Huffingtonpost ran a story heaping praise on a guy for demonstrating GR with the old "rubber sheet" analogy. This demo bothers me for several reasons, not least of which is that the surface is negatively curved, on which parallel geodesics diverge -- the exact opposite of what is supposedly being demonstrated. But, it made me wonder: Is there a comparable 2D visualization of warped space, that extends to infinity like the rubber sheet, with positive curvature? If one imagines a basketball pressed against the rubber sheet, the portion of the sheet in contact with the ball would be positively curved, but the rest would (as before) be negatively curved, one assumes. I also assume (due to converging parallel geodesics) that a massive object creates positive curvature, and that this curvature extends to infinity. Yet, I am unable to imagine a 2D representation of this; every example of positive curvature I've seen is on a closed surface (i.e., a sphere). Are my assumptions about curvature wrong, or is this a property of 3D surfaces that cannot be reproduced on 2D surfaces (or both)? Thank you.