Sources for Exploring Fractals

Images

Fern. David G. Green Fractals and Scale
Plane. Dryden Photo Archive.
Photos. Courtesy of Edward A. Connors, University of Massachusetts Amherst.

Sites of Interest

The Fractal Microscope is a nice interactive tool which allows the user to zoom in multiple times on the Mandelbrot set. It is a good tool for looking at the idea of self-similarity.

The Fractal pictures and Animations site at Rennes, France has many interesting pictures.

There is a FAQ site about fractals at Ohio State which gives some good explanations and ideas for further exploration.

There is the Spanky Fractal Database (yes, the name is pretty silly) which has lots of charming images as well as a good list of other fractal related www sites including a site with fractal generated music.

The Australian National University has a database for complex systems.

The Boston University Mathematics Department presents The Dynamical Systems and Technology Project by Prof.R.L. Devaney.


References

Briggs, John. (1992). Fractals: the Patterns of Chaos. 
     New York: Touchstone.

Camp, Dane R. (1991, April). "A fractal Excursion." 
     Mathematics Teacher LXXXIV (4), 265-75.

Connors, Mary Ann and Haralampus, Anna Rose.  (1991). 
     Exploring Fractal Dimension.Unpublished booklet.

Connors, Mary Ann and Haralampus, Anna Rose.  (1994,
     1995). Exploring Fractals: From Cantor Dust to the Fractal
     Skewed Web.  Unpublished booklet.

Crichton, Michael.  (1990).  Jurassic Park. 
     New York:  Ballentine Books.

Devaney, Robert L. (1990). Chaos, Fractals and Dynamics.
     Menlo Park: Addison-Wesley.

Gleick, James. (1987). Chaos: Making a New Science.
     New York: Viking.

Jacobs, Harold R. (1982) Mathematics A Human Endeavor.
     New York: Freeman

Mandelbrot, Benoit.  (1983). The Fractal Geometry of Nature.
     San Francisco: Freeman

McGuire, Michael. (1991). An Eye For Fractals. Redwood
     City: Addison-Wesley.

National Council of Teachers of Mathematics (1989). 
     Curriculum and Evaluation Standards for School Mathematics.
     Reston, Virginia: The Council

Oliver, Dick.  (1992).  Fractal Vision. 
     Carmel, IN:  SAMS Publishing.

Peitgen, Heinz-Otto. et al. (1991).  Fractals for the
     Classroom: Strategic Activities Volume One.  New York: 
     Springer-Verlag.

Peitgen, Heinz-Otto.,and Saupe, Dietmar. eds. (1988). 
     The Science of Fractal Images. New York: Springer-Verlag

Peterson, Ivars. (1988) The Mathematical Tourist. New
     York: Freeman

Rucker, Rudy. (1987). Mind Tools. Boston: Freeman

Seymour, Dale. (1986).  Visual Patterns in Pascal's
     Triangle.Palo Alto, CA:  Dale Seymour Publications
 
Steen, Lynn Arthur. (1990). On the Shoulders of Giants
     New Approaches to Numeracy. Washington, D.C.: National
     Academy Press

Stewart, Ian. (1982). Les Fractals Les Chroniques
     de Rose Polymath. Paris: Belin

Acknowledgements

To Jessica Norman and Wei Shen for their contribution to setting up the "Exploring Fractals" Project on the World Wide Web.


(c) Copyrighted 1994,1995,1996,and 1997 by Mary Ann Connors. All rights reserved. If you wish to use any of the text or images in Exploring Fractals please contact its author Mary Ann Connors at the following address. Thank you.

Dr. Mary Ann Connors
Department of Mathematics & Statistics
Lederle Graduate Research Tower
University of Massachusetts
Amherst, MA 01003
Email:
mconnors@math.umass.edu
mconnors@math.umass.edu