Superfractals

Superfractals

Volumn 9780521844932, Issue , 2012, Pages 1-448

  Barnsley, Michael Fielding ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER GRAPHICS; GENE ENCODING; SIGNAL PROCESSING;

COMPLEX STRUCTURE; DETERMINISTIC APPROACH; ITERATED FUNCTION SYSTEM; ORIGINAL IMAGES; SUPERFRACTALS;

FRACTALS;

EID: 84929739903     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9781107590168     Document Type: Book

References (98)

1. Arbeiter, Matthias. Random recursive construction of self-similar fractal measures. The noncompact case. Probab. Theory Related Fields88(1991), no. 4, 497–520.
2. Asai, T. Fractal image generation with iterated function set. Ricoh Technical Report No. 24, November 1998, pp. 6–11.
3. Barlow, M. T.; Hambly, B. M. Transition density estimates for Brownian motion on scale irregular Sierpinski gaskets. Ann. Inst. H. Poincaré Probab. Statist.33 (1997), no. 5, 531–557.
4. Barnsley, M. F.; Demko, S. Iterated function systems and the global construction of fractals. Proc. Roy. Soc. London Ser. A399(1985), no. 1817, 243–275.
5. Barnsley, M. F.; Ervin, V.; Hardin, D.; Lancaster, J. Solution of an inverse problem for fractals and other sets. Proc. Nat. Acad. Sci. USA83(1986), no. 7, 1975–1977.
6. Barnsley, Michael F. Fractal functions and interpolation. Constr. Approx.2 (1986), no. 4, 303–329.
7. Barnsley, Michael F.; Elton, J. H. A new class of Markov processes for image encoding. Adv. Appl. Probab.20(1988), no. 1, 14–32.
8. Barnsley, M. F.; Reuter, L.; Jacquin, A.; Malassenet, F.; Sloan, A. Harnessing chaos for image synthesis. Computer Graphics22(1988), 131–140.
9. Barnsley, Michael. Fractals Everywhere. Boston MA, Academic Press, 1988.
10. Barnsley, Michael F.; Elton, John H.; Hardin, Douglas P. Recurrent iterated function systems. Fractal approximation. Constr. Approx.5(1989), no. 1, 3–31.
11. Barnsley, Michael F.; Harrington, Andrew N. The calculus of fractal interpolation functions. J. Approx. Theory57(1989), no. 1, 14–34.
12. Barnsley, Michael F.; Hurd, Lyman P. Fractal Image Compression. Illustrations by Louisa F. Anson. Wellesley MA, A. K. Peters, 1993.
13. Barnsley, Michael F. Fractals Everywhere, second edition. Revised with the assistance of and a foreword by Hawley Rising, III. Boston MA, Academic Press Professional, 1993.
14. Barnsley, Michael F. Iterated function systems for lossless data compression. In Fractals in Multimedia(Minneapolis MN, 2001), pp. 33–63. IMA Vol. Math. Appl., vol. 132. New York, Springer, 2002.
15. Barnsley, Michael F.; Barnsley, Louisa F. Fractal transformations. In The Colours of Infinity: The Beauty and Power of Fractals, pp. 66–81. London, Clear Books, 2004.
16. Barnsley, Michael; Hutchinson, John; Stenflo, Örjan. Afractal valued random iteration algorithm and fractal hierarchy. Fractals13(2005), no. 2, 111–146.
17. Barnsley, M. F. Theory and application of fractal tops. Preprint, Australian National University, 2005.
18. Barnsley, M. F. Theory and application of fractal tops. In Fractals in Engineering: New Trends in Theory and Applications, J. Lévy-Véhel; E. Lutton (eds.), pp. 3–20. London, Springer-Verlag, 2005.
19. Barnsley, M. F.; Hutchinson, J. E.; Stenflo, Ö. V-variable fractals. In preparation.
20. Barnsley, M. F.; Hutchinson, J. E.; Stenflo, Ö. V-variable fractals and dimensions. In preparation.
21. Barnsley, M. F.; Hutchinson, J. E.; Stenflo, Ö. V-variable fractals and correlated random fractals. In preparation.
22. Berger, Marc A. An Introduction to Probability and Stochastic Processes. Springer Texts in Statistics. New York, Springer-Verlag, 1993.
23. Berger, Marcel. Geometry, vols. I and II. Translated from the French by M. Cole and S. Levy. Universitext. Berlin, Springer-Verlag, 1987.
24. Billingsley, Patrick. Ergodic Theory and Information. New York, London, Sydney, John Wiley & Sons, 1965.
25. Brannan, David A.; Esplen, Matthew F.; Gray, Jeremy J. Geometry. Cambridge, Cambridge University Press, 1999.
26. Coxeter, H. S.M. The Real Projective Plane. New York, McGraw-Hill, 1949.
27. Demko, S.; Hodges, L.; Naylor, B. Constructing fractal objects with iterated function systems. Computer Graphics19(1985), 271–278.
28. Diaconis, Persi; Freedman, David. Iterated random functions. SIAM Rev. 41 (1999), no. 1, 45–76.
29. Dudley, Richard M. Real Analysis and Probability. Pacific Grove CA, Wadsworth & Brooks/Cole Advanced Books & Software, 1989.
30. Dunford, N.; Schwartz, J. T. Linear Operators. Part I: General Theory, third edition. New York, John Wiley & Sons, 1966.
31. Edgar, Gerald A. Integral, Probability, and Fractal Measures. New York, Springer, 1998.
32. Eisen, Martin. Introduction to Mathematical Probability Theory. Englewood Cliffs NJ, Prentice-Hall, 1969.
33. Elton, John H. An ergodic theorem for iterated maps. Ergodic Theory Dynam. Systems7(1987), no. 4, 481–488.
34. Falconer, Kenneth. Random fractals. Math. Proc. Cambridge Philos. Soc.100(1986), no. 3, 559–582.
35. Falconer, Kenneth. Fractal Geometry. Mathematical Foundations and Applications. Chichester, John Wiley & Sons, 1990.
36. Fathauer, R. Dr. Fathauer's Encyclopedia of Fractal Tilings. Version 1.0, 2000. http://members.cox.net/fractalenc.
37. Feller, William. An Introduction to Probability Theory and its Applications, vol. I, third edition. New York, London, Sydney, John Wiley & Sons, 1968.
38. Fisher, Yuval (ed.) Fractal Image Compression. Theory and Application. New York, Springer-Verlag, 1995.
39. Forte, B.; Mendivil, F. A classical ergodic property for IFS: a simple proof. Ergodic Theory Dynam. Systems18(1998), no. 3, 609–611.
40. Gardner, Martin. Rep-tiles. The Colossal Book of Mathematics: Classic Puzzles, Paradoxes and Problems. pp. 46–58. New York, London, W.W. Norton & Co., 2001.
41. Graf, Siegfried. Statistically self-similar fractals. Probab. Theory Related Fields74(1987), no. 3, 357–392.
42. Grünbaum, Branko; Shephard, G. C. Tilings and Patterns. New York, W. H. Freeman and Co., 1987.
43. Hambly, B. M. Brownian motion on a random recursive Sierpinski gasket. Ann. Probab.25(1997), no. 3, 1059–1102.
44. Hata, Masayoshi, On the structure of self-similar sets. Japan J. Appl. Math.2(1985), no. 2, 381–414.
45. Hénon, M. Atwo-dimensional mapping with a strange attractor. Comm.Math. Phys. 50(1976), no. 1, 69–77.
46. Hoggar, S. G. Mathematics for Computer Graphics. Cambridge, Cambridge University Press, 1992.
47. Horn, Alistair N. IFSs and the interactive design of tiling structures. In Fractals and Chaos, pp. 119–144. New York, Springer, 1991.
48. Hutchinson, John E. Fractals and self-similarity. Indiana Univ. Math. J.30(1981), no. 5, 713–747.
49. Hutchinson, John E.; Rüschendorf, Ludger. Random fractal measures via the contraction method. Indiana Univ. Math. J.47(1998), no. 2, 471–487.
50. Hutchinson, John E. Deterministic and random fractals. In Complex Systems, pp. 127–166, Cambridge, Cambridge University Press, 2000.
51. Hutchinson, John E.; Rüschendorf, Ludger. Selfsimilar fractals and selfsimilar random fractals. In Fractal Geometry and Stochastics, II(Greifswald/Koserow, 1998), pp. 109–123. Progress in Probability, vol. 46. Basel, Birkhäuser, 2000.
52. Hutchinson, John E.; Rüschendorf, Ludger. Random fractals and probability metrics. Adv. in Appl. Probab.32(2000), 925–947.
53. Jacquin, Arnaud. Image coding based on a fractal theory of iterated contractive image transformations. IEEE Trans. Image Proc.1(1992), 18–30.
54. Kaandorp, Jaap A. Fractal modelling. Growth and Form in Biology. With a forward by P. Prusinkiewicz. Berlin, Springer-Verlag, 1994.
55. Kaijser, Thomas. On a new contraction condition for random systems with complete connections. Rev. Roumaine Math. Pures Appl.26(1981), no. 8, 1075–1117.
56. Katok, Anatole; Hasselblatt, Boris. Introduction to the modern theory of dynamical systems. With a supplementary chapter by Anatole Katok and Leonardo Mendoza. In Encyclopedia of Mathematics and Its Applications, vol. 54. Cambridge, Cambridge University Press, 1995.
57. Keeton, W. T.; Gould, J. L.; Gould, C. G. Biological Science, fifth edition. New York, London, W. W. Norton & Co., 1993.
58. Kieninger, B. Iterated Function Systems on Compact Hausdorff Spaces. Aachen, Shaker-Verlag, 2002.
59. Kifer, Yuri. Fractals via random iterated function systems and random geometric constructions. In Fractal Geometry and Stochastics(Finsbergen, 1994), pp. 145–164. Progress in Probability, vol. 37. Basel, Birkhäuser, 1995.
60. Kunze, H.; Vrscay, E. Inverse problems for ODEs using the Picard contraction mapping. Inverse Problems15(1999).
61. Lasota, A.; Yorke, James A. On the existence of invariant measures for piecewise monotonic transformations. Trans. Amer. Math. Soc.186(1973), 481–488.
62. Lu, N. Fractal Imaging. San Diego, Academic Press, 1997.
63. Mandelbrot, Benoit B. Fractals: Form, Chance, and Dimension. Translated from the French. Revised edition. San Francisco, W. H. Freeman and Co., 1977.
64. Mandelbrot, Benoit B. The Fractal Geometry of Nature. San Francisco, W. H. Freeman, 1983.
65. Mandelbrot, Benoit B. Amultifractalwalk downWall Street. Scientific American, February 1999, 70–73.
66. Massopust, Peter R. Fractal Functions, Fractal Surfaces, and Wavelets. San Diego CA, Academic Press, 1994.
67. Mauldin, R. Daniel; Williams, S. C. Random recursive constructions: asymptotic geometrical and topological properties. Trans. Amer. Math. Soc.295(1986), no. 1, 325–346.
68. Mauldin, R. Daniel; Williams, S. C. Hausdorff dimension in graph directed constructions. Trans. Amer. Math. Soc.309(1988), no. 2, 811–829.
69. McGhehee, Richard. Attractors for closed relations on compact Hausdorff spaces. Indiana Univ. Math. J.41(1992), no. 4, 1165–1209.
70. Mendelson, Bert. Introduction to Topology, British edition. London, Glasgow, Blackie & Son, 1963.
71. Mochizuki S.; Horie, D.; Cai, D. Stealing Autumn Color. ACM SIGGRAPH poster, 2005. See http://mochi.jpn.org/temp/mochipdf.zip.
72. Moran, P. A. P. Additive functions of intervals and Hausdorff measure. Proc. Cambridge Philos. Soc.42(1946), 15–23.
73. Mumford, David; Series, Caroline; Wright, David. Indra's Pearls. The Vision of Felix Klein. New York, Cambridge University Press, 2002.
74. Navascués, M. A. Fractal polynomial interpolation. Z. Anal. Anwendungen24(2005), no. 2, 401–418.
75. Nitecki, Zbigniew H. Topological entropy and the preimage structure of maps. Real Anal. Exchange29(2003/4), no. 1, 9–41.
76. Onicescu, O.; Mihok, G. Sur les chaînes de variables statistiques. Bull. Sci. Math. de France59(1935), 174–192.
77. Parry, William. Symbolic dynamics and transformations of the unit interval. Trans. Amer. Math. Soc.122(1966), 368–378.
78. Peitgen, H.-O.; Richter, P. H. The Beauty of Fractals. Images of Complex Dynamical Systems. Berlin, Springer-Verlag, 1986.
79. Peruggia, Mario. Discrete Iterated Function Systems. Wellesley MA, A. K. Peters, 1993.
80. Prusinkiewicz, Przemyslaw; Lindenmayer, Aristid. The Algorithmic Beauty of Plants. With the collaboration of James S. Hanan, F. David Fracchia, Deborah R. Fowler, Martin J. M. de Boer and Lynn Mercer. The Virtual Laboratory. New York, Springer-Verlag, 1990.
81. Rachev, Svetlozar T. Probability Metrics and the Stability of Stochastic Models. Wiley Series in Probability and Statistics. Chichester, JohnWiley & Sons, 1991.
82. Rényi, A. Representations for real numbers and their ergodic properties. Acta Math. Acad. Sci. Hungar.8(1957), 477–493.
83. Ruelle, David. Zeta-functions for expanding maps and Anosov flows. Invent. Math.34(1976), no. 3, 231–242.
84. Sagan, Hans. Space-Filling Curves. Universitext. New York, Springer-Verlag, 1994.
85. Scealy, R. V-Variable Fractal Interpolation. In preparation.
86. Schattschneider, D. M. C. Escher: Visions of Symmetry, second edition. New York, Harry N. Abrams, 2004.
87. Scientific Workplace 4.0. MacKichan Software, 2002.
88. Shields, Paul C. The Ergodic Theory of Discrete Sample Paths. Graduate Studies in Mathematics, vol. 13. Providence RI, American Mathematical Society, 1996.
89. Solomyak, Boris. Dynamics of self-similar tilings. Ergodic Theory and Dynam. Systems17(1997), no. 3, 695–738. Corrections in Ergodic Theory and Dynam. Systems 19 (1999), no. 6, 1685.
90. Stenflo, Örjan. Markov chains in random environments and random iterated function systems. Trans. Amer. Math. Soc.353(2001), no. 9, 3547–3562.
91. Stenflo, Örjan. Uniqueness of invariant measures for place-dependent random iterations of functions. In Fractals in Multimedia(Minneapolis MN, 2001), pp. 13–32. IMA Vol. Math. Appl. New York, Springer-Verlag, 2002.
92. Stewart, Ian; Clarke, Arthur C.; Mandelbrot, Benôıt et al. In The Colours of Infinity: The Beauty and Power of Fractals. London, Clear Books, 2004.
93. Szoplik, T. (ed.) Selected Papers on Morphological Image Processing: Principles and Optoelectronic Implementations.Vol.MS127, SPIE. Optical Engineering Press, 1996.
94. The history of mathematics. In The New Encyclopaedia Britannica, fifteenth edition, vol. II, pp. 656–657. Chicago, London, 1979.
95. Tosan, Eric; Excoffier, Thierry; Rondet-Mignotte, Martine. Création de formes et de couleurs avec les IFS. Preprint 2005. Université Claude Bernard, France.
96. Tricot, Claude. Curves and Fractal Dimension. With a foreword by Michel Mendès France. Translated from the 1993 French original. New York, Springer-Verlag, 1995.
97. Vrscay, Edward R. From fractal image compression to fractal-based methods in mathematics. In Fractals in Multimedia(Minneapolis MN, 2001), pp. 65–106. IMA Vol. Math. Appl., vol. 132. New York, Springer, 2002.
98. Werner, Ivan. Ergodic theorem for contractive Markov systems. Nonlinearity17(2004), no. 6, 2303–2313.