A Julia set 
consisting of a set of isolated points which is formed by
taking a point outside an underlying set 
(e.g., the Mandelbrot set).
If the point is outside but near the boundary of 
, the Fatou set resembles the Julia
set for nearby points within 
. As the point moves further away, however, the set becomes
thinner and is called Fatou dust.
Fatou Set
See also
Fatou Dust, Julia SetExplore with Wolfram|Alpha
References
Schroeder, M. Fractals, Chaos, Power Laws. New York: W. H. Freeman, p. 39, 1991.Wells, D. The Penguin Dictionary of Curious and Interesting Geometry. London: Penguin, pp. 72-73, 1991.Referenced on Wolfram|Alpha
Fatou SetCite this as:
Weisstein, Eric W. "Fatou Set." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FatouSet.html