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As of 1996, the best source of information on fractals is no longer the printed text. Electronic archives are available for easy browsing with a World Wide Web (WWW) navigator (browser). The best place to start is with a frequently-asked question (faq) file available at: http://www.ccn.cs.dal.ca/~aa459/sci-fractals/faq-html/ or ftp://rtfm.mit.edu/pub/pub/usenet/news.answers/sci-fractals/faq.As for books, most have either "no" mathematics or "too much" for the average class. An example of a book which has "no" math at all is the Tao of Chaos, by Katya Waller, 1994 (Kairos Center, 800-624-4697). Though found in the "mathematics" section of the bookstore, here is a sampe "workshop":
Share a communion using chunks of yeast bread and apple juice. The yeast bread represents analog exponential growth, and the apple juice represents pressing into good service the tricky apple of linear knowledge.There are also many examples of books with "too much" math, including Benoit Mandelbrot's Fractal Geometry of Nature, 1983 (W. H. Freeman). Though a very useful introduction to fractals, the details assume a working knowledge of topology and metric spaces. Michael Barnsley's Fractals Everywhere , 1993 (Academic Press) will introduce you to these things step-by-step, but is still very advanced. It even says: "One still needs a grounding in concepts in metric space theory and eventually measure theory to get a working understanding of the subject [ fractal geometry ]."The quest for a "middle ground" continues. Springer Verlag's 4-volume set Fractals for the Classroom, 1992 has many great ideas, but is not a ready-to-use textbook. Peak &Frame's Chaos Under Control, 1994 (W. H. Freeman) focuses on chaos theory more than "classic" fractals and has exercises only in an appendix. Ronald Lewis has published his own useful 300-page lab manual (705-566-3264 , ronalewi@village.ca).
Maybe publishers do not want to risk a fractal "textbook". Maybe they don't want to do what Dynamic Press (Santa Cruz, CA) did with The Fractal Explorer in 1991. Linda Garcia wrote a 108-page introduction to fractal dimension and self-similarity with a good balance between "no" math and "too much". But then as of 1995, Dynamic Press either no longer exists or is impossible to find. Garcia's book is very much out of print.
Many algebra textbooks now at least mention that fractals exist. In fact, a whole section (7 pages) on Fractals has been included in UCSMP's Advanced Algebra (1993), published by Scott, Foresman. This is a great start, but could still be improved. One caption is completely un-explained: "Picture of a discretized Boundary Value Problem using f(m) = m - m3 in 6-space and represented in 2-space". By showing a nice picture but not the mathematics behind it, then the message sent is: "fractals are too hard for you". Theoni Pappas has a better message in Fractals, Googles and other Mathematical Tales, 1993, (World Wide Publishing/Tetra). She tells a story that ends with this:
The beauty of the formation of the snowflake fractal dazzled the other shapes. They had to admit that fractlas were fascinating. They decided that they would be proud to have fractals as members of their convention. In fact, they were so proud, they asked the fractal to lead the parade.Hopefully, the demand for a fractal textbook will grow as teachers learn more about the subject. Fractals will be part of the future mathematics curriculum. But good things take time, you know. We'll have to just wait &see...
Mark F. Harbison
Sacramento City College, CA
email: MHfractal@aol.com
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