next up previous
Next: Golden Ratio Up: Index of Topics Previous: Teaching Geometry with Technology

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. Jtex2html_wrap_inline465rgens, 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, Jtex2html_wrap_inline465rgens, 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, Jtex2html_wrap_inline465rgens, 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.

next up previous
Next: Golden Ratio Up: Index of Topics Previous: Using Microcomputers to

Judith Cederberg

Disclaimer