Fractals

  1. Banchoff, Thomas F.  “Dimension” in On the Shoulders of Giants, Lynn Arthur Steen, Ed., National Academy Press, Washington DC 1990, 11-59.
  2. Bannon, Thomas J. “Fractals and Transformations.” Mathematics Teacher 84 (March 1991): 178-85.
  3. Barcellos, Anthony “The Fractal Geometry of Mandelbrot.” College Mathematics Journal 15 (March 1984): 98-114.
  4. *Barnsley, Michael Fractals Everywhere. San Diego, CA: Academic Press, 1988.
  5. Barton, Ray. “Chaos and Fractals.” Mathematics Teacher 83 (October 1990):524-29.
  6. Bedford, Crayton; “The Case for Chaos,” The Mathematics Teacher, April 1998, p 276-281.
  7. Bennett, Dan “A Fractal Class Activity: The Sierpinski Gasket.” Discovering Geometry Newsletter 1 (Fall 1989): 3 Berkeley, CA: Key Curriculum Press.
  8. Camp, Dane R. “Benoit Mandelbrot: The Euclid of Fractal Geometry” Mathematics Teacher. 93:8 (Nov. 2000): 708-712.
  9. Camp, Dane R. “A Fractal Excursion.” Mathematics Teacher. 84 (April 1991): 265-75.
  10. Cibes, Margaret. “The Sierpinski Triangle: Deterministic versus Random Models.” Mathematics Teacher 83 (November 1990): 617-21.
  11. Devaney, Robert L. Chaos, Fractals, and Dynamics: Computer Experiments in Mathematics. Menlo Park, CA: Addison-Wesley, 1990.
  12. Devaney, Robert L. and Keen, Linda; Chaos and Fractals: The Mathematics Behind the Computer Graphics, AMS, 1989. T385.C454.
  13. Devaney, Robert L, Complex Dynamical Systems: The Mathematics Behind the Mandelbrot and Julia Sets, AMS, 1994. QA614.8.C645.
  14. *Dewdney, A.K. “Computer Recreations.” Scientific American, August 1985, December 1986, July 1987, November 1987, February 1989, May 1990.
  15. Egsgard, John C. “An Interesting Introduction to Sequences and Series.” Mathematics Teacher 81 (February 1988): 108-111.
  16. Flake, Gary W. The Computational Beauty of Nature. MIT Press, 1998.
  17. Fleishmann, M., Tildesley, D.J., Ball, R.C., Fractals in the Natural Sciences
  18. Garcia, Linda; The Fractal Explorer Dynamic Press, Santa Cruz, CA 1991. JNC
  19. Gilmore, Elizabeth B. “Elementary Fractal Investigation.” Math Times Journal 1 (No. 4): 30-39.
  20. Gleick, James Chaos: Making a New Science. New York, NY: Viking Penguin, 1987.
  21. *Goldberger, Ary L., Rigney, David R., and West, Bruce J. “Chaos and Fractals in Human Physiology.” Scientific American February 1990: 42-49.
  22. Goldenberg, E. Paul “Seeing Beauty in Mathematics: Using Fractal Geometry to Build a Spirit of Mathematical Inquiry.” MAA Note: Visualization in Teaching and Learning Mathematics, Washington, DC: MAA, 1991.
  23. Hofstadter, Douglas R. “Strange attractors: mathematical patterns delicately poised between order and chaos.” Scientific American November 1981: 22-43.
  24. Jrgens, Hartmut, Peitgen, Heinz-Otto and Saupe, Dietmar “The Language of Fractals.” Scientific American (August 1990): 60-67.
  25. Kern, Jane F. and Mauk, Cherry C. “Exploring Fractals-A Problem-solving Adventure Using Mathematics and Logo.” Mathematics Teacher 83 (March 1990): 179-85, 244.
  26. *Mandelbrot, Benoit B. The Fractal Geometry of Nature. Rev. ed.  New York: W. H. Freeman & Co., 1983.
  27. *McDermott, Joanne “Geometrical Forms Known As Fractals Find Sense in Chaos.” Smithsonian 14 (December 1983): 110-117.
  28. Martelli, Dang, Seph; “Defining Chaos,” Mathematics Magazine, April 1998, p 112-122.
  29. *Peitgen, Heinz-Otto, Jrgens, Hartmut, and Saupe, Dietmar Fractals for the Classroom, Part One: Introduction to Fractals and Chaos. New York, NY: Springer-Verlag, (Published in cooperation with, and also available from the NCTM), 1992.
  30. *Peitgen, Heinz-Otto, Jrgens, Hartmut, and Saupe, Dietmar Fractals for the Classroom-Strategic Activities, Volume One. New York, NY: Springer-Verlag, (Published in cooperation with, and also available from the NCTM), 1991. Includes a set of nine slides.
  31. *Peitgen, Heinz-Otto and Saupe, Dietmar (eds.) The Science of Fractal Images. New York, NY: Springer-Verlag, 1988.
  32. *Peitgen, Heinz-Otto and Richter, P.H. (eds.) The Beauty of Fractals: Images of Complex Dynamical Systems. New York, NY: Springer-Verlag, 1986.
  33. Peterson, Ivars “Time To Relax.” Science News 135 (March 11, 1989): 157-159.
  34. Peterson, Ivars “Packing It In: Fractals Play An Important Role in Image Compression.” Science News 131 (May 2, 1987): 283-285.
  35. Peterson, Ivars “Ants In Labyrinths and Other Fractal Excursions.” Science News 21 (Jan. 21, 1984): 42-43.
  36. Pickover, The Pattern Book: Fractals, Art and Nature, World Scientific, TR in May ’96 Monthly.
  37. Sanders, Leonard M. “Fractal Growth.” Scientific American January 1987: 94-101.
  38. Seum, Roberta and Offerman, Theresa R. “Fractally Speaking.” A talk given at the MCTM Spring Conference, April 1990.
  39. Simmt, Elaine and Davis, Brent; “Fractal Cards: A Space for Exploration in Geometry and Discrete Mathematics,” The Mathematics Teacher, February 1998, p 102-108.
  40. Steen, Lynn A. “Fractals: A World of Nonintegral Dimensions.” Science News 112 (August 20, 1977): 122-123.
  41. Stewart, Ian Does God Play Dice? The Mathematics of Chaos . Blackwell Publishers , 1994.
  42. Stewart, Ian “The two-and-a-halfth dimension.” The Problems of Mathematics. Oxford: Oxford University Press, 1987.
  43. Thornburg, David D. Discovering Apple Logo: An Invitation to the Art and Pattern of Nature. Reading, MA: Addison-Wesley, 1983.
  44. Wegner, Timothy, and Peterson, Mark Fractal Creations. The Waite Group Press, Mill Valley, CA 1991.
  45. Zobitz, Jennifer “Fractals: Mathematical Monsters.” Pi Mu Epsilon Journal 8 (Fall 1987): 425-440.