A finitely generated discontinuous group of linear fractional transformations 
acting on a domain in the complex
plane.
The Apollonian gasket corresponds to a limit set that is invariant under a Kleinian group (Wolfram 2002, p. 986).
Kleinian Group
See also
Apollonian Gasket, Linear Fractional TransformationExplore with Wolfram|Alpha
References
Ford, L. R. Automorphic Functions, 2nd ed. New York: Chelsea, 1951.Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 425, 1980.Kra, I. Automorphic Forms and Kleinian Groups. Reading, MA: W. A. Benjamin, 1972.Mumford, D.; Series, C.; and Wright, D. J. Indra's Pearls: An Atlas of Kleinian Groups. Cambridge, England: Cambridge University Press, 2002.Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, p. 986, 2002.Referenced on Wolfram|Alpha
Kleinian GroupCite this as:
Weisstein, Eric W. "Kleinian Group." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/KleinianGroup.html