There exists this seemingly ordinary function of $x$ and $y$:

$4x^3-ax^2y+9xy^2-9y^3-36x+36y+10b=0$

where $a$ and $b$ are parameters that you can set by clicking (and dragging if you like) inside the yellow square.

Go ahead, try it, you will find it is quite interesting to see how this function behaves!

Enter for $a$ and/or for $b$ or click in the yellow rectangle of $a$ vs $b$ axes