There are numerous applets on this page that may be used to investigate the dynamics of singularly perturbed maps in the complex plane.

**Degree four
maps.**
This applet draws the Julia set and
parameter plane for the function **F(z) = z ^{2} + c /
z^{2}**.

**Higher
degree rational maps.**
This applet draws the Julia set and
parameter plane for the function **F(z) = z ^{n} + c /
z^{m}**.

**Perturbations of the Douady rabbit.**
This applet draws the Julia set and
parameter plane for the function **F(z) = z ^{a} -.12... + .75...i + c /
z^{2}**, 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) = z ^{2} -1 + c /
z^{2}**, 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) = z ^{3} -i + c /
z^{3}**, i.e., singular perturbations of the cubic polynomial whose filled Julia set is the rat.

**Sebastian's
family.**
This applet draws the Julia set and
parameter plane for the function **F(z) = (z + C) ^{n+d} /
z^{d}** which is semi-conjugate to the higher degree rational maps.

**Anti-holomorphic
family.**
This applet is not quite ready yet. It will draw the Julia sets and
parameter plane for functions that are anti-holomorphic singular perturbations.

**Perturbations of the airplane.**
This applet draws the Julia set and
parameter plane for the function **F(z) = z ^{2} -1.75473 + c /
z^{2}**, i.e., singular perturbations of the quadratic polynomial
whose filled Julia set is the airplane.