We have two applets that may be used to investigate the dynamics of certain classes of rational functions of the complex plane. They are:
Degree three maps. This applet draws the Julia set and
parameter plane for the function F(z) = z2 + c / z.
Degree four
maps.
This applet draws the Julia set and
parameter plane for the function F(z) = z2 + c /
z2.
Higher
degree rational maps.
This applet draws the Julia set and
parameter plane for the function F(z) = zn + c /
zm.
Perturbations of the Douady rabbit.
This applet draws the Julia set and
parameter plane for the function F(z) = za -.12... + .75...i + c /
z2, i.e., singular perturbations of the quadratic polynomial whose filled Julia set is the Douady rabbit.
Perturbations of the basilica.
This applet draws the Julia set and
parameter plane for the function F(z) = z2 -1 + c /
z2, i.e., singular perturbations of the quadratic polynomial whose filled Julia set is the basilica.
Perturbations of the cubic rat (or mouse).
This applet draws the Julia set and
parameter plane for the function F(z) = z3 -i + c /
z3, i.e., singular perturbations of the cubic polynomial whose filled Julia set is the rat.