Adams, R. McC. "Ancient Sumer, Modern Iraq," Scientific American, July 1994. |
Auster, P. Mr. Vertigo Viking, 1994. |
Avron, J., and Simon, B., "Almost periodic Hill's equation and the rings of Saturn," Phys. Rev. Let. 46 (1981), 1166-1168. |
Bak, P., How Nature Works: The Science of Self-Organized Criticality, Springer, 1996. |
Bak, P., Chen, K., "Self-organized criticality," Sci. Am. Jan, 1991. |
Bak, P., Tang, C., and Wiesenfeld, K., "Self-organized criticality," Phys. Rev. A 38 (1988), 364-374. |
Bandt, C., "Self-similar sets 5. Integer matrices and fractal tilings of Rn," Proc. Amer. Math. Soc., 112 (1991), 549-562. |
Banks, J., Brooks, J., Cairns, G., Davis, G., and Stacey, P., "On Devaney's definition of chaos," American Mathematical Monthly 99 (1992), 332-334. |
Barnsley, M., Fractals Everywhere, Academic Press, San Diego, 1993. (2nd Ed.) |
Beach, D., ed., Aspects of Schenkeian Theory, Yale University Press, New Haven, 1983. |
Bedient, R., Frame, M., Gross, K., Lanski, J., Sullivan, B., "Higher block IFS 1: memory reduction and dimension computation," Fractals 18 (2010), 145-155. |
Ben-Jacob, E., Shochet, O., Cohen, I., Tenenbaum, A., Czirok, A., and Vicsek, T., "Cooperative strategies in formation of complex bacterial patterns," Fractals 4 (1995), 849-868. |
Berlyne, D., Aesthetics and Sociobiology, Appleton-Century-Crofts, New York, 1971. |
Bois, Y-A., Corwart, J., Pacquement, A., Ellsworth Kelly. The Years in France, 1948-1954, National Gallery of Art, Washington, 1992 |
Borges, J. L. The Aleph and Other Stories 1933-1969, E. P. Dutton, 1978. |
Borges, J. L. Labyrinths, New Directions, 1962. |
Boyajian, G., and Lutz, T., "Evolution of biological complexity and its relation to taxonomic longevity in the Ammonoidea," Geology 20 (1992), 983-6. |
Brady, R., and Ball, R., "Fractal growth of copper electrodeposits," Nature 309 (1984), 225-229. |
Browne, M., "J. S. Bach + Fractals = New Music," New York Times, Tuesday, April 16 (1991), C1. |
Caley, A., "The Newton-Fourier imaginary problem," Amer. J. Math 2 (1879), 97. |
Clarke, A., The Ghost from the Grand Banks, Bantam, 1990. |
Coleman, P., "Fractals and the universe," Fractals 3 (1995), 567-579. |
Coleman, P., Pietronero, L., "The fractal structure of the universe," Physics Reports, 213 (1992), 311-389. |
Cook, M., "Universality in elementary cellular automata" Complex Systems, (2004), 1-40. |
Coulette, P. and Tresser, C., "Iteration d'endomorphismes et groupe de renormalisation," J. De Physique Colloque C 539 (1978), C5-25. |
Courtial, J., Leach, J., and Padgett, M., "Fractals in pixellated video feedback," Nature 414 (2001), 864. |
Courtial, J. and Padgett, M., "Monitor-outside-a-monitor effect and self-similar fractal structures in the eigenmodes of unstable optical resonators," Physical Review Letters 85 (2000), 5320-5323. |
Cowart, J., "Method and motif: Ellsworth Kelly's 'Chance' grids and his development of color panel painting, 1948-1951," pages 37-45 of Ellsworth Kelly: The Years in France. 1948-1954, National Gallery of Art, Washington, 1992. |
Crichton, M., Jurassic Park, Alfred A. Knopf, New York, 1990. |
Cruthcfield, J., "Space-time dynamics in video feedbacks," Physcia D 10 (1984), 229-245. |
Curry, J. H., Garnett, L., and Sullivan, D., "On the iteration of a rational function: computer experiments with Newton's method," Commun. Math. Phys. 91 (1983), 267-277. |
Cutting, J., DeLong, J., Nothelfer, C., "Attention and the evolution of Holywood film," Psychological Science (2010), DOI:10.1177/0956797610361679 |
Darst, R., Palagallo, J., Price, T., "Fractal tilings in the plane," Mathematics Magazine, 71 (1998), 12-23. |
Dekking, F., "Recurrent sets," Advances in Mathematics 44 (1982), 78-104. |
Descharnes, R., Dali, Harry Abrams, NY, 1985. |
Devaney, R., Introduction to Chaotic Dynamical Systems 2nd Ed, Addison-Wesley, 1989. |
Ditto, W., Rauseo, S., and Spano, M., "Experimental Control of Chaos," Physical Review Letters 65 (1990), 3211-3214. |
Doran, M., ed., Conversations with Cézanne, Univ. of California Press, 2001 |
Douady, A., and Hubbard, J., "Etude dynamique des polynomes complexes, I, II" Publ. Math. Orsay 1984, 1985. |
Douady, A., and Hubbard, J., "On the dynamics of polynomial-like mappings," Ann. Sci. Ecole Norm. Sup,, 18 (1985), 287-343. |
Eglash, R., African Fractals, Rutgers University Press, 1999. |
Falconer, K., Fractal Geometry. Mathematical Foundations and Applications 2nd ed., Wiley, 2003. |
Falconer, K., Techniques in Fractal Geometry, Wiley, 1997. |
Feder, F., Jossang, T. and Rosenqvist, E., "Scaling behavior and cluster fractal dimension determined by light scattering from aggregating proteins," Physical Review Letters 53 (1984), 1403-1406. |
Feigenbaum, M., "Quantitative universality for a class of nonlinear transformations," J. Stat. Phys. 19 (1978), 25-52. |
Frame, M., Johnson, B., and Sauerberg, J., "Fixed points and Fermat: a dynamical systems approach to number theory," American Mathematical Monthly, 107 (2000), 422-428. |
Frame, M. and Lanski, J., "When is a recurrent IFS attractor a standard IFS attractor?" Fractals, 7 (1999), 257-266. |
Frame, M. and Mandelbrot, B. B. (eds) Fractals, Graphics, and Mathematics Education, Mathematical Association of America, 2001. |
Frame, M., Neger, N., "Videofeedback with mirrors - analog iterated function systems," Fractals 16 (2008), 275-285. |
Frame, M., Neger, N., "Fractal tetrahedra: what's left in, what's left out, and how to build one in four dimensions," Computers & Graphics 32 (2008), 371-381. |
Frame, M., Neger, N., "Pascal's triangles, dimensions, and the probability of finding odd numbers," Computers & Graphics 34 (2010), 158-166. |
Fricke, R., and Klein, F., Vorlesungen uber die Theorie der automorphen Funktionen, Teubner (Johnson reprint), Leipzig, Germany, 1897. |
H. Fujikawa, M. Matsushita, "Fractal growth of Bacillus subtilis on agar plates," J. Phys. Soc. Japan 58 (1989), 3875-3878. |
H. Fujikawa, M. Matsushita, "Bacterial fractal growth in the concentration field of a nutrient," J. Phys. Soc. Japan 60 (1991), 88-94 |
Gardner, M., Wheels, Life, and Other Mathematical Amusements, Viking, 1987. |
Garfinkel, A., Spano, M., Ditto, W., and Weiss, J. "Controlling Cardiac Chaos," Science 257 (1992), 1230-1235. |
Gleick, J., Chaos. Making a New Science, Freeman, San Francisco, 1983. |
Goldberger, A., Rigney, D., and West, B., "Chaos and fractals in human physiology," Scientific American, February 1990, 42-49. |
Goossen, E., Ellsworth Kelly, Museum of Modern Art, New York, 1973. |
Gould, S., Full House: The Spread of Excellence from Plato to Darwin, Harmony Books, New York, 1996. |
Gray, C., The Russian Experiment in Art 1863-1922Thames and Hudson, 1962. |
Grebogi, C., Ott, E., and Yorke, J., "Basin boundary metamorpheses: changes in accessible boundary orbits," Physica D 24 (1987), 243-262. |
Guckenheimer, J., and McGehee, R., "A proof of the Mandelbrot n2 conjecture," Institute Mittag-Leffler, Report 15, 1984. |
Hack, J. "Studies of longitudinal stream profiles in Virginia and Maryland," U. S. Geological Survey Professional Papers 294-B (1957), 45-97. |
Henderson, L., The Fourth Dimension and NonEuclidean Geometry in Modern Art, Princeton University Press Press, 1983. |
Hersey, G., The Monumental Impulse, Architecture's Biological Roots, MIT Press, 1999. |
Hohlfeld, R., and Cohen, N., "Self-similarity and the geometric requirements for frequency independence in antennae," Fractals 7 (1999), 79-84. |
Hofstadterand, D., Godel, Escher, Bach: as Eternal Golden Braid. Basic Books, 1979. |
Hofstadterand, D., and Dennett, D., The Mind's I. Fantasies and Reflections on Self and Soul. Basic Books, 1981. |
Holland, J., "Genetic algorithms," Scientific American, July 1992. |
Holland, J., Hidden Order. How Adaptation Builds Complexity, Addison-Wesley, 1995. |
Hsu, K., and Hsu, A., "Fractal geometry of music," Proc. Natl. Acad. Sci. USA 87 (1990), 938-941. |
Hsu, K., and Hsu, A., "Self-similarity of the '1/f' noise' called music," Proc. Natl. Acad. Sci. USA 88 (1991), 3507-3509. |
Hurwitz, H., Frame, M., and Peak, D., "Scaling symmetries in nonlinear dynamics: a view from parameter space," Physica D 81 (1995), 23-31. |
Hutchinson, J., "Fractals and self-similarity," Indiana Univ. Math. J. 30 (1981), 713-747. |
Jackson, W., "Other shore fractals: Hindu transcendence symbols and the modelling of wholeness" |
Jackson, W., Heaven's Fractal Net. Retrieving Lost Visions in the Humanities, Indiana Univ. Pr. 2004. |
Janson, H., History of Art, Fourth Edition, Abrams, 1991. |
Jeffrey, H. J., "Chaos game visualization of sequences," Computers & Graphics 16 (1992), 25-33. |
Kalda, J., "Fractal model of blood vessel system," Fractals 1 (1993), 191-197. |
Labini, F., Montuori, M., Pietronero, L., "Scale-invariance of galaxy clustering," Physics Reports, 293 (1998), 61-226. |
Langton, C., "Studying artificial life with cellular automata," Physica D 22 (1986), 120-149. |
Lapidus, M. L., "Fractal drum, inverse spectral problems for elliptic operators and a partial resolution of the Weyl-Berry conjecture," Trans. Amer. Math. Soc. 325 (1991), 465-529. |
Lavaurs, P., "Une description combinatoire de l'involution define par M sur les rationnels a denominateur impair," C. R. Acad. Sci. Paris 303 (1986), 143-146. |
Leach, J., Padgett, M., and Courtial, J., "Fractals in pixellated video feedback," Contemporary Physics 44 (2003), 137-143. |
Lei, T., "Similarity between the Mandelbrot set and Julia sets," Commun. Math. Phys. 134 (1990), 567-616. |
Lem, S., The Invincible Penguin, 1973. |
Lewis, M., and Rees, D., "Fractal structures of proteins," Science 230 (1985), 1163-1165. |
Li, T.-Y., and Yorke, J., "Period three implies chaos," American Mathematical Monthly 82 (1975), 985-992. |
Lightman, A., Einstein's Dreams, Warner, New York, 1994. |
Ligon, W., "Fractal structures obtained by electrodeposition of silver at an air-water interface," J. Chem. Ed. 64 (1987), 1053. |
Lindenmayer. A., "Mathematical models for cellular interactions in development. I and II," Journal of Theoretical Biology 18 (1968), 280-315. |
Lovejoy, S. "Area-perimeter relation for rain and cloud areas," Science 216 (1982), 185-187. |
Magnus, W., Noneuclidean Tesselations and Their Groups, Academic Press, 1974. |
Mandelbrot, B. B., The Fractal Geometry of Nature, W. H. Freeman, San Francisco, 1982. |
Mandelbrot, B. B., Fractals and Scaling in Finance, Selecta Vol E, Springer-Verlag, New York, 1997. |
Mandelbrot, B. B., "How long is the coast of Britain? Statistical self-similarity and fractional dimension," Science 156 (1967), 636-638. |
Mandelbrot, B. B., "On the dynamics of iterated maps. III: The individual molecules of the M-set, self-similarity properties, the N-2 rule, and the N-2 conjecture," pgs 213-224 in Chaos, Fractals, and Dynamics, P. Fischer and W. Smith, eds, Marcel Dekker, 1985. |
Mandelbrot, B. B., Multifractals and 1/f Noise. Wild Self-Affinity in Physics, Selecta Vol N, Springer-Verlag, New York, 1999. |
Mandelbrot, B. B., "Self-Inverse Fractals Osculated by Sigma-Discs and the Limit Sets of Inversion Groups," Mathematical Intelligencer 5 (1983), 9-17. |
Mandelbrot, B. B., and Frame, M., "The canopy and shortest path in a self-contacting fractal tree," Mathematical Intelligencer 21 (1999), 18-27. |
Mandelbrot, B. B., "A fractal walk down Wall Street," Scientific American, Feb. 1999, 70-73. |
Mandelbrot, B. B., Hudson, R., The (Mis)Behavior of Markets. A Fractal View of Risk, Ruin, and Reward, Basic Books, 2004. |
Mandelbrot, B. B., Vespignani, A., and Kaufman, H., "Crosscut analysis of large radial DLA: departures from self-similarity and lacunarity effects," Europhysics Letters 32 (1995), 199-204. |
Mandelbrot, B., and Wallis, J., "Noah, Joseph and operational hydrology," Water Resources Research 4 (1968), 909-918. |
Matsushita, M., Fujikawa, H., "Diffusion-limited growth in bacterial colony formation," Physica A 168 (1990), 498-506. |
Matsushita, M., Sano, M., Hayakawa, Y., Honjo, H., and Sawada, Y. "Fractal structures of zinc metal leaves grown by electrodeposition," Physical Review Letters 53 (1984), 286-289. |
Matsuura, S., Miyazima, S., "Self-affine fractal growth front of Aspergillus oryzae," Physica A 191 (1992), 30-34. |
Matsuura, S., Miyazima,, S., "Colony of the fungus Aspergillus oryzae and self-affine fractal geometry of growth fronts," Fractals 1 (1993), 11-19. |
Matsuura, S., Miyazima, S., "Formation of ramified colony of Aspergillus oryzae on agar media," Fractals 1 (1993), 336-345. |
May, R., "Simple mathematical models with very complicated dynamics," Nature 261 (1976), 459-467. |
McMullen, C. "The Mandelbrot set is universal," pages 1-17 of The Mandelbrot Set, Theme and Variations, Tan Lei, ed., Cambridge University Press (2000). |
Meakin, P., "Computer simulation of growth and aggregation processes," pp 111-135 of On Growth and Form: Fractal and Non-Fractal Patterns in Physics, E. Stanley and N. Ostrowsky, eds., Nijhoff, Boston, 1986. |
Meara, A., Down the Garden Paths, Long Warf Theater, 1998. |
Metropolis, N., Stein, M., and Stein, P., "On finite limit sets for transformations of the unit interval," Journal of Combinatorial Theory 15 (1973), 25-44. |
Moon, F., "Fractal boundary for chaos in a two-state mechanical oscillator," Physical Review Letters 53 (1984), 962-964. |
Moore, R., Treatise of Invertebrate Paleontology, Geological Society of America, 1957. |
Musgrave, F. K., and Mandelbrot, B. B., "The art of fractal landscapes," IBM Journal of Research and Development 35 (1991), 535-540. |
Musser, G., "Practical Fractals," Scientific American July 1999, 38. |
Nabokov, V., The Eye, Vintage Press, 1990. |
Niemeyer, L., Pietronero, L., Wiesmann, H., "Fractal dimension of dielectric breakdown," Physical Review Letters 52 (1984), 1033-1036. |
Nonnenmacher, T. F., Losa, G. A., and Weibel, E. R. (Eds.), Fractals in Biology and Medicine, Birkhauser-Verlag, Basel and Boston, 1994. |
O'Brien, F., The Third Policeman, Dalkey Archive Press, 2002. |
Ott, E., Grebogi, C., and Yorke, J., "Controlling Chaos," Physical Review Letters 64 (1990), 1196-1199. |
Patterson, L., "Diffusion-limited aggregation and two-fluid displacements in porous media," Physical Review Letters 52 (1984), 1621-1624. |
Peak, D. and Frame, M., Chaos Under Control: The Art and Science of Complexity, W.H. Freeman, New York, 1994. |
Peebles, P., Physical Cosmology, Princeton University Press, 1971. |
Peebles, P., The Large-Scale Structure of the Universe, Princeton University Press, 1980. |
Peebles, P., "The fractal galaxy distribution," Physica D 38 (1989), 273-278. |
Peebles, P., Principles of Physical Cosmology, Princeton University Press, 1993. |
Peitgen, H.-O., Jurgens, H., and Saupe, D., Chaos and Fractals: New Frontiers of Science, Springer-Verlag, Berlin and New York, 1992. |
Peitgen, H.-O., Jurgens, H., Saupe, D., and Zahlten, C., Fractals: An Animated Discussion, W. H. Freeman, New York, 1990. (With interviews of Edward Lorenz and Benoit B. Mandelbrot.) |
Peitgen, H.-O., and Richter, P. H., The Beauty of Fractals: Images of Complex Dynamical Systems, Springer-Verlag, Berlin and New York, 1986. |
Peitgen, H.-O., and Saupe, D. (eds), The Science of Fractal Images, Springer-Verlag, New York, 1988. |
Philip, A. G. ., Robucci, A., and Frame, M., "A new scaling along the spike of the Mandelbrot set,'' Computers & Graphics 16 (1992), 223-234. |
Pietronero, L., "The fractal structure of the universe: correlations of galaxies and clusters and the average amss density," Physics A 144 (1987), 257-284. |
Pollard-Gott, L., "Fractal repetition in the poetry of Wallace Stevens," Language and Style 19 (1989), 233-249. |
Poundstone, W., The Recursive Universe, Contemporary Books, Chicago, 1985. |
Powers, R., Galatea 2.2 Harper, 1995. |
Powers, R., The Goldbug Variations Harper, 1992. |
Powers, R., Plowing the Dark Farrar, Straus and Giroux, 2000. |
Prusinkiewicz, P., and Hanan, J., Lindenmayer Systems, Fractals, and Plants, Springer-Verlag, New York, 1989. |
Richardson, L., "The problem of contiguity: An appendix of statistics of deadly quarrels," General Systems Yearbook 6 (1961), 139-187. |
Robbins, D., "Larry Poons: Creation of the Complex Surface," in Larry Poons: Paintings 1963-1990, Salander-O'Reilly Galleries, New York, 1990. |
Roberts, D., and Turcotte, D., "Fractality and self-organized crticality of wars," Fractals 6 (1998), 351-357. |
Rudin, W., Principles of Mathematical Analysis, McGraw-Hill, 1953. |
Sapoval, B., "Experimental observation of local modes in fractal drums," Physica D 38 (1989), 296-298. |
Sapoval, B., Gobron, T., and Margolina, A., "Vibrations of fractal drums," Physical Review Letters 67 (1991), 2974-2977. |
Schenker, H., Free Composition, transl. E. Oster, Longman, New York, 1973. |
Schermer, M., "The chaos of History: on a chaotic model that represents the role of contingency and necessity in historical sequences," Nonlinearity Today, 2 (1993), 1-13. |
Schreiner, O., The Story of an African Farm, Penguin Books, 1995. Originally published in 1883. |
Shearer, R. R., "Chaos theory and fractal geometry: their potential impact on the future of art," Leonardo 25 (1992), 143-152. |
Shishikura, M., "The Hausdorff dimension of the boundary of the Mandelbrot set and Julia sets," Annals of Mathematics 147 (1998), 225-267. |
Simmt, E., and Davis, B., "Fractal cards: a space for exploration in geometry and discrete mathematics," The Mathematics Teacher 91 (1998), 102-108. |
Snow, R., "Fractal sinuoisty of stream channels," p 99-109 of Fractals in Geophysics, C. Scholz, B. Mandelbrot, eds., Birkhauser Verlag, Basel, 1989. |
Sorkin, G., "Simulated annealing on fractal fitness landscapes," Algorithmica 6 (1991), 367-418. |
Stewart, I. "Order within the chaos game," Dynamics Newsletter 3 (1989), 4-9. |
Stoppard, T., Arcadia, Faber & Faber, 1993. |
Tan Lei, "Ressemblance entre l'ensemble de Mandelbrot et l'ensemble de Julia au voisinage d'un point de Misiurewicz," p. 139-152 in Douady, A., and Hubbard, J., "Etude dynamique des polynomes complexes II," Publ. Math. Orsay 1985. |
Taylor, R. P., "Order in Pollock's chaos," Scientific American December 2002, 116-121. |
Taylor, R. P., Micolich, A. P., Jonas, D., "Fractal analysis of Pollock's drip paintings," Nature 399 (1999), 422. |
Turcotte, D., "Fractals in geology and geophysics," p 171-196 of Fractals in Geophysics, C. Scholz, B. Mandelbrot, eds., Birkhauser Verlag, Basel, 1989. |
Turing, A., "The chemical basis of morphogenesis," Philosophical Transactions B 237 (1952), 37-72. |
Updike, J., Roger's Version, Knopf, 1986. |
Uribe, D., Fractal Cuts Tarquin Publishers, 1993. |
Vellekoop, M., and Berglund, R., "In intervals, transitivity = chaos," American Mathematical Monthly 101 (1994), 353-355. |
Voss, R., "Long-range fractal correlations in DNA introns and exons," Fractals 2 (1994), 1-6. |
Voss, R. F., "Random fractals: self-affinity in noise, music, mountains, and clouds," Physica D 38 (1989), 362-371. |
Voss, R. F. and Clarke, J., "1/f noise in music and speech," Nature 258 (1975), 317-318. |
West, B., Fractal Physiology and Chaos in Medicine, World Scientific, Singapore, 1990. |
Weyl, H., Symmetry, Princeton University Press, 1952. |
Wilhelm, K., Death Qualified, St. Martin's, 1991. |
Willinger, W., and Paxson, V., "Where mathematics meets the internet," Notices of the AMS 45 (1998), 961-970. |
Witten, T., and Sander, L., "Diffusion-limited aggregation," Physical Review B 27 (1983), 5686-5697. |
Witten, T., and Sandler, L., "Diffusion-limited aggregation, a kinetic critical phenomenon," Physical Review Letters 47 (1981), 1400-1403. |
Wolfram, S., "Universality and complexity in cellular automata," Physica D 10 (1984), 1-35. |
Wolfram, S., Theory and Applications of Cellular Automata, World Scientific, 1986. |
Wolfram, S., A New Kind of Science, Wolfram Media, 2002. |
Young, D. "A local activator-inhibitor model of vertebrate skin patterns," Mathematical Biosciences 72 (1984), 51-58. |