Einstein's rubber

I like the idea of a billiards/pool/snooker table ( I don't know of a single word for these games) that has the gravity look to it . A table where all the balls have a region of sink of there own or as a group .

To do this the rubber or elastic sheet would have to be special and maybe boardering on magic . If ordinary elastic is used I would imagine, with the one ball case, the stretch would pull in all directions making a cup out to the cushions . This doesn't model the exponential decrease of gravity .

The normal elastic (guessing) would have chains in directions allowing the weight of the ball to be vectored to the cushion . I propose a special rubber to try a get the chains are lined up vertically with cross-links at the top and bottom .

IIIIIIII giving IIIIII\/\/\/IIIIIII when downward pressured .

Depending on the density of hinge cross-links and how the chains transfer the balls weight, the cup formed may better model gravity for the ball game .

Another Try:

A technological way of staging the Einstein sheet would be to have pins underneath the elastic controlled by magnetic actuators that stop the stretching reaching the cushions. Imagine one of those pin pictures covered with elastic . A camera with a bird's eye view from above could generate data allowing plotted ball paths and the rigidisation of the correct pins . As a ball goes over a pin, the pin is allowed to go with the elastic but pins further out from underneath the ball have control placed on them and they deform less .

The more pins the more perfect a circle around a ball otherwise the balls would be contained in line sided geometrical shapes .

This second method would be open to programming and therefore more unthought of ideas because change would be easier than changing the table's elastic with a new formula .

Third Try:

Using a standard table cover the slate in memory foam . Memory foam conforms to shape under heat . Use balls with a high heat retention or balls that can be heated while in play (lights, microwaves) as to make them deform the foam . The foam would have to have cross-links horizontally as to widen the defomation caused by the hot ball .