Bibliography for the Mandelbrot Set

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  1. Visible and nonexistent trees of Mandelbrot sets. Dissertation, University of Jyväskylä, Jyväskylä, 2003. Report.
    Kauko, Virpi
    University of Jyväskylä Department of Mathematics and Statistics, 86. University of Jyväskylä, Jyväskylä, 2003. 26 pp. ISBN: 951-39-1318-X, MathSciNet.  
  2. Parametric 2-dimensional L systems and recursive fractal images: Mandelbrot set, Julia sets and biomorphs
    Ortega A.; de la Cruz M.; Alfonseca M.
    Computers and Graphics, February 2002, vol. 26, no. 1, pp. 143-149(7), Ingenta.  
  3. Generalized Mandelbrot sets for meromorphic complex and quaternionic maps.
    Buchanan, Walter; Gomatam, Jagannathan; Steves, Bonnie
    Internat. J. Bifur. Chaos Appl. Sci. Engrg. 12 (2002), no. 8, 1755--1777, MathSciNet.  
  4. Pi in the Mandelbrot set.
    Klebanoff, Aaron
    Fractals 9 (2001), no. 4, 393--402, MathSciNet.  
  5. Julia and Mandelbrot sets of Chebyshev families.
    Peherstorfer, Franz; Stroh, Christoph
    Internat. J. Bifur. Chaos Appl. Sci. Engrg. 11 (2001), no. 9, 2463--2481, MathSciNet.  
  6. The Mandelbrot set is universal.
    McMullen, Curtis T.
    The Mandelbrot set, theme and variations, 1--17, London Math. Soc. Lecture Note Ser., 274, Cambridge Univ. Press, Cambridge, 2000, MathSciNet.  
  7. A generalized Mandelbrot set for bicomplex numbers.
    Rochon, Dominic
    Fractals 8 (2000), no. 4, 355--368, MathSciNet.  
  8. The Mandelbrot set, the Farey tree, and the Fibonacci sequence.
    Devaney, Robert L.
    Amer. Math. Monthly 106 (1999), no. 4, 289--302, Jstor.  
  9. An abstract Mandelbrot set algorithm for z^n + c.
    Kern, Albert; Frame, Michael
    Fractals 6 (1998), no. 1, 1--10, MathSciNet.  
  10. The Mandelbrot set. (Spanish)
    Rubiano, Gustavo
    Bol. Mat. (N.S.) 3 (1996), no. 1, 25--36, MathSciNet.  
  11. The rigorous solutions of some nonlinear complex dynamical systems. The filled Julia set and the Mandelbrot set.
    Matayoshi, Gousirou; Matayoshi, Seitarou
    Bull. College Sci. Univ. Ryukyus No. 63 (1996), 63--71, MathSciNet.  
  12. On the cusp and the tip of a midget in the Mandelbrot set antenna.  
    Romera, M.; Pastor, G.; Montoya, F.
    Phys. Lett. A  221  (1996),  no. 3-4, 158--162, MathSciNet.  
  13. Discrete dynamics of quaternionic maps: generalisation of the Mandelbrot set.
    McFarlane, Isobel; Gomatam, Jagannathan
    Proceedings of Dynamic Systems and Applications, Vol. 2 (Atlanta, GA, 1995), 383--390, Dynamic, Atlanta, GA, 1996, MathSciNet.  
  14. A Parameterization of the Period 3 Hyperbolic Components of the Mandelbrot Set  
    Dante Giarrusso; Yuval Fisher  
    Proceedings of the American Mathematical Society, Vol. 123, No. 12. (Dec., 1995), pp. 3731-3737, Jstor.  
  15. Can We See the Mandelbrot Set?  
    John Ewing  
    The College Mathematics Journal, Vol. 26, No. 2. (Mar., 1995), pp. 90-99, Jstor.  
  16. Is the Mandelbrot Set Decidable?
    Smale S.
    Mathematical Social Sciences, December 1995, vol. 30, no. 3, pp. 328-328(1), Ingenta.  
  17. Generalization of the Mandelbrot Set: Quaternionic Quadratic Maps
    Gomatam J.; Doyle J.; Steves B.; McFarlane I.
    Chaos, Solitons and Fractals, June 1995, vol. 5, no. 6, pp. 971-986(16), Ingenta.  
  18. On the complement of the Mandelbrot set.
    Levin, G. M.
    Israel J. Math. 88 (1994), no. 1-3, 189--212, MathSciNet.  
  19. The "mystery" of the quadratic Mandelbrot set.
    Metzler, Wolfgang
    Amer. J. Phys. 62 (1994), no. 9, 813--814, MathSciNet.  
  20. Spirals in the Mandelbrot set. I, II, III.
    Stephenson, John
    Phys. A 205 (1994), no. 4, 634--645, 646--655, 656--664, MathSciNet.  
  21. The Mandelbrot Set and sigma-Automorphisms of Quotients of the Shift  
    Pau Atela  
    Transactions of the American Mathematical Society, Vol. 335, No. 2. (Feb., 1993), pp. 683-703, Jstor.  
  22. Symbolic dynamics for angle-doubling on the circle. II. Symbolic description of the abstract Mandelbrot set
    Bandt C.; Keller K.
    Nonlinearity, 1993, vol. 6, no. 3, pp. 377-392(16), Ingenta.  
  23. Formulae for cycles in the Mandelbrot set. II.
    Stephenson, John; Ridgway, Douglas T.
    Phys. A 190 (1992), no. 1-2, 104--116, MathSciNet.  
  24. The area of the Mandelbrot set.
    Ewing, John H.; Schober, Glenn
    Numer. Math. 61 (1992), no. 1, 59--72, MathSciNet.  
  25. Nonanalytic dynamics for generating the Mandelbrot set: a tutorial.
    Metzler, W.; Brelle, A.; Schmidt, K.-D.
    Internat. J. Bifur. Chaos Appl. Sci. Engrg. 2 (1992), no. 2, 241--250, MathSciNet.  
  26. The Orbit Diagram and the Mandelbrot Set  
    Robert L. Devaney  
    The College Mathematics Journal, Vol. 22, No. 1. (Jan., 1991), pp. 23-38, Jstor.  
  27. The Mandelbrot Set in the Classroom  
    Frantz, Marny and Sylvia Lazarnick  
    The Math. Teach., (1991), V. 84, No. 3, pp. 173-177.
  28. Formulae for cycles in the Mandelbrot set.
    Stephenson, John
    Current problems in statistical mechanics (Washington, DC, 1991). Phys. A 177 (1991), no. 1-3, 416--420, MathSciNet.  
  29. Similarity between the Mandelbrot set and Julia sets.
    Tan, Lei
    Comm. Math. Phys. 134 (1990), no. 3, 587--617, MathSciNet.  
  30. The Mandelbrot set for binary numbers.
    Senn, Peter
    Amer. J. Phys. 58 (1990), no. 10, 1018, MathSciNet.  
  31. A Mandelbrot Set whose Boundary is Piecewise Smooth  
    M. F. Barnsley; D. P. Hardin  
    Transactions of the American Mathematical Society, Vol. 315, No. 2. (Oct., 1989), pp. 641-659, Jstor.  
  32. On the Structure of the Mandelbar Set  
    Crowe, W. D. and R. Hasson and P. J. Rippon and P. E. D. Strain-Clark  
    Nonlinearity, (1989), V. 2, pp. 541-553
  33. The beauty and complexity of the Mandelbrot set.
    Hubbard, John
    American Mathematical Society, Providence, RI, 1989. 1 videocassette (NTSC; 1/2 inch; VHS) (73 min.); sd., col. ISBN: 1-878310-02-X, MathSciNet.  
  34. Looking at the Mandelbrot Set (in Computer Corner)  
    Mark Bridger  
    The College Mathematics Journal, Vol. 19, No. 4. (Sep., 1988), pp. 353-363, Jstor.  
  35. The Mandelbrot set.
    Branner, Bodil
    Chaos and fractals (Providence, RI, 1988), 75--105, Proc. Sympos. Appl. Math., 39, Amer. Math. Soc., Providence, RI, 1989, MathSciNet.  
  36. The Mandelbrot set: a paradigm for experimental mathematics.
    Peitgen, Heinz-Otto; Jürgens, Hartmut; Saupe, Dietmar
    Educational computing in mathematics (Rome, 1987), 99--113, p. 284, North-Holland, Amsterdam, 1988, MathSciNet.  
  37. Julia Sets and Mandelbrot-Like Sets Associated With Higher Order Schroder Rational Iteration Functions: A Computer Assisted Study  
    Edward R. Vrscay  
    Mathematics of Computation, Vol. 46, No. 173. (Jan., 1986), pp. 151-169, Jstor.  
  38. Mandelbrot sets for pairs of affine transformations in the plane.
    Vrscay, Edward R.
    J. Phys. A 19 (1986), no. 11, 1985--2001, MathSciNet.  
  39. A Multivariate Weierstrass-Mandelbrot Function  
    M. Ausloos; D. H. Berman  
    Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 400, No. 1819. (Aug. 8, 1985), pp. 331-350, Jstor.  
  40. The Mandelbrot set in a model for phase transitions.
    Peitgen, Heinz-Otto; Richter, Peter H.
    Workshop Bonn 1984 (Bonn, 1984), 111--134, Lecture Notes in Math., 1111, Springer, Berlin, 1985, MathSciNet.  
  41. The Fractal Geometry of Mandelbrot  
    Anthony Barcellos  
    The College Mathematics Journal, Vol. 15, No. 2. (Mar., 1984), pp. 98-114, Jstor.  
  42. 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.  

 

 

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