Appendices
Chaos, Fractals, Dimension
mathematics in the age of the computer
©1995-1998 Glenn Elert
All Rights Reserved--Fair Use Encouraged
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A.1 Annotated Bibliography of Printed Resources
There are thousands of printed resources on chaos, fractals, and dimension.
These are the sources that inspired me to write this paper.
- Barnsley, Michael. Fractals Everywhere.
San Diego, CA: Academic Press, 1988.
If you want to really learn about fractals, this is the textbook I recommend.
Easy to read.
- Devaney, Robert L. "Overview: Dynamics of
Simple Maps" Chaos and Fractals: The Mathematics Behind the Computer
Graphics. Robert L. Devaney & Linda Keen, editors. Providence,
RI: American Mathematical Society, 1988.
- Dewdney, A. K. "Mathematical Recreations:
Leaping into Lyapunov Space" Scientific American. September
1991: 178180.
- Gleick, James. Chaos: Making a New Science.
New York: Viking, 1987.
More of a history lesson than a mathematics lesson.
- Harrison, Jenny. "Introduction to Fractals"
Chaos and Fractals: The Mathematics Behind the Computer Graphics.
Robert L. Devaney & Linda Keen, editors. Providence, RI: American Mathematical
Society, 1988, 107126.
- Hocking, John G. & Young, Gail S. Topology.
New York: Dover, 1961.
Gail S. Young was my topology professor at Columbia University. The Dover
reprint of this textbook is wonderfully inexpensive. I can easily recommend
it for its price alone (something around $9 US).
- Hofstadter, Douglas R. Metamagical Themas:
Questing for the Essence of Mind and Pattern. New York: Basic Books,
1985.
This was my first introduction to the world of chaos. The description is
amazingly simple, but the conclusions are profound. By just goofing around
with the parabola, one can generate an entirely new field of mathematics.
How amazing is that?
- Keen, Linda "Julia Sets" Chaos and
Fractals: The Mathematics Behind the Computer Graphics. Robert L. Devaney
& Linda Keen, editors. Providence, RI: American Mathematical Society,
1988, 5774.
- Kline, Morris. Mathematical Thought from Ancient
to Modern Times. New York: Oxford University Press, 1972.
- Lauwerier, Hans. Fractals: Endlessly Repeated
Geometrical Figures. translated by Sophia Gill-Hoffstädt. Princeton,
NJ: Princeton University Press, 1991.
- Mandelbrot, Benoit B. The Fractal Geometry
of Nature. revised edition. New York: W. H. Freeman and Company, 1977.
The book that introduced the Mandelbrot set (called the mu-set). Wanders
around a bit, but very entertaining. Hundreds of physical examples are
included.
- Markus, Mario. "Chaos in Maps with Continuous
and Discontinuous Maxima" Computers in Physics. September/October
1990: 481493.
- Nicolis, Grégoire & Prigogine, Ilya.
Exploring Complexity: An Introduction. New York: Freeman, 1989.
- Penrose, Roger. The Emperor's New Mind.
New York: Oxford University Press, 1989.
- Pickover, Clifford A. Chaos in Wonderland:
Visual Adventures in a Fractal World. New York: St Martin's, 1995.
Relevant excepts from this book can be found at The
15 Most Famous Transcendental Numbers on Dr. Pickover's Web site.
- Pickover, Clifford A. "The World of Chaos"
Computers in Physics. September/October 1990: 460487.
- Symon, Keith R. Mechanics. 3rd edition.
Reading, MA: Addison Wesley, 1971.
My undergraduate mechanics textbook and the resource I used to remind myself
of all the mathematics behind the harmonic oscillator.
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