Iterated Function System
A finite set of contraction maps 
for 
, 2, ..., 
, each with a contractivity factor 
, which mapa compact Metric Space onto itself. It is the basis for Fractal image compression techniques.
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. 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.