Iterated Function System
A finite set of contraction maps 
for 
, 2, ..., 
, each with a contractivity factor 
, which map a compact metric
space onto itself. It is the basis for fractal image
compression techniques.
SEE ALSO: Barnsley's Fern,
Self-Similarity
REFERENCES:
Barnsley, M. F. "Fractal Image Compression." Not. Amer. Math. Soc. 43,
657-662, 1996.
Barnsley, M. Fractals
Everywhere, 2nd ed. Boston, MA: Academic Press, 1993.
Barnsley, M. F. and Demko, S. G. "Iterated Function Systems and the Global Construction of Fractals." Proc. Roy. Soc. London, Ser. A 399,
243-275, 1985.
Barnsley, M. F. and Hurd, L. P. Fractal
Image Compression. Wellesley, MA: A K Peters, 1993.
Bogomolny, A. "The Collage Theorem." http://www.cut-the-knot.org/ctk/ifs.shtml.
Diaconis, P. M. and Shashahani, M. "Products of Random Matrices and Computer
Image Generation." Contemp. Math. 50, 173-182, 1986.
Fisher, Y. Fractal
Image Compression. New York: Springer-Verlag, 1995.
Hutchinson, J. "Fractals and Self-Similarity." Indiana Univ. J. Math. 30,
713-747, 1981.
Wagon, S. "Iterated Function Systems." §5.2 in Mathematica
in Action. New York: W. H. Freeman, pp. 149-156, 1991.
Referenced on Wolfram|Alpha:
Iterated Function System
CITE THIS AS:
Weisstein, Eric W. "Iterated Function System."
From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/IteratedFunctionSystem.html
Contact the MathWorld Team
Apollonian gasket
