Chaos, fractals, and Arcadia

Chaos, Fractals, and Arcadia

Summary

The play Arcadia is a wonderful experience for all students. It is fast-paced, witty, and thoroughly enjoyable. Best of all, it can be combined with some wonderful mathematical ideas to give students a truly interdisciplinary experience.

For more information on the history of the subject of chaos, consult [G]. Some of the mathematical and biological underpinnings of the subject may be found in [D] or [May]. Fractals are described in [B], [Man], or [PR]. Some other Java applets dealing with the chaos game may be found at the Dynamical Systems and Technology Project at Boston University website.

References

[B] Barnsley, M. Fractals Everywhere Academic Press, Boston, 1988.

[CD] Choate, J. and Devaney, R. L. Chaos: A Toolkit of Dynamics Activities Key Curriculum Press, Emeryville, CA.

[D] Devaney, R. L. Chaos, Fractals, and Dynamics: Computer Experiments in Mathematics Addison-Wesley Co., Menlo Park, Calif., 1989.

[G] Gleick, J. Chaos: Making a New Science, Viking, New York, 1987.

[LC] Lee, K. and Cohen, Y. Fractal Attraction. Academic Press.

[May] May, R. B. Simple mathematical models with complicated dynamics. Nature. 261, 459-467, (1976).

[PR] Peitgen, H.-O. and Richter, P. The Beauty of Fractals, Springer-Verlag, Heidelberg, 1986.

[Man] Mandelbrot, B. The Fractal Geometry of Nature. San Francisco: Freeman, 1983.

[S] Stoppard, T. Arcadia. London: Faber and Faber, 1993.

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