A game which takes place on a hyperbolic board like this:
Apart from the innermost and outermost rings, each circle has the same environment, connected to 2 circles further in and 4 circles further out.
Players start in control of one location on the outermost ring, evenly spaced out. The idea is to take control somehow of the remainder of the board.
The number of players determines the size of the board. Players probably start with control of one circle on the outermost ring, at a suitable spacing. The board can be extended with as many rings as required without altering the local geometry, so very large numbers of players could share the board. In this form the game would suit an online or play by email implementation.
Theme is that players are wizards battling in the spirit realm for mastery of successively more powerful beings. The innermost ring of 4 could represent the elements or something. Mortlake was the home of John Dee, and is a suitably sinister and wizardy name.
That’s as far as I got. Someday a cool mechanic may suggest itself but it hasn’t yet.