. A, 38, 4943, 10.1103/PhysRevA.38.4943 Nelson, 1988, 193 Plischke, 1988, Phys. Rev. A, 38, 4943, 10.1103/PhysRevA.38.4943 Termonia, 1986, Nature, 320, 429, 10.1038/320429a0 Statistical Models for the Fracture of Disordered Media, H. Herrmann, ed. Kardar, 1990 Villain, 1984, Phys. Rev. Lett., 52, 1543, 10.1103/PhysRevLett.52.1543 Kardar, 1989, Europhys. Lett., 8, 233, 10.1209/0295-5075/8/3/005 Grinsein, 1984, Phys. Res. B, 29, 6389, 10.1103/PhysRevB.29.6389 Buinsma, 1984, Phys. Rev. Lett., 52, 1547, 10.1103/PhysRevLett.52.1547 Sapoval, 1985, J. Phys. (Paris) Lett., 46, L149, 10.1051/jphyslet:01985004604014900 Bunde, 1985, J. Phys. A, 18, L285, 10.1088/0305-4470/18/6/004 Rosso, 1985, Phys. Rev. B, 32, 6053, 10.1103/PhysRevB.32.6053 R. M. Ziff and B. Sapoval, preprint. Rosso, 1986, Phys. Rev. Lett., 57, 3195, 10.1103/PhysRevLett.57.3195 Kolb, 1987, Europhys. Lett., 3, 33, 10.1209/0295-5075/3/1/006 Kawasaki, 1972, Vol. 2, 442 Kawasaki, 1976, Vol. 5a, 165 P. Meakin, unpublished. Meakin, 1986, Phys. Rev. A, 33, 1365, 10.1103/PhysRevA.33.1365 Meakin, 1985, Phys. Rev. A, 32, 2364, 10.1103/PhysRevA.32.2364 Meakin, 1986, Phys. Rev. A, 34, 3325, 10.1103/PhysRevA.34.3325 Amitrano, 1986, Phys. Rev. Lett., 57, 1016, 10.1103/PhysRevLett.57.1016 Nagatini, 1987, Phys. Rev. A, 36, 5812, 10.1103/PhysRevA.36.5812 Ball, 1985, Phys. Rev. Lett., 55, 1406, 10.1103/PhysRevLett.55.1406 R.C. Ball and M. Blunt, preprint. Hayakawa, 1987, Phys. Rev., 36, 1963, 10.1103/PhysRevA.36.1963 M. Blunt and R. C. Ball, preprint Meakin, 1987, Phys. Rev. A, 36, 325, 10.1103/PhysRevA.36.325 Cates, 1986, Phys. Rev. Lett., 56, 2497, 10.1103/PhysRevLett.56.2497 Meakin, 1987, J. Chem. Phys., 86, 4648, 10.1063/1.452705 Meakin, 1988, J. Chem. Phys., 88, 2042, 10.1063/1.454080 Blunt, 1989, Phys. Rev. A, 39, 5801, 10.1103/PhysRevA.39.5801 de Arcangelis, 1983, Phys. Rev. B, 31, 4725, 10.1103/PhysRevB.31.4725 Rammal, 1985, Phys. Rev. Lett., 54, 1718, 10.1103/PhysRevLett.54.1718 Blumenfeld, 1987, Phys. Rev. B, 35, 3524, 10.1103/PhysRevB.35.3524 Hansen, 1989, J. Phys. (France), 50, 733, 10.1051/jphys:01989005007073300 Cates, 1987, Phys. Rev. A, 35, 4907, 10.1103/PhysRevA.35.4907 C. Meneveau and A. Chhabra, preprint (1989). S.J. Lee and T.C. Halsey, preprint (1990). Doud M. and J. E. Martin in The Fractal Approach to Heterogeneous Chemistry: Surfaces, Colloids, Polymers D. Avnir, edp. 109. P. Meakin, Encyclopedia of Polymer Science and Engineering. Brinker, 1989 Stauffer, 1982, Vol. 44 Stapleton, 1980, Phys. Rev. Lett., 45, 1456, 10.1103/PhysRevLett.45.1456 Peebles, 1989, Physica D, 38, 273, 10.1016/0167-2789(89)90205-4 Pietronero, 1987, Physica, 144, 257, 10.1016/0378-4371(87)90191-9 Coleman, 1990, 349 de Gennes, 1979 de Gennes, 1980, C.R. Acad. Sci., 291, 17 Daccord, 1984, J. Phys. (Paris) Lett., 45, 199, 10.1051/jphyslet:01984004505019900 Isaacson, 1980, J. Phys. (Paris) Lett., 41, L469, 10.1051/jphyslet:019800041019046900 Bouchard, 1986, J. Phys. (Paris) Lett., 47, 1273, 10.1051/jphys:019860047080127300 J.E. Martin, J. Wilcoxan and D. Adolf, preprint. Voss, 1982, Phys. Rev. Lett., 49, 1441, 10.1103/PhysRevLett.49.1441 Kapitulnik, 1982, Phys. Rev. Lett., 49, 1444, 10.1103/PhysRevLett.49.1444 S. Reich, preprint. Wilkinson, 1983, J. Phys. A, 16, 3365, 10.1088/0305-4470/16/14/028 Wilkinson, 1984, J. Phys., A17, L129 Lenormand, 1980, C.R. Acad. Sci. (Paris) B, 291, 279 Chandler, 1982, J. Fluid Mech., 119, 249, 10.1017/S0022112082001335 Furuberg, 1988, Phys. Rev. Lett., 61, 2117, 10.1103/PhysRevLett.61.2117 Lenormand, 1985, Phys. Rev. Lett., 54, 2226, 10.1103/PhysRevLett.54.2226 Malφy, 1987 Lenormand, 1984, Soc. Petrol. Eng. Paper 13264 Shaw, 1987, Phys. Rev. Lett., 59, 1671, 10.1103/PhysRevLett.59.1671 A.T. Skjeltorp, private communication. Dias, 1986, J. Phys. A, 19, 3131, 10.1088/0305-4470/19/15/034 Chayes, 1987, Ann. Probab., 15, 1272, 10.1214/aop/1176991976 Chayes, 1985, Commun. Math Phys., 101, 383, 10.1007/BF01216096 Feder, 1986, 8, 531 P. Meakin, unpublished. Brady, 1984, Nature, 309, 225, 10.1038/309225a0 Ball, 1986, 69 Matsushita, 1989, 161 Van Damme, 1989, 199 Daccord, 1987, Nature, 325, 41, 10.1038/325041a0 Daccord, 1987, Phys. Rev. Lett., 58, 479, 10.1103/PhysRevLett.58.479 Lenormand, 1987, Phys. Rev. Lett., 36 Daccord, 1989 Avnir, 1984, Nature, 308, 261, 10.1038/308261a0 Avnir, 1983, Nouv. J. Chim., 7, 71 Avnir, 1983, J. Chem. Phys., 79, 3566, 10.1063/1.446211 Farin, 1984, Part. Sci. Technology, 2, 27, 10.1080/02726358408906391 Farin, 1989, 271 Avnir, 1985, J. Colloid Interfae Sci., 103, 112, 10.1016/0021-9797(85)90082-7 Pfeifer, 1984, J. Stat. Phys., 36, 699, 10.1007/BF01012933 Rojanski, 1986, Phys. Rev. Lett., 56, 2505, 10.1103/PhysRevLett.56.2505 Pfeifer, 1989, Phys. Rev. Lett., 62, 1997, 10.1103/PhysRevLett.62.1997 M. Kardar and J.O. Indekeu, preprint. Avnir, 1989, Langmuir, 5, 1431, 10.1021/la00090a032 Dubinin, 1988, 127 Pfeifer, 1989 Krim, 1990 Wang, 1989, J. Vac. Sci. Tech A, 7, 2481, 10.1116/1.575881 Krim, 1989 Mandelbrot, 1978, Nature, 308, 731 Passoja, 1978, Microstruct. Sci., 6, 143 Langford, 1989, J. Mater. Res., 4, 1272, 10.1557/JMR.1989.1272 Mackin, 1989 Pande, 1987, Acta Metal., 35, 1633, 10.1016/0001-6160(87)90110-6 Flory, 1971 Flory, 1949, J. Chem. Phys., 17, 303, 10.1063/1.1747243 Alexander, 1982, J. Physique Lett., 43, 625, 10.1051/jphyslet:019820043017062500 Ben Avraham, 1982, J. Phys. A, 15, L691, 10.1088/0305-4470/15/12/007 Rammal, 1983, J. Physique Lett., 44, L13, 10.1051/jphyslet:0198300440101300 Family, 1984, J. Phys. A, 17, L285, 10.1088/0305-4470/17/5/013 Kittel, 1986 Alexander, 1981, Rev. Mod. Phys., 53, 175, 10.1103/RevModPhys.53.175 Orbach, 1986, Scaling Phenomena in Disordered Systems A. Aharony, O. Entin-Wohlman and R. Orbach in Time Dependent Effects in Disordered Materials, NATO ASI, Geilo, Norway. Grest, 1984, J. Phys. (Paris), 45, L1155, 10.1051/jphyslet:0198400450240115500 Yahubo, 1987, Phys. Rev. B, 36, 8933, 10.1103/PhysRevB.36.8933 Orbach, 1989, Physica B, 38, 266 Courtens, 1989, Physica D, 38, 41, 10.1016/0167-2789(89)90172-3 Vacher, 1988, Phys. Rev. B, 37, 6500, 10.1103/PhysRevB.37.6500 Vacher, 1989, Phys. Rev. B, 39, 7384, 10.1103/PhysRevB.39.7384 Tsujimi, 1988, Phys. Rev. Lett., 60, 2757, 10.1103/PhysRevLett.60.2757 Courtens, 1989, 423, 55 Calemczuk, 1987, Europhys. Lett., 3, 1205, 10.1209/0295-5075/3/11/009 A.M. de Goer, R. Calemczuk, B. Salce, J. Bon, E. Bonjour and R. Maynard, Phys. Rev. B, to be published. Uemura, 1986, Phys. Rev. Lett., 57, 1947, 10.1103/PhysRevLett.57.1947 Uemura, 1987, Phys. Rev. Lett., 36, 7024 Tua, 1983, Phys. Lett. A, 98, 357, 10.1016/0375-9601(83)90236-0 Alexander, 1983, Phys. Rev. B, 28, 4615, 10.1103/PhysRevB.28.4615 Orbach, 1986, Science, 231, 814, 10.1126/science.231.4740.814 Prasad, 1988, Phys. Rev. Lett., 61, 74, 10.1103/PhysRevLett.61.74 Meneveau, 1987, Nucl. Phys. B. Proc. Suppl., 2, 49, 10.1016/0920-5632(87)90008-9 Jensen, 1985, Phys. Rev. Lett., 55, 2798, 10.1103/PhysRevLett.55.2798 Jensen, 1988, 292 Su, 1987, Phys. Rev. A, 36, 3515, 10.1103/PhysRevA.36.3515 Nittmann, 1987, Phys. Rev. Lett., 58, 619, 10.1103/PhysRevLett.58.619 Stanley, 1987, 145 Maløy, 1987, 111 Feder, 1990 Thompson, 1987, Phys. Rev. Lett., 58, 29, 10.1103/PhysRevLett.58.29 Hinrichsen, 1989, Structure and Geometry of Two Dimensional Random Systems Noyes, 1961, Prog. Reac. Kinet., 1, 128 Calef, 1983, Ann. Rev. Phys. Chem., 34, 493, 10.1146/annurev.pc.34.100183.002425 Blumen, 1986, 199 P. Meakin Reactions in Compartmentalized Fluids, W. Knoche Blumen, 1989, 423, 189 Ovchinnikov, 1976, Chem. Phys., 28, 215, 10.1016/0301-0104(78)85052-6 Toussaint, 1983, J. Chem. Phys., 78, 2642, 10.1063/1.445022 von Smoluchowski, 1916, Z. Phys., 17, 585 von Smoluchowski, 1917, Z. Phys. Chem., 92, 129 Weiss, 1983, Adv. Chem. Phys., 52, 363, 10.1002/9780470142769.ch5 Meakin, 1984, J. Phys. A, 17, L173, 10.1088/0305-4470/17/4/004 Kang, 1984, Phys. Rev. Lett., 52, 955, 10.1103/PhysRevLett.52.955 Torney, 1987, International J. Supercomputer Appl., 1, 33, 10.1177/109434208700100204 Kopelman, 1988, Science, 241, 1620, 10.1126/science.241.4873.1620 Kopelman, 1986, J. Stat. Phys., 42, 185, 10.1007/BF01010846 Klymko, 1982, J. Phys. Chem., 86, 3686, 10.1021/j100216a003 Klymko, 1983, J. Phys. Chem., 87, 4565, 10.1021/j100246a006 Martin, 1989, Phys. Rev. A, 39, 6003, 10.1103/PhysRevA.39.6003 Meakin, 1989, Physica A, 155, 21, 10.1016/0378-4371(89)90049-6 Anaker, 1987, Phys. Rev. Lett., 58, 289, 10.1103/PhysRevLett.58.289 Lindenberg, 1988, Phys. Rev. Lett., 60, 1777, 10.1103/PhysRevLett.60.1777 Farin, 1988, J. Amer. Chem. Soc. Farin, 1987 Farin, 1988 D. Farin and D. Avnir, preprint. Holdren, 1985, Geochim, Cosmochim Acta, 49, 675, 10.1016/0016-7037(85)90162-0 Silverberg, 1986, Ann. Israel Phys. Soc., 8, 451 Meakin, 1986, Ann. Israel Phys. Soc., 8, 490 Chen, 1985, J. Chem. Phys., 80, 2982, 10.1063/1.447012 Meakin, 1985, J. Chem. Phys., 82, 3786, 10.1063/1.448890 Hess, 1986, Z. Phys. B, 64, 65, 10.1007/BF01313690 Van Sarloos, 1987, Physica A, 147, 280, 10.1016/0378-4371(87)90111-7 Wiltzius, 1987, Phys. Rev. Lett., 58, 710, 10.1103/PhysRevLett.58.710 Chen, 1987, Phys. Rev. Lett., 59, 2121, 10.1103/PhysRevLett.59.2121 Pusey, 1987, Phys. Rev. Lett., 59, 2122, 10.1103/PhysRevLett.59.2122 Wiltzius, 1987, Phys. Rev. Lett., 59, 2123, 10.1103/PhysRevLett.59.2123 Meakin, 1989, Langmuir, 5, 510, 10.1021/la00086a038 Berry, 1986, Optima Acta, 33, 577, 10.1080/713821987 Chen, 1988, Phys. Rev. B, 37, 5232, 10.1103/PhysRevB.37.5232 Chen, 1987, Phys. Rev. Lett., 58, 1996, 10.1103/PhysRevLett.58.1996 E.L. Wright, preprint. W.D. Brown and R.C. Ball, unpublished. Deptuk, 1985, Phys. Rev. Lett., 54, 913, 10.1103/PhysRevLett.54.913 Forsman, 1987, Can. J. Phys., 65, 767, 10.1139/p87-112 Gronauer, 1986, 167 Woignier, 1988, J. Phys. (Paris), 49, 289, 10.1051/jphys:01988004902028900 Buscall, 1988, J. Chem. Soc. Faraday Trans, 84, 10.1039/f19888404249 Buscall, 1987, J. Non-Newtonian Fluid Mech., 24, 183, 10.1016/0377-0257(87)85009-7 Berry, 1989, Physica D, 38, 29, 10.1016/0167-2789(89)90169-3 Nelson, 1989, Nature, 339, 611, 10.1038/339611a0 Meakin, 1988, The Astrophysical Journal, 328, L39, 10.1086/185172 Weidenschilling, 1989 Aharony, 1985, 289 Stanley, 1984, Phys. Rev. B, 29, 522, 10.1103/PhysRevB.29.522 Witten, 1984, Phys. Rev. B, 30, 4093, 10.1103/PhysRevB.30.4093 Kaufman, 1987, Phys. Rev. B, 35, 1881, 10.1103/PhysRevB.35.1881 Kaufman, 1986, Phys. Rev. Lett., 56, 1932, 10.1103/PhysRevLett.56.1932 Meakin, 1984, J. Phys. A, 17, L975, 10.1088/0305-4470/17/18/008 Meakin, 1983, Phys. Rev. Lett., 51, 1457, 10.1103/PhysRevLett.51.1457 Sahimi, 1985, Phys. Rev. A, 32, 590, 10.1103/PhysRevA.32.590 Le Mehaute, 1983, Solid State Ionics, 9, 17, 10.1016/0167-2738(83)90207-2 Liu, 1985, Phys. Rev. Lett., 55, 529, 10.1103/PhysRevLett.55.529 Kaplan, 1983, Phys. Rev. B, 32, 7360, 10.1103/PhysRevB.32.7360 Sapoval, 1987, Solid State Ionics, 23, 253, 10.1016/0167-2738(87)90002-6 Halsey, 1987, Phys. Rev. A, 35, 3512, 10.1103/PhysRevA.35.3512 de Levie, 1990, Electrochemica Acta, 35, 1045, 10.1016/0013-4686(90)90040-7 Nyikos, 1985, Electrochimica Acta, 30, 1533, 10.1016/0013-4686(85)80016-5 J.P. Clerc, A.M.S. Tremblay, G. Allsinet and C.D. Mitescu, J. Phys. (Paris) Keddam, 1986, C.R. Acad. Sci. Ser., 2, 281 Blunt, 1989, J. Phys. A, 22, 1179, 10.1088/0305-4470/22/8/029 Sapoval, 1988, Phys. Rev. A, 38, 5867, 10.1103/PhysRevA.38.5867 Halsey, 1987, Phys. Rev. A, 36, 5877, 10.1103/PhysRevA.36.5877 T.C. Halsey and M. Leibig, preprint. Bates, 1988, Phys. Rev. Lett., 60, 627, 10.1103/PhysRevLett.60.627 Sapoval, 1991 Armstrong, 1976, J. Electroanal. Chem., 72, 237, 10.1016/S0022-0728(76)80312-9 Keddam, 1988, Electrochim. Acta, 33, 445, 10.1016/0013-4686(88)85045-X LeMehaute, 1989, 311