I'm not sure if this is what you're looking forhelpful, but here is an example. The following picture shows the filled Julia set for $z^6 - 1$.
and the following picture shows the filled Julia set for $(z^2-1)^3$:
This is the case where $f(z) = z^2 - 1$ and $g(z) = z^3$. Note that the bottom image is a double cover of the top, while the top image is a triple cover of the bottom.
(These images were produced using Mathematica.)
I'm not sure if this is what you're looking for, but here is an example. The following picture shows the filled Julia set for $z^6 - 1$.
and the following picture shows the filled Julia set for $(z^2-1)^3$:
This is the case where $f(z) = z^2 - 1$ and $g(z) = z^3$. Note that the bottom image is a double cover of the top, while the top image is a triple cover of the bottom.
(These images were produced using Mathematica.)
I'm not sure if this is helpful, but here is an example. The following picture shows the filled Julia set for $z^6 - 1$.
and the following picture shows the filled Julia set for $(z^2-1)^3$:
This is the case where $f(z) = z^2 - 1$ and $g(z) = z^3$. Note that the bottom image is a double cover of the top, while the top image is a triple cover of the bottom.
(These images were produced using Mathematica.)
I'm not sure if this is what you're looking for, but here is an example. The following picture shows the filled Julia set for $z^6 - 1$.
and the following picture shows the filled Julia set for $(z^2-1)^3$:
This is the case where $f(z) = z^2 - 1$ and $g(z) = z^3$. Note that the bottom image is a double cover of the top, while the top image is a triple cover of the bottom.
(These images were produced using Mathematica.)
