Some definitions
Suppose f is a complex function, and z is a
complex number.
Consider the sequence of complex numbers z, f(z), f(f(z)), ...
The sequence is called the orbit of z under
f.
Whenever the magnitude of every complex number in the orbit
of z under f
is bounded by some constant M, the orbit of z
under f is said to be bounded.
Otherwise, the orbit of z under f is
said to escape to infinity.
The Filled Julia Set,K, for a complex function f
is the
set of all points on the complex plane whose orbits under f
are bounded.
The Julia Set,J, is the boundary of K.
