Bibliography for Fractals

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  1. Complex Patterns on the Plane: Different Types of Basin Fractalization in a Two-Dimensional Mapping
    Lo´pez-Ruiz R.; Fournier-Prunaret D.
    International Journal of Bifurcation and Chaos, February 2003, vol. 13, no. 2, pp. 287-310(24), Ingenta.  
  2. A technique for measuring the density and complexity of understorey vegetation in tropical forests
    Marsden S.J.; Fielding A.H.; Mead C.; Hussin M.Z.
    Forest Ecology and Management, 15 July 2002, vol. 165, no. 1, pp. 117-123(7), Ingenta.    
  3. Progressing geometrically from ancient thought to fractals.
    McCartney, Mark
    Internat. J. Math. Ed. Sci. Tech. 32 (2001), no. 6, 937--944, MathSciNet.  
  4. Analysis of c-plane fractal images.
    Wang, Xingyuan; Liu, Xiangdong; Zhu, Weiyong; Gu, Shusheng
    Fractals 8 (2000), no. 3, 307--314, MathSciNet.  
  5. Fractal analysis of heart rate dynamics as a predictor of mortality in patients with depressed left ventricular function after acute myocardial infarction - chaos theory, fractals, and complexity at the bedside
    Makikallio T.H.; Hoiber S.; Kober L.; Torp-Pedersen C.; Peng C.-K.; Goldberger A.L.; Huikuri H.V.
    The American Journal of Cardiology, 15 March 1999, vol. 83, no. 6, pp. 836-839(4), Ingenta.    
  6. Time Course of Reactions Controlled and Gated by Intramolecular Dynamics of Proteins: Predictions of the Model of Random Wall on Fractal Lattices  
    M. Kurzynski; K. Palacz; P. Chelminiak  
    Proceedings of the National Academy of Sciences of the United States of America, Vol. 95, No. 20. (Sep. 29, 1998), pp. 11685-11690, Jstor.  
  7. Bud-Sequence conjecture on M fractal image and M-J conjecture between C and Z planes from z < - z w+c (w=+i)
    Chen N.; Zhu W.
    Computers & Graphics, August 1998, vol. 22, no. 4, pp. 537-546(10), Ingenta.    
  8. Fractal Geometry Gets the Measure of Life's Scales (in Research News)  
    Nigel Williams  
    Science, New Series, Vol. 276, No. 5309. (Apr. 4, 1997), p. 34, Jstor.  
  9. On the Inverse Fractal Problem for Two-Dimensional Attractors  
    A. Deliu; J. Geronimo; R. Shonkwiler  
    Philosophical Transactions: Mathematical, Physical and Engineering Sciences, Vol. 355, No. 1726. (May 15, 1997), pp. 1017-1062, Jstor.  
  10. Fractal Geometry of Bean Root Systems: Correlations between Spatial and Fractal Dimension (in Structure and Development)  
    Kai L. Nielsen; Jonathan P. Lynch; Howard N. Weiss  
    American Journal of Botany, Vol. 84, No. 1. (Jan., 1997), pp. 26-33, Jstor.  
  11. Fractals in Linear Algebra (in Computer Corner)  
    James A. Walsh  
    The College Mathematics Journal, Vol. 27, No. 4. (Sep., 1996), pp. 298-304, Jstor.  
  12. Sylow Fractals (in Notes)  
    Ben Brewster; Michael B. Ward  
    Mathematics Magazine, Vol. 68, No. 5. (Dec., 1995), pp. 372-376, Jstor.  
  13. Fractal Dimension as a Quantitative Measure of Complexity in Plant Development  
    John D. Corbit; David J. Garbary  
    Proceedings: Biological Sciences, Vol. 262, No. 1363. (Oct. 23, 1995), pp. 1-6, Jstor.  
  14. Earthquakes in the Los Angeles Metropolitan Region: A Possible Fractal Distribution of Rupture Size (in Reports)  
    S. E. Hough  
    Science, New Series, Vol. 267, No. 5195. (Jan. 13, 1995), pp. 211-213, Jstor.  
  15. Fractals in Earthquakes  
    Mitsuhiro Matsuzaki  
    Philosophical Transactions: Physical Sciences and Engineering, Vol. 348, No. 1688, Chaos and Forecasting. (Sep. 15, 1994), pp. 449-457, Jstor.  
  16. Fractal images of generalized Mandelbrot sets.
    Shiah, Aichyun; Ong, Kim-Khoon; Musielak, Zdzislaw E.
    Fractals 2 (1994), no. 1, 111--121, MathSciNet.  
  17. Fractal Basin Street Blues  
    Maurice Machover  
    Mathematics Magazine, Vol. 66, No. 4. (Oct., 1993), p. 226, Jstor.  
  18. Particles Floating on a Moving Fluid: A Dynamically Comprehensible Physical Fractal (in Research Article)  
    John C. Sommerer; Edward Ott  
    Science, New Series, Vol. 259, No. 5093. (Jan. 15, 1993), pp. 335-339, Jstor.  
  19. An Example of a Two-Term Asymptotics for the "Counting Function" of a Fractal Drum  
    Jacqueline Fleckinger-Pelle; Dmitri G. Vassiliev  
    Transactions of the American Mathematical Society, Vol. 337, No. 1. (May, 1993), pp. 99-116, Jstor.  
  20. Fractals and Cosmological Large-Scale Structure (in Reports)  
    Xiaochun Luo; David N. Schramm  
    Science, New Series, Vol. 256, No. 5056. (Apr. 24, 1992), pp. 513-515, Jstor.  
  21. Fractal music, hypercards and more dots.  
    Gardner, Martin
    Mathematical recreations from Scientific American magazine. W. H. Freeman and Company, New York, 1992. x+327 pp. ISBN: 0-7167-2188-0; 0-7167-2189-9, MathSciNet.  
  22. Fractals Illustrate the Mathematical Way of Thinking (in Classroom Computer Capsule)  
    Yves Nievergelt  
    The College Mathematics Journal, Vol. 22, No. 1. (Jan., 1991), pp. 60-64, Jstor.  
  23. Teaching about Fractals (in Computer Corner)  
    Stephen J. Willson  
    The College Mathematics Journal, Vol. 22, No. 1. (Jan., 1991), pp. 56-59, Jstor.  
  24. Number Systems With a Complex Base: a Fractal Tool for Teaching Topology (in The Teaching of Mathematics)  
    Daniel Goffinet  
    The American Mathematical Monthly, Vol. 98, No. 3. (Mar., 1991), pp. 249-255, Jstor.  
  25. Beating a Fractal Drum (in Research News)  
    Faye Flam  
    Science, New Series, Vol. 254, No. 5038. (Dec. 13, 1991), p. 1593, Jstor.  
  26. Newton's Method and Fractal Patterns  
    Straffin, Philip D.
    UMAP J., (1991), V. 12, No. 2, pp. 147-164, and UMAP, Module 716, pp. 1-18, COMAP, Inc. Lexington, MA 02420 USA. COMAP   
  27. Fractals and Transformations  
    Bannon, Thomas J.  
    Math. Teach., (1991), V. 81, No. 3, pp. 178-185.
  28. Blake and Fractals  
    J. D. Memory  
    Mathematics Magazine, Vol. 63, No. 4. (Oct., 1990), p. 280, Jstor.  
  29. Fractal Geometry of Music  
    Kenneth J. Hsu; Andreas J. Hsu  
    Proceedings of the National Academy of Sciences of the United States of America, Vol. 87, No. 3. (Feb., 1990), pp. 938-941, Jstor.  
  30. Polymers, Fractals, and Ceramic Materials  
    Dale W. Schaefer  
    Science, New Series, Vol. 243, No. 4894. (Feb. 24, 1989), pp. 1023-1027, Jstor.  
  31. Fractal Reaction Kinetics  
    Raoul Kopelman  
    Science, New Series, Vol. 241, No. 4873. (Sep. 23, 1988), pp. 1620-1626, Jstor.  
  32. A Computer Algorithm for Determining the Hausdorff Dimension of Certain Fractals  
    Lucy Garnett  
    Mathematics of Computation, Vol. 51, No. 183. (Jul., 1988), pp. 291-300, Jstor.  
  33. The science of fractal images.
    With contributions by Yuval Fisher and Michael McGuire. Barnsley, Michael F.; Devaney, Robert L.; Mandelbrot, Benoit B.; Peitgen, Heinz-Otto; Saupe, Dietmar; Voss, Richard F.
    Springer-Verlag, New York, 1988. xiv+312 pp. ISBN: 0-387-96608-0, MathSciNet.  
  34. Chaos, Strange Attractors, and Fractal Basin Boundaries in Nonlinear Dynamics  
    Celso Grebogi; Edward Ott; James A. Yorke  
    Science, New Series, Vol. 238, No. 4827. (Oct. 30, 1987), pp. 632-638, Jstor.  
  35. Fractals: Math. Monsters  
    Zobitz, Jennifer
    Pi Mu Epsilon J., (1987), V. 8, No. 7, pp. 425-440.
  36. Fractal Surfaces of Proteins (in Reports)  
    Mitchell Lewis; D. C. Rees  
    Science, New Series, Vol. 230, No. 4730. (Dec. 6, 1985), pp. 1163-1165, Jstor.  
  37. Additional Perspectives on Fractals  
    Barcellos and Mandelbrot
    The College Mathematics Journal, Vol. 15, No. 2. (Mar., 1984), pp. 115-119, Jstor.  
  38. The Fractal Geometry of Mandelbrot  
    Anthony Barcellos  
    The College Mathematics Journal, Vol. 15, No. 2. (Mar., 1984), pp. 98-114, Jstor.  
  39. Self-Inverse Fractals Osculated by Sigma-Discs and the Limit Sets of Inversion Groups  
    Mandelbrot, Benoit B.  
    Math. Intell., (1983), V. 5, No. 2, pp. 9-17.
  40. Fractal Geometry Derived from Complex Bases  
    Gilbert, William J.  
    Math. Intell., (1982), V. 4, pp. 78-86, MathSciNet.  
  41. On the Weierstrass-Mandelbrot Fractal Function  
    M. V. Berry; Z. V. Lewis  
    Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 370, No. 1743. (Apr. 24, 1980), pp. 459-484, Jstor.  
  42. Stochastic Models for the Earth's Relief, the Shape and the Fractal Dimension of the Coastlines, and the Number-Area Rule for Islands  
    Benoit B. Mandelbrot  
    Proceedings of the National Academy of Sciences of the United States of America, Vol. 72, No. 10. (Oct., 1975), pp. 3825-3828, Jstor.  

 

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(c) John H. Mathews 2003