Non-Euclidean Geometry

Looking at the above equations, the only place where geometry comes into the picture is in the computation of the M and N fields. So it seems reasonable that if we could define the neighborhoods in some more generic way, then we could obtain a generalization of the above equations. Indeed, a similar idea was proposed in Rafler's original work to extend SmoothLife to spherical domains; but why should we stop there? [...]

But this isn't the only way we could define this distance. While the above formula is pretty easy to calculate, it by far not the only way such a distance could be defined. Another method is that we can formulate the path length variationally. That is we describe the distance between points p and q as a type of optimization problem; that is it is the arc length of the shortest path connecting the two points.

From the SmoothLife guy.