Following my previous post, here is a new beauty I was able to find recently. The following is an animation of the families: $$S_{D}=\{(x,y, f(z)): (x_{n+1},y_{n+1}) = (Im(f(x_{n} + y_n i)\cdot\sin{\frac{D}{f}}, Re(f(x_{n} + y_n i))\cdot\cos{\frac{D}{f}})\}$$ Where $f(z)=\frac{1}{(z^{1.5}+1)^t}, t$ from $1$ to $2$ by $0.01$ steps. Each frame is a complete family plot, calculated using $D \in [0,8 \cdot 10^3], n \in [0,8 \cdot 10^3]$ zoom into region $z=[+/-5]+[+/-5]i$. It took me some days to render it as well:
And this is the family of dynamical systems of $f(z)=\frac{1}{(z^{1.5}+1)^0.9}$, Rorschach test anyone?
I am trying to find some academic group working on this kind of complex maps to share these "stochastic" models. If I am able to make some advances on this topic I will post the news here. Crossing fingers!
