Generating square vector field

[Superposed_Cat]

Hi all, my friend is writing a sci-fi/fantasy book and for it he asked me for a function that generates a vector field like picture A. So far the closest I've got is i*-(1/x)+1/-yj, which generates B. How would I generate B without using conditions? any help appreciated, thanks.

 

[Superposed_Cat]

Is it even possible?

 

[Jorriss]

By generate do you mean, does there exist a scalar function such that the gradient of this scalar function is the given vector field?

 

[Superposed_Cat]

yes.

 

[Superposed_Cat]

*bump*