Subsubsection 1.1.1.3 Other Julia sets
If we iterate other types of functions, more behavior is possible. Here are a couple more examples:
Figure Figure 1.1.6 shows the Julia set of the cubic polynomial
\begin{equation*}
f(z)=\displaystyle \left(-0.090706+0.27145~ i\right)+\left(2.41154-0.133695~ i\right)z^{2}-z^{3}.
\end{equation*}
It was generated with the web app here:
https://marksmath.org/visualization/polynomial_julia_sets/.
Figure Figure 1.1.7 shows the Julia set of the rational function
\begin{equation*}
\displaystyle f(x) = \frac{z^5+0.01}{z^{3}}.
\end{equation*}
It was generated with the web app here: