Julia Sets Works Cited

Works Cited in
Julia Jewels: An Exploration of Julia Sets

Alligood KT, Sauer TD, Yorke JA. Chaos: An Introduction to Dynamical Systems. Springer-Verlag 1996. (A good overall mathematical review.)

Bourke P. "Fractal Dimension Calculator." (Macintosh software written Feb. 1993). Accessed 5 May 2000 <http://www.swin.edu.au/astronomy/pbourke/fractals/fracdim/>

Brin M [inferred]. "What is the Mandelbrot Set?" Accessed 7 March 2000 <http://www.math.binghamton.edu/MATH/topics/mandel/>
(Many full-sized color images with black and white thumbnail diagrams showing the mapping of the M set to Julia sets.)

Cayley A. "The Newton-Fourier Imaginary Problem." Amer. J. Math. 2, 1879 92
(Cited in Peitgen et al 1992 p. 775)

Elert G. The Chaos Hypertextbook: Strange and Complex. Accessed 5 March 2000 <http://hypertextbook.com/chaos/>.
(This site provides a good list of available Macintosh-oriented software for generating fractals.)

Pfingstl M. "ChaosPro v. 2.0." Accessed 6 March 2000 (former URL http://home.att.net/~Paul.N.Lee/ChaosPro.HTML)
(This is a 32-bit updated version of FractInt.exe which appears to work quite well but does not have all the choices of WinFract.exe.)

Gagliardo M. "The Julia Sets and Other Fractals." Accessed 7 March 2000, URL formerly http://rene.ma.utexas.edu/users/mgags/julia.html

Griffin N. "GETTING FRACTINT." Windows version 18.21. Accessed 5 March 2000 formerly at http://spanky.triumf.ca/www/fractint/getting.html
(This site provides links to obtain the fractal generating software FractInt.exe for DOS and WinFract.exe for 16-bit Windows.)

Griffin N. "WELCOME to the Fractint WWW page." Accessed 5 March 2000 formerly at http://spanky.triumf.ca/www/fractint/fractint.html

Joyce DE. "Julia and Mandelbrot Set Explorer." Accessed 6 March 2000 <http://aleph0.clarku.edu/~djoyce/julia/explorer.html>.

Julia G. "Mémoire sur l'itération des fonctions rationnelles." Journal de Math. Pure et Appl. 8 (1918) 47-245.
Republished in Hervé M (ed.) Oeuvres de Gaston Julia: Vol. I. Gauthiers-Villars 1968 121-333.
(This is Julia's original description of Julia Sets.)

Mandelbrot BB. The Fractal Geometry of Nature (Updated and Augmented). W. H. Freeman and Co. 1983 (Revised edition of Fractals c. 1977).
(The mother of all works in the computer era on fractals and strange attractors but nearly incomprehensible.)

"The Math Forum." Accessed 19 February 2006 <http://mathforum.org/>.
(An excellent starting place for obtaining mathematical information and materials at all levels.)

Mitsuhiro S. "The Hausdorff Dimension of the Boundary of the Mandelbrot Set and Julia Sets." Ann. Math. 147 (1998) No. 2 225-267.

Peitgen H, Jurgens H, and Saupe D. Chaos and Fractals: New Frontiers of Science. Springer-Verlag, 1992.
(A superb and detailed textbook discussing many aspects of fractals and chaos, including the Julia and Mandelbrot sets.)

Peitgen HO and Richter PH. The Beauty of Fractals: Images of Complex Dynamical Systems. Springer-Verlag 1986.
(An often quoted work which I have not had the chance to review in detail.)

Saupe D. "Efficient Computation of Julia Sets and Their Fractal Dimension." Physica D28 (1987) 358-370 [cited in Peitgen et al. 967].