Compactified Minkowski?

I am trying to compactify Minkowski space, but all I manage
to get is kinds of clovers or squares, while what I'm after
is circles (i.e. the locus of points whose *proper* distance
from the origin is constant).
See <https://www.desmos.com/calculator/b2bl9jiwo8>
Note that I would like to keep it in terms of (y,x) coords,
as that naturally maps to the (t,x) of space-time.
Can anyone suggest scaling formulas (or fix the diagram)?
-Julio