I tried the following code
\begin{axis}[
hide axis,
colormap/cool,
]
\addplot3[
surf,
samples=101,
domain=-1.1:0.5,
]
{sqrt(x^2+x^3-y^2)};
\end{axis}
\end{tikzpicture}
But the quality I get is terrible:.
It should look more like the following image divided by half: .
I also tried using mesh instead of surf but it didn't work either.