@neauoire Just saw it now. It's really interesting, I don't think I've ever seen it before; at a cursory glance it doesn't seem to be equivalent to either manhattan or chebyshev?

(Manhattan is dx+dy, Chebyshev is max(dx,dy), and yours seems to be max(dx,dy)+min(dx,dy)/2, if I'm reading it correctly.)

I should play around with it a bit and do some comparisons.