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.
Iterated Function System
See also
Barnsley's Fern, Self-SimilarityExplore with Wolfram|Alpha
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 SystemCite this as:
Weisstein, Eric W. "Iterated Function System." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/IteratedFunctionSystem.html