WOLFRAM|DEMONSTRATIONS PROJECT

The Perturbed Rat

​
Re λ
0.001
Im λ
​
Recently, Blanchard, Devaney, Garijo, and Russell have studied rational maps of the form
F
λ
(z)=
n
z
+λ
-n
z
+c
, where
λ
and
c
are complex-valued parameters. This Demonstration considers the special case when
c=-
and
n=3
. When both the real and imaginary parts of
λ
are equal to zero, we obtain a Julia set called "the rat". When
λ
is nonzero, there is a pole of order three at the origin that changes the structure of the Julia set and perturbs the rat.