Abstract
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References
BAISH, J. W. & Jain, R. K. Fractals and Cancer. Cancer Research, 60, pp. 3683–3688, 2000.
BALESTRA, C., Marroni, A., Farkos, B., Peetrons, P., Vanderschueren, F., Duboc, E., Snoeck, T. & Germonpré, P. The Fractal Approach as a Tool to Understand Asymptomatic Brain. Fractals, 12(1), pp. 67–72, 2004.
BARNSLEY, M. F. Fractal functions and interpolation. Journal Constructive Approximation, 2(1), pp. 303-329, 1986.
BOXT L. M., Katz J., Leibovitch L. S., Jones R., Esser P. D. & Reid L. Fractal analysis of pulmonary arteries: The fractal dimension is lower in pulmonary hypertension. Journal of Thoracic Imaging, 9(1), pp. 8–13, 1994.
CHAND, A. K. B. & Kapoor, G. P. Generalized cubic spline fractal interpolation functions. SIAM Journal on Numerical Analysis, 44(2), pp. 655–676, 2006.
COHEN, N. Fractal Antenna Applications in Wireless Telecommunications.
IEEE Proc. Professional. Program Electronics Industry Forum, pp. 43-49, 1997.
CROSS, S. S. Fractals in Pathology, Journal of Pathology, 182, pp. 1–8, 1997.
DAXER A. Characterisation of the neovascularisation process in diabetic retinopathy by means of fractal geometry: Diagnostic implications. Graefe’s Arch Clin Exp Ophthalmol, 231, pp. 681–686, 1993.
FLAKE, G. W. The computational beauty of nature, MIT Press, 1998. Fisher, Y. Fractal image compression, Springer-Verlag, New York, 1995.
HAHN, H. K., Evertsz, C. J. G., Fasel, J. H. D. & Peitgen, H. O. Fractal Properties Segment Anatomy and Interdependence of the Human Portal Vein and the Hepatic Vein in 3D. Fractals, 11, pp. 53-62, 2003.
HAVLIN S., Buldyrev S.V., Goldberger A.L., Mantegna R.N., Ossadnik S.M., Peng C.K., Simon M. & Stanley H. E. Fractals in Biology and
Medicine. Chaos Solitons & Fractals, 6, pp. 171-201, 1995.
HECK, A. & Perdang, J. M. Applying Fractals in Astronomy, Springer-Verlag, 1991.
HUTCHINSON, J. E. Fractals and self-similarity. Indiana University Mathematics Journal, 30(5), pp. 713–747, 1981.
IANNACCONE, P. M. & Khokha, M. Fractal Geometry in Biological Systems, CRC Press, 1996.
IVERSEN P. O. & Nicolaysen G. Fractals describes blood fl ow heterogeneity within skeletal muscle and within myocardium. American
Journal of Physioly, 268, pp. H112–H116, 1995.
JACQUIN, A.E. Fractal image coding: A review. Proceedings of the IEEE, 81(10), pp. 1451-1465, 1993.
JEAN-FRANÇOIS GOUYET & AMY L. R. Physics and Fractal Structures. American Journal of Physics, 65(7), pp. 676-677, 1997.
KELLER, J. M., Chen, S., and Crownover, R. M. Texture description and segmentation through fractal geometry. Computer Vision, Graphics, and Image Processing, 45, pp. 150-166, 1989.
KIM K. & Yoon S.-M. Dynamical behavior of continuous tick data in futures exchange market. Fractals, 11, pp. 131–136, 2003.
KIM, S. Player’s Positional Dependence of Fractal Behaviors in a Soccer Game. Fractals, 14(1), pp. 71-76, 2006.
KOSTOFF, R. N., Shlesinger, M. F. & Malpohl, G. Fractals text mining using bibliometrics and database tomography. Fractals, 12(1), pp. 1-16, 2004.
KURNAZ, M. L. Application of Detrended Fluctuation Analysis to Monthly Average of the Maximum Daily Temperatures to Resolve Different Climates. Fractals, 12(4), pp. 365-373, 2004.LAZARECK, L. Verch, G. & Peter, A. F. Fractals in circuits. Canadian Conference on Electrical and Computer Engineering, 2001.
LESMOIR-GORDON, N., Rood, W. & Edney, R.Introducing Fractal Geometry, ICON Books UK, 2000.
LIN D. C. Model the fractal component in heart rate variability as a dyadic bounded cascade. Fractals, 11, pp. 63-76, 2003.
LINDENMAYER, A. Mathematical Models for Cellular Interaction in Development, Parts I and II. Journal of Theoretical Biology, 18, pp.
280–315, 1968.
LEFEBRE F., BENALI H., Gilles R., Kahn E. & Di Paola R. A fractal approach to the segmentation of microcalcifi cation in digital mammograms. Med Phys, 22, pp. 381–390, 1995.
LOOCKE, P. V. Visualization of Data on Basis of Fractal Growth. Fractals, 12(1), pp. 123-136, 2004.
M. F. BARNSLEY & L. P. Hurd. Fractal image compression, A. K. Peters, Boston, 1992.
MANDELBROT, B. The Fractal Geometry of Nature, W. H. Freemand and Company, 1983.
MANDELBROT, B. B. Self-affi ne fractals and fractal dimension. Physica Scripta, 32, p.257-260, 1985.
MANDELBROT, B. B. Fractal Geometry: What Is It, and What Does It Do? Proc. of the Royal Society of London A, 423, pp. 3-16, 1989.
MANDELBROT, B. B. & Hudson, R. L. The (Mis)behavior of Markets - A Fractal View of Risk, Ruin, and Reward, Basic Books, 2004.
MANDELBROT, B. B. Fractals and Scaling in Finance, Springer, 2005.
MANDELBROT, B. B. & van Ness, J. W. Fractional Brownian Motions, Fractional Noises and Applications. SIAM Review, 10(4), pp. 422–
437, 1968.
MATIA K., Ashkenazy Y. & Stanley H. E. Multifractal properties of price fl uctuations of stock and commodities. Europhysics Letters, 61, pp. 422-428, 2003.
MEYER, M., Stiedl, O. & Kerman, B. Discrimination by Multifractal Spectrum Estimation of Human Heartbeat. Fractals, 11(2), pp. 195–
204, 2003.NAGAO, M., Murase, K., Kikuchi, T., Ikeda, M., Nebu, A., Fukuhara, R., Sugawara, Y., Miki, H., Ikezoe, J. Fractal Analysis of Cerebral Blood Flow Distribution in Alzheimer’s Disease. J Nucl Med, 42, pp. 1446-1450, 2001.
NG, T., Chang, S., Hsu, J., Xie, L. & Tsui, M. Physics-motivated features for distinguishing photographic images and computer graphics. Proceedings of the 13th Annual ACM international Conference on Multimedia, pp. 239-248, 2005.
NAVASCUÉS, M. A. & Sebastián, M. V. Generalization of Hermite functions by fractal interpolation. Journal of Approximation Theory,
131(1), pp. 19-29, 2004.
NICOLLET, M., Lemarchand, A. & Cavaciuti, N. Detection of atmospheric turbulence by multifractal analysis using wavelets. Fractals,
12(2), pp. 211-221, 2004.
PEITGEN, H.-O & Saupe, D. The Science of Fractal Images, Springer-Verlag, 1988.
PENTLAND A. P. Fractal-based description of natural scenes”, IEEE Trans. on Pattern Analysis and Machine Intelligence, 6, pp. 661-674, 1984.
PRIEBE C. E., Solka J. L., Lorey R. A. et al. The application of fractal analysis to mammographic tissue classifi cation”, Cancer Lett, 77,
pp. 83–189, 1994.
PRUSINKIEWICZ, P. & Lindenmayer, A. The Algorithmic Beauty of Plants, Springer-Verlag, 1990.
REEVES, W. T. Particle Systems - A Technique for Modeling a Class of Fuzzy Objects. ACM Transactions on Graphics, 2(2), pp. 91–108, 1983.
ROOM, P., Hanan, J. & Prusinkiewicz, P. Virtual Plants: New Perspectives for Ecologists, Pathologists and Agricultural Scientists, Trends in Plant Science, 1(1), pp. 33–38, 1996.
SAUPE, D. & Hamzaoui, R. A bibliography for fractal image compression. Institut für Informatik, Universität Freiburg, Germany. Available as ftp://www.informatik.uni-freiburg.de/documents/papers/fractal/biblio.ps.gz, 1996.
SENGUPTA, R., Dey, N., Datta, A. K. & Ghosh, D. Assessment of Musical Quality of Tanpura by Fractal-Dimensional Analysis. Fractals,
13(3), pp. 245-252, 2005.SHINMOTO, J. & Takeo, F. The Hausdorff Dimension of Sub-Self-Similar Sets, Fractals, 11(1), pp. 9-18. 2003.
SIMS, K. Artifi cial Evolution for Computer Graphics. Computer Graphics, 25(4), pp. 319–328, 1991.
SMITH, A. R. Plants, Fractals, and Formal Languages. Computer Graphics, 18(3), pp. 1–10, 1984.
SONG, C. T. P., Hall, P. S. & Ghafouri-Shiraz, H. Shorted fractal Sierpinski monopole antenna. IEEE Transactions on Antennas and Propagation, 52(10), pp. 2564-2570, 2004.
SZILARD, A. L. and Quinton, R. E. An Interpretation for DOL systems by Computer Graphics. The Science Terrapin, 4, pp. 8–13, 1979.
WOHLBERG, B. & De Jager, G. A review of the fractal image coding literature. IEEE Transactions on Image Processing, 8(12), pp. 1716-
1729, 1999.
WOYSHVILLE M. J., Calabrese J. R. Quantifi cation of occipital EEG changes in Alzheimer’s disease utilizing a new metric: the fractal dimension. Biol Psych, 35, pp. 381–387, 1994.
YANG, X., Chiocetti, J., Papadopoulos, D. & Sussman, L. Fractal Antenna Elements and Arrays. Applied Microwave & Wireless, 11(5), pp. 34-46, 1999.
ZIETSCH, B. & Elston, G. N. Fractal Analysis of Pyramidal Cells in the Visual Cortex of the Galago (Otolemur Garnetti): Regional Variation in Dendritic Branching Patterns Between Visual Areas. Fractals, 13(2), pp. 83-90, 2005.
BALESTRA, C., Marroni, A., Farkos, B., Peetrons, P., Vanderschueren, F., Duboc, E., Snoeck, T. & Germonpré, P. The Fractal Approach as a Tool to Understand Asymptomatic Brain. Fractals, 12(1), pp. 67–72, 2004.
BARNSLEY, M. F. Fractal functions and interpolation. Journal Constructive Approximation, 2(1), pp. 303-329, 1986.
BOXT L. M., Katz J., Leibovitch L. S., Jones R., Esser P. D. & Reid L. Fractal analysis of pulmonary arteries: The fractal dimension is lower in pulmonary hypertension. Journal of Thoracic Imaging, 9(1), pp. 8–13, 1994.
CHAND, A. K. B. & Kapoor, G. P. Generalized cubic spline fractal interpolation functions. SIAM Journal on Numerical Analysis, 44(2), pp. 655–676, 2006.
COHEN, N. Fractal Antenna Applications in Wireless Telecommunications.
IEEE Proc. Professional. Program Electronics Industry Forum, pp. 43-49, 1997.
CROSS, S. S. Fractals in Pathology, Journal of Pathology, 182, pp. 1–8, 1997.
DAXER A. Characterisation of the neovascularisation process in diabetic retinopathy by means of fractal geometry: Diagnostic implications. Graefe’s Arch Clin Exp Ophthalmol, 231, pp. 681–686, 1993.
FLAKE, G. W. The computational beauty of nature, MIT Press, 1998. Fisher, Y. Fractal image compression, Springer-Verlag, New York, 1995.
HAHN, H. K., Evertsz, C. J. G., Fasel, J. H. D. & Peitgen, H. O. Fractal Properties Segment Anatomy and Interdependence of the Human Portal Vein and the Hepatic Vein in 3D. Fractals, 11, pp. 53-62, 2003.
HAVLIN S., Buldyrev S.V., Goldberger A.L., Mantegna R.N., Ossadnik S.M., Peng C.K., Simon M. & Stanley H. E. Fractals in Biology and
Medicine. Chaos Solitons & Fractals, 6, pp. 171-201, 1995.
HECK, A. & Perdang, J. M. Applying Fractals in Astronomy, Springer-Verlag, 1991.
HUTCHINSON, J. E. Fractals and self-similarity. Indiana University Mathematics Journal, 30(5), pp. 713–747, 1981.
IANNACCONE, P. M. & Khokha, M. Fractal Geometry in Biological Systems, CRC Press, 1996.
IVERSEN P. O. & Nicolaysen G. Fractals describes blood fl ow heterogeneity within skeletal muscle and within myocardium. American
Journal of Physioly, 268, pp. H112–H116, 1995.
JACQUIN, A.E. Fractal image coding: A review. Proceedings of the IEEE, 81(10), pp. 1451-1465, 1993.
JEAN-FRANÇOIS GOUYET & AMY L. R. Physics and Fractal Structures. American Journal of Physics, 65(7), pp. 676-677, 1997.
KELLER, J. M., Chen, S., and Crownover, R. M. Texture description and segmentation through fractal geometry. Computer Vision, Graphics, and Image Processing, 45, pp. 150-166, 1989.
KIM K. & Yoon S.-M. Dynamical behavior of continuous tick data in futures exchange market. Fractals, 11, pp. 131–136, 2003.
KIM, S. Player’s Positional Dependence of Fractal Behaviors in a Soccer Game. Fractals, 14(1), pp. 71-76, 2006.
KOSTOFF, R. N., Shlesinger, M. F. & Malpohl, G. Fractals text mining using bibliometrics and database tomography. Fractals, 12(1), pp. 1-16, 2004.
KURNAZ, M. L. Application of Detrended Fluctuation Analysis to Monthly Average of the Maximum Daily Temperatures to Resolve Different Climates. Fractals, 12(4), pp. 365-373, 2004.LAZARECK, L. Verch, G. & Peter, A. F. Fractals in circuits. Canadian Conference on Electrical and Computer Engineering, 2001.
LESMOIR-GORDON, N., Rood, W. & Edney, R.Introducing Fractal Geometry, ICON Books UK, 2000.
LIN D. C. Model the fractal component in heart rate variability as a dyadic bounded cascade. Fractals, 11, pp. 63-76, 2003.
LINDENMAYER, A. Mathematical Models for Cellular Interaction in Development, Parts I and II. Journal of Theoretical Biology, 18, pp.
280–315, 1968.
LEFEBRE F., BENALI H., Gilles R., Kahn E. & Di Paola R. A fractal approach to the segmentation of microcalcifi cation in digital mammograms. Med Phys, 22, pp. 381–390, 1995.
LOOCKE, P. V. Visualization of Data on Basis of Fractal Growth. Fractals, 12(1), pp. 123-136, 2004.
M. F. BARNSLEY & L. P. Hurd. Fractal image compression, A. K. Peters, Boston, 1992.
MANDELBROT, B. The Fractal Geometry of Nature, W. H. Freemand and Company, 1983.
MANDELBROT, B. B. Self-affi ne fractals and fractal dimension. Physica Scripta, 32, p.257-260, 1985.
MANDELBROT, B. B. Fractal Geometry: What Is It, and What Does It Do? Proc. of the Royal Society of London A, 423, pp. 3-16, 1989.
MANDELBROT, B. B. & Hudson, R. L. The (Mis)behavior of Markets - A Fractal View of Risk, Ruin, and Reward, Basic Books, 2004.
MANDELBROT, B. B. Fractals and Scaling in Finance, Springer, 2005.
MANDELBROT, B. B. & van Ness, J. W. Fractional Brownian Motions, Fractional Noises and Applications. SIAM Review, 10(4), pp. 422–
437, 1968.
MATIA K., Ashkenazy Y. & Stanley H. E. Multifractal properties of price fl uctuations of stock and commodities. Europhysics Letters, 61, pp. 422-428, 2003.
MEYER, M., Stiedl, O. & Kerman, B. Discrimination by Multifractal Spectrum Estimation of Human Heartbeat. Fractals, 11(2), pp. 195–
204, 2003.NAGAO, M., Murase, K., Kikuchi, T., Ikeda, M., Nebu, A., Fukuhara, R., Sugawara, Y., Miki, H., Ikezoe, J. Fractal Analysis of Cerebral Blood Flow Distribution in Alzheimer’s Disease. J Nucl Med, 42, pp. 1446-1450, 2001.
NG, T., Chang, S., Hsu, J., Xie, L. & Tsui, M. Physics-motivated features for distinguishing photographic images and computer graphics. Proceedings of the 13th Annual ACM international Conference on Multimedia, pp. 239-248, 2005.
NAVASCUÉS, M. A. & Sebastián, M. V. Generalization of Hermite functions by fractal interpolation. Journal of Approximation Theory,
131(1), pp. 19-29, 2004.
NICOLLET, M., Lemarchand, A. & Cavaciuti, N. Detection of atmospheric turbulence by multifractal analysis using wavelets. Fractals,
12(2), pp. 211-221, 2004.
PEITGEN, H.-O & Saupe, D. The Science of Fractal Images, Springer-Verlag, 1988.
PENTLAND A. P. Fractal-based description of natural scenes”, IEEE Trans. on Pattern Analysis and Machine Intelligence, 6, pp. 661-674, 1984.
PRIEBE C. E., Solka J. L., Lorey R. A. et al. The application of fractal analysis to mammographic tissue classifi cation”, Cancer Lett, 77,
pp. 83–189, 1994.
PRUSINKIEWICZ, P. & Lindenmayer, A. The Algorithmic Beauty of Plants, Springer-Verlag, 1990.
REEVES, W. T. Particle Systems - A Technique for Modeling a Class of Fuzzy Objects. ACM Transactions on Graphics, 2(2), pp. 91–108, 1983.
ROOM, P., Hanan, J. & Prusinkiewicz, P. Virtual Plants: New Perspectives for Ecologists, Pathologists and Agricultural Scientists, Trends in Plant Science, 1(1), pp. 33–38, 1996.
SAUPE, D. & Hamzaoui, R. A bibliography for fractal image compression. Institut für Informatik, Universität Freiburg, Germany. Available as ftp://www.informatik.uni-freiburg.de/documents/papers/fractal/biblio.ps.gz, 1996.
SENGUPTA, R., Dey, N., Datta, A. K. & Ghosh, D. Assessment of Musical Quality of Tanpura by Fractal-Dimensional Analysis. Fractals,
13(3), pp. 245-252, 2005.SHINMOTO, J. & Takeo, F. The Hausdorff Dimension of Sub-Self-Similar Sets, Fractals, 11(1), pp. 9-18. 2003.
SIMS, K. Artifi cial Evolution for Computer Graphics. Computer Graphics, 25(4), pp. 319–328, 1991.
SMITH, A. R. Plants, Fractals, and Formal Languages. Computer Graphics, 18(3), pp. 1–10, 1984.
SONG, C. T. P., Hall, P. S. & Ghafouri-Shiraz, H. Shorted fractal Sierpinski monopole antenna. IEEE Transactions on Antennas and Propagation, 52(10), pp. 2564-2570, 2004.
SZILARD, A. L. and Quinton, R. E. An Interpretation for DOL systems by Computer Graphics. The Science Terrapin, 4, pp. 8–13, 1979.
WOHLBERG, B. & De Jager, G. A review of the fractal image coding literature. IEEE Transactions on Image Processing, 8(12), pp. 1716-
1729, 1999.
WOYSHVILLE M. J., Calabrese J. R. Quantifi cation of occipital EEG changes in Alzheimer’s disease utilizing a new metric: the fractal dimension. Biol Psych, 35, pp. 381–387, 1994.
YANG, X., Chiocetti, J., Papadopoulos, D. & Sussman, L. Fractal Antenna Elements and Arrays. Applied Microwave & Wireless, 11(5), pp. 34-46, 1999.
ZIETSCH, B. & Elston, G. N. Fractal Analysis of Pyramidal Cells in the Visual Cortex of the Galago (Otolemur Garnetti): Regional Variation in Dendritic Branching Patterns Between Visual Areas. Fractals, 13(2), pp. 83-90, 2005.
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